Table 2- Factorizations of 2^n-1, n odd, n<1500 n Prime Factors 3 7 5 31 7 127 9 (3) 73 11 23.89 13 8191 15 (3,5) 151 17 131071 19 524287 21 (3,7) 7*.337 23 47.178481 25 (5) 601.1801 27 (3,9) 262657 29 233.1103.2089 31 2147483647 33 (3,11) 599479 35 (5,7) 71.122921 37 223.616318177 39 (3,13) 79.121369 41 13367.164511353 43 431.9719.2099863 45 (3,5,9,15) 631.23311 47 2351.4513.13264529 49 (7) 4432676798593 51 (3,17) 103.2143.11119 53 6361.69431.20394401 55 (5,11) 881.3191.201961 57 (3,19) 32377.1212847 59 179951.3203431780337 61 2305843009213693951 63 (3,7,9,21) 92737.649657 65 (5,13) 145295143558111 67 193707721.761838257287 69 (3,23) 10052678938039 71 228479.48544121.212885833 73 439.2298041.9361973132609 75 (3,5,15,25) 100801.10567201 77 (7,11) 581283643249112959 79 2687.202029703.1113491139767 81 (3,9,27) 2593.71119.97685839 83 167.57912614113275649087721 85 (5,17) 9520972806333758431 87 (3,29) 4177.9857737155463 89 618970019642690137449562111 91 (7,13) 911.112901153.23140471537 93 (3,31) 658812288653553079 95 (5,19) 191.420778751.30327152671 97 11447.13842607235828485645766393 99 (3,9,11,33) 199.153649.33057806959 101 7432339208719.341117531003194129 103 2550183799.3976656429941438590393 105 (3,5,7,15,21,35) 29191.106681.152041 107 162259276829213363391578010288127 109 745988807.870035986098720987332873 111 (3,37) 321679.26295457.319020217 113 3391.23279.65993.1868569.1066818132868207 115 (5,23) 14951.4036961.2646507710984041 117 (3,9,13,39) 937.6553.86113.7830118297 119 (7,17) 239.20231.62983048367.131105292137 121 (11) 727.1786393878363164227858270210279 123 (3,41) 3887047.177722253954175633 125 (5,25) 269089806001.4710883168879506001 127 170141183460469231731687303715884105727 129 (3,43) 11053036065049294753459639 131 263.10350794431055162386718619237468234569 133 (7,19) 163537220852725398851434325720959 135 (3,5,9,15,27,45) 271.348031.49971617830801 137 32032215596496435569.5439042183600204290159 139 5625767248687.123876132205208335762278423601 141 (3,47) 4375578271.646675035253258729 143 (11,13) 724153.158822951431.5782172113400990737 145 (5,29) 2679895157783862814690027494144991 147 (3,7,21,49) 7*.2741672362528725535068727 149 86656268566282183151.8235109336690846723986161 151 18121.55871.165799.2332951.7289088383388253664437433 153 (3,9,17,51) 919.75582488424179347083438319 155 (5,31) 31*.311.11471.73471.4649919401.18158209813151 157 852133201.60726444167.1654058017289.2134387368610417 159 (3,53) 6679.13960201.540701761.229890275929 161 (7,23) 1289.3188767.45076044553.14808607715315782481 163 150287.704161.110211473.27669118297.36230454570129675721 165 (3,5,11,15,33,55) 2048568835297380486760231 167 2349023.79638304766856507377778616296087448490695649 169 (13) 4057.6740339310641.3340762283952395329506327023033 171 (3,9,19,57) 93507247.3042645634792541312037847 173 730753.1505447.70084436712553223.155285743288572277679887 175 (5,7,25,35) 39551.60816001.535347624791488552837151 177 (3,59) 184081.27989941729.9213624084535989031 179 359.1433.1489459109360039866456940197095433721664951999121 181 43441.1164193.7648337.7923871097285295625344647665764672671 183 (3,61) 367.55633.37201708625305146303973352041 185 (5,37) 1587855697992791.7248808599285760001152755641 187 (11,17) 707983.1032670816743843860998850056278950666491537 189 (3,7,9,21,27,63) 1560007.207617485544258392970753527 191 383.7068569257.39940132241.332584516519201.87274497124602996457 193 13821503.61654440233248340616559.14732265321145317331353282383 195 (3,5,13,15,39,65) 134304196845099262572814573351 197 7487.26828803997912886929710867041891989490486893845712448833 199 164504919713.4884164093883941177660049098586324302977543600799 201 (3,67) 1609.22111.87449423397425857942678833145441 203 (7,29) 136417.121793911.11348055580883272011090856053175361113 205 (5,41) 2940521.70171342151.3655725065508797181674078959681 207 (3,9,23,69) 79903.634569679.2232578641663.42166482463639 209 (11,19) 94803416684681.1512348937147247.5346950541323960232319657 211 15193.60272956433838849161.3593875704495823757388199894268773153439 213 (3,71) 66457.2849881972114740679.4205268574191396793 215 (5,43) 1721.731516431.514851898711.297927289744047764444862191 217 (7,31) 5209.62497.6268703933840364033151.378428804431424484082633 219 (3,73) 3943.671165898617413417.4815314615204347717321 221 (13,17) 1327.2365454398418399772605086209214363458552839866247069233 223 18287.196687.1466449.2916841.1469495262398780123809.P24 225 (3,5,9,15,25,45,75) 115201.617401.1348206751.13861369826299351 227 26986333437777017.P52 229 1504073.20492753.59833457464970183.P39 231 (3,7,11,21,33,77) 463.P34 233 1399.135607.622577.P57 235 (5,47) 2391314881.72296287361.P35 237 (3,79) 1423.49297.23728823512345609279.31357373417090093431 239 479.1913.5737.176383.134000609.P49 241 22000409.P66 243 (3,9,27,81) 487.16753783618801.192971705688577.3712990163251158343 245 (5,7,35,49) 1471.P48 247 (13,19) 15809.6459570124697.402004106269663.P34 249 (3,83) 1621324657.P40 251 503.54217.178230287214063289511.61676882198695257501367.P26 253 (11,23) 23*.4103188409.199957736328435366769577.P32 255 (3,5,15,17,51,85) 106591.949111.P28 257 535006138814359.1155685395246619182673033.P39 259 (7,37) 2499285769.P56 261 (3,9,29,87) P51 263 23671.13572264529177.120226360536848498024035943.P36 265 (5,53) 29324808311.197748738449921.P38 267 (3,89) 78903841.28753302853087.P32 269 13822297.P74 271 15242475217.P72 273 (3,7,13,21,39,91) 108749551.4093204977277417.86977595801949844993 275 (5,11,25,55) 382027665134363932751.P40 277 1121297.31133636305610209482201109050392404721.P40 279 (3,9,31,93) 16183.34039.1437967.833732508401263.2034439836951867299888617 281 80929.P80 283 9623.68492481833.P71 285 (3,5,15,19,57,95) 1491477035689218775711.25349242986637720573561 287 (7,41) 17137716527.P62 289 (17) 12761663.179058312604392742511009.P52 291 (3,97) 272959.2065304407.5434876633.P34 293 40122362455616221971122353.P63 295 (5,59) 4721.132751.5794391.128818831.3812358161.452824604065751.P22 297 (3,9,11,27,33,99) 8950393.P48 299 (13,23) 599.9341359.14718679249.13444476836590589479. .51441563151591093599.260242449712509916159 301 (7,43) 490631.365505823711978039310711.P47 303 (3,101) 607.P58 305 (5,61) 1831.2441.4271.270841.484074637694471.P42 307 14608903.85798519.23487583303.78952752017.P57 309 (3,103) 1953272766780718501831.P40 311 5344847.2647649373910205158468946067671.P57 313 10960009.14787970697180273.3857194764289141165278097.P47 315 (3,5,7,9,15,21,35,45,63,105) 870031.983431.P32 317 9511.587492521482839879.4868122671322098041565641.P49 319 (11,29) 18503.64439.84819793631.P64 321 (3,107) 17866285599391.P51 323 (17,19) 647.7753.39044358788825633753.P61 325 (5,13,25,65) 7151.51879585551.P58 327 (3,109) 20597276734348736647.33157029794959983067039.P23 329 (7,47) 12503.200033.9106063.270447871.P58 331 16937389168607.865118802936559.P72 333 (3,9,37,111) 1999.10657.169831.1238761.36085879.199381087. .698962539799.4096460559560875111 335 (5,67) 464311.1532217641.P65 337 18199.2806537.95763203297.726584894969.P68 339 (3,113) 10113049.320021624768405574452943847.P34 341 (11,31) 5560125493425335999.126901141805369975317583.P49 343 (7,49) 6073159.1428389887.62228099977.P62 345 (3,5,15,23,69,115) P54 347 14143189112952632419639.P83 349 1779973928671.34720396273212657799920861294559.P62 351 (3,9,13,27,39,117) 446473.29121769.571890896913727.93715008807883087.P21 353 931921.2927455476800301964116805545194017.P67 355 (5,71) 121932688511.P73 357 (3,7,17,21,51,119) 4999.245262248913715001137177.P31 359 719.855857.778165529.65877330027880703. .370906580744492785430299503112990447.P39 361 (19) 9522401530937.36450568206770608791178096385783.P59 363 (3,11,33,121) 8713.7593961.75824014993.P45 365 (5,73) 8761.13828603741081.82595052745831.P56 367 12479.51791041.78138581882953.301311116540899114446723859201.P56 369 (3,9,41,123) 6376386802464073.P57 371 (7,53) 743.2969.63781899287.204712366597949333831.P57 373 25569151.P105 375 (3,5,15,25,75,125) 751.P58 377 (13,29) 5279.148055441.359661017.P81 379 180818808679.P103 381 (3,127) 2287.15241.349759.P63 383 1440847.7435494593.503823044204581129045587727. .15174923558680812616818436353130417.P39 385 (5,7,11,35,55,77) 55441.1971764055031.P56 387 (3,9,43,129) 11492353.22763003975641.6834040335349578249140287.P31 389 56478911.4765678679.P100 391 (17,23) 37537.25806248225716242845491832244899635927231330561.P55 393 (3,131) 36093121.51118297.58352641.P55 395 (5,79) 12641.5435488351.16203007441.P70 397 2383.6353.50023.53993.202471.5877983. .814132872808522587940886856743.1234904213576000272542841146073.P31 399 (3,7,19,21,57,133) 73417.83791.P56 401 856971565399.2136958965524920285681. .594538100848945223169882301931953.P55 403 (13,31) 45137.8532838289.P94 405 (3,5,9,15,27,45,81,135) 537841.11096527935003481.P44 407 (11,37) 3257.3068001817.1826375940722234754636475033.P68 409 4480666067023.76025626689833.P97 411 (3,137) 823.27261904199932321.647923469936355993348337.P39 413 (7,59) 2006647231.6774027833473375976915021445395839.P62 415 (5,83) 470933694191.3028917598961.130666175908831. .32367218471375835379289471.P35 417 (3,139) 7606017793609.P70 419 839.903780021613921.5800422716722833271214743. .10287968884341772230096159036619433593.P47 421 614002928307599.P112 423 (3,9,47,141) 1617189999730415801728461273583.P53 425 (5,17,25,85) P97 427 (7,61) 33282089.P101 429 (3,11,13,33,39,143) 17286204937.1065107717756542892882802586807.P33 431 863.3449.36238481.76859369.558062249.4642152737. .142850312799017452169.P70 433 22086765417396827057.737748363812546584876297. .5028667832511715101284999.P63 435 (3,5,15,29,87,145) 256582225885581001782477601.P42 437 (19,23) 3198841.5579617.6203145044672921.P90 439 104110607.127321491658223.122551752733003055543.P90 441 (3,7,9,21,49,63,147) 126127.309583.5828257.4487533753346305838985313.P34 443 887.207818990653657.P117 445 (5,89) 2671.1460384540571001412284141831845453026637206635511.P55 447 (3,149) P89 449 1256303.6871197486841.3578620616468306981503. .526385733768051189441947168504909159.P59 451 (11,41) 18041.216481.9718704501529.538939720215834697.P80 453 (3,151) 790468905817.P79 455 (5,7,13,35,65,91) 200201.P82 457 150327409.P130 459 (3,9,17,27,51,153) 407770693450231393.24418671951944649151.P50 461 2767.358228856441770927.7099353734763245383.P99 463 11113.3407681.448747600991881.239932071009857681156251129. .385606580062688087218266143.P62 465 (3,5,15,31,93,155) 2791.103231.P65 467 121606801.1148984537885906196977362003686090739460725564747973734847.P76 469 (7,67) 70321958644800017.1839633098314450447.P84 471 (3,157) P94 473 (11,43) 12853303.133139883512681.4193551379485561391. .1703616691469833244854254847.P60 475 (5,19,25,95) 4751.18020551.1369738735713888876695951. .113709467433878120743807151.P48 477 (3,9,53,159) 94447.4879711.242003089.P74 479 33385343.6293443049. .683481445118041278287416124073722711169070307627777892361.P71 481 (13,37) 138724733805016586033.5800976318060644948970424014255729.P76 483 (3,7,21,23,69,161) 967.18423553.172384633.1186694555374004016103.P41 485 (5,97) 10084875238121.34224064338126003049783351. .6424414731245950286450458211761.P46 487 4871.P143 489 (3,163) 836191.355307401.116539854237679.619079222361672204943.P48 491 983.7707719.110097436327057.6976447052525718623. .19970905118623195851890562673.3717542676439779473786876643915388439.P41 493 (17,29) 3616649.10353001.P121 495 (3,5,9,11,15,33,45,55,99,165) 991.334202934764737951438594746151.P40 497 (7,71) 6959.254461617383.P111 499 20959.1998447222711143545931606352264121.P113 501 (3,167) 25129004796912072003423103.P75 503 3213684984979279.12158987054135300783.1873030665061080894263.P96 505 (5,101) 1906785849099933631.P102 507 (3,13,39,169) P94 509 12619129.19089479845124902223.647125715643884876759057.P104 511 (7,73) 15212471. .144780974187086260903935034761413745643636578290924150417.P67 513 (3,9,19,27,57,171) 57457.35473416481.121323854647.2237717449946593.P56 515 (5,103) 1031.989831.960954217134424245898328814050043401.P78 517 (11,47) 82721.387348809.1292800939332382943. .270374114136830957955241.26302895729179572365768002599674239.P49 519 (3,173) 1039.P101 521 P157 523 160188778313202118610543685368878688932828701136501444932217468039063.P90 525 (3,5,7,15,21,25,35,75,105,175) 4201.7351.181165951.P57 527 (17,31) 13306086595097866632236752730067629415649399. .50061214622509969230528187280149191683596667776057.P52 529 (23) 54999142147740840245669969.347916608026315949237260151. .9114901722266383629807574332217258944092868367.P55 531 (3,9,59,177) 1063.288236359.196629322303.15888898944343. .8099559410464120708848563721343.P38 533 (13,41) 166297.744487658617.P128 535 (5,107) 12841.95231.879622391.331343920853356078376431. .23718232032401560617445166686464799001.P49 537 (3,179) 4297.16111.196543.P94 539 (7,11,49,77) 234341789260493933662402728271919.P95 541 4312790327.6115209994009.77146448294831869472151022106713. .904106555381898703253733254107256591.P73 543 (3,181) 1087.534955385319592511227419175872576025063351.P64 545 (5,109) 3271.213641.18109412991311.2511696210834096991. .7647513170903349335637401.P65 547 5471.172720604638150729.157552196128597543991.P124 549 (3,9,61,183) 38431.1386525709821079.P89 551 (19,29) 4409.14327.27551.P140 553 (7,79) 166153042787383.P127 555 (3,5,15,37,111,185) 27751.P83 557 3343.21993703.4565508951414453792719. .22053236096920219270632521586535711.P101 559 (13,43) 3180000071.9215285895065526291256518741915902569.P105 561 (3,11,17,33,51,187) 146983.2009643799642447.P77 563 2815747080256641401887817.13299213974872825932452460424235657.P111 565 (5,113) 185318160171793066961.29444549303703754611026537050435001.P80 567 (3,7,9,21,27,63,81,189) P98 569 15854617.55470673.182602768015690099110572536951. .110582329556343704552404016904356632250881.P87 571 5711.27409.69693366045316671685098712301007940958018325270028\ 49548226132675916172927.P91 573 (3,191) 32788207.P107 575 (5,23,25,115) 1151.13220653410551.P117 577 3463.132305774316967.P157 579 (3,193) P116 581 (7,83) 798037199.175908273685537. .15444711420006203351165170879848557117713.P85 583 (11,53) 755569.65780528969.106077807287.P129 585 (3,5,9,13,15,39,45,65,117,195) 2400314671.339175003117573351. .255375215316698521591.P40 587 554129.2926783.39483330766889.73208283304744901303. .3728298863422039632638351.P107 589 (19,31) 18083479.36064471. .2023706519999643990585239115064336980154410119.P103 591 (3,197) 407791.50070703.304292056417.P93 593 104369.3061144307110551703729. .4027016481761119763553952463965455549881.P113 595 (5,7,17,35,85,119) 34511.199921.69935987114957671.P90 597 (3,199) 5066143.1445406523039.P101 599 16659379034607403556537. .148296291984475077955727317447564721950969097.P114 601 3607.64863527. .643390760896826272806925563059612685509039265031067456849993.P110 603 (3,9,67,201) 648168721774409511378116151410898673195879.P78 605 (5,11,55,121) 3631.143448045841.P118 607 P183 609 (3,7,21,29,87,203) 15109165329245515231985834925494692879.P65 611 (13,47) 1223.1609655415875897360904371080437164611501156560743.P115 613 44599476833089207.332817722770314187794325446534549089.P133 615 (3,5,15,41,123,205) 1231.49201.92757531554705041. .3427007094604641668368081.P48 617 59233.68954123297. .157751978115225385495647532421006478127229405644601.P120 619 110183.710820995447. .109378681671075297195692480234213908123642560192251038455204252439.P105 621 (3,9,23,27,69,207) 624456487.93747988411543.P97 623 (7,89) 74383430474532481. .74716964067758844321661890925503011337830328521.P95 625 (5,25,125) 1277297679372570001.573759820507018639639785001. .18152902839291497575027462639977160832701118299213751.P54 627 (3,11,19,33,57,209) 11287.12471031.89856878697433. .8778523027466598416204656058467252273.P47 629 (17,37) 45470534643405479586527115047619453123209. .205296815265168567756164047567360097447247109142889252157111.P74 631 333628015107245479.474640860193534882628078580680807822523991.P131 633 (3,211) 2399291551.17689153588009.60560850681938908875991. .9970146666059203361408046051199.P50 635 (5,127) 5081. .83615338235826681881707602454578099792649940383635851698961.P89 637 (7,13,49,91) 3823.15289.31945881241.153925026222241.8573192048327176271. .6044274266901603399200353.153472677405951306470238401460959.P44 639 (3,9,71,213) 1279.84462210560148142953097. .1329628131546931497103420134367.28435302301212461494420074814087.P39 641 35897.49999.1173835097.2401258891949526685926151441.745276300\ 734440606226386924312213175677903182797334854064486587296999.P79 643 3189281.2253242905260567022502639105439342883316820723480243\ 4915090881303620353.P117 645 (3,5,15,43,129,215) 46441.4175568751.1728221461577944661374351. .83212524822005103181053031.P37 647 303303806129303896428103.11502383762931955619183430785983.P141 649 (11,59) 649001.23952086159.34418203155300430111979265857.P130 651 (3,7,21,31,93,217) 1303.1191622782866437328993110351.P79 653 78557207.289837969.16008527538753578495897. .3044938125828889184039273431.3786707123184812723340717607.P103 655 (5,131) 597361.2576754528566814601.351182936972570824983481. .15333541100090824437129533485272856744656791.P66 657 (3,9,73,219) 73*.10178663167.27265714183.5271393791658529. .2762194134676763431.42185927552983763147431373719.P45 659 1319.11527429277532648241.626564962613678012662146877852049.P144 661 1330270433.3370159489168519.1009157848082361225065617. .118420287267066844820208926433723871.P116 663 (3,13,17,39,51,221) 47737. .1817023253798585112376955621635919346759818823715057.P60 665 (5,7,19,35,95,133) 161517058694951.P117 667 (23,29) 12007.458897.88039999.246270735864387271375789289856617. .14508653262991734676225669411020750337.P98 669 (3,223) 182224921317852297530287.P111 671 (11,61) 116356769.33491655209.64110547427930873. .13646560594525825890627182668772241639702837721889959372317451952089.P78 673 581163767.41283139633378645724930694480520226273492263. .68396769572915971687133122358352070840260017483089158059519.P92 675 (3,5,9,15,25,27,45,75,135,225) 1605151. .1094270085398478390395590841401.2842496263188647640089794561760551.P39 677 1943118631.531132717139346021081.978146583988637765536217. .53625112691923843508117942311516428173021903300344567.P98 679 (7,97) 6791.59753.93703. .1337351764099536062382592381405648316666025584913912478511.P103 681 (3,227) 962744903648208108713898832235090314894033.P94 683 1367.4348364991126096947957239584170488612997681442834426624\ 02095922180462812746769.P125 685 (5,137) 119191.7084271.83648644144524510111773141111.P123 687 (3,229) 6871.2104809991.175932323679511304414371921.P98 689 (13,53) 135995976143.1067583682127. .1372617429248257063179636119999552844862152089.P120 691 906642603313.10488160032325844521.2833637724427940664433391497. .16636201944470267267182958207.P122 693 (3,7,9,11,21,33,63,77,99,231) 289511839.2868251407519807.P85 695 (5,139) 3452778071.3578189431.225797717267637708506527464987314161. .901584692755427378722839770656354167189649601351.P64 697 (17,41) 16729.P189 699 (3,233) 1401190779823.1917765426328344646895407. .23482447257772948338207752516264041.P69 701 796337.2983457.28812503.1073825104511.9983923992673. .15865578195367.40686928318417.P140 703 (19,37) 35284030283053759.1294046302848776287.11931812674076681849. .167823649475113693461122232089506777. .59588714597816906383348767955828416209.P69 705 (3,5,15,47,141,235) 157925605323676378629391.P88 707 (7,101) 126729751.128782811543.700553271665826444242790841. .3598194408030741269333601460682311. .51903872795463977962670556595700473584389435543.P54 709 216868921.1391646221255097953.P187 711 (3,9,79,237) 5689.41851365145831.864328108984548257763049805767. .19573690271784800408214873038427972853220421889.P48 713 (23,31) 68449.335203548019575991076297. .25302796036126213353739363322307560110912714814142460639.P115 715 (5,11,13,55,65,143) 249602191565465311.598887853030285391.P110 717 (3,239) 40153.12417007.58392032593.55009358369431. .199987538790826996082414586220862745720625115339053303.P54 719 1439.772207.737572843389436536903316910033561929012829990389769.P157 721 (7,103) 10550281065119153.P168 723 (3,241) 1447.7480159.102072660983478595344638863.P109 725 (5,25,29,145) 448477751.245573800535260692993906074551. .177457540153273192963355393450351. .3306918468362395868346324514646813146301551.P56 727 176062917118154340379348818723316116707774911664453004727494\ 49436575622328171096762265466521858927.P122 729 (3,9,27,81,243) 80191.97687.379081. .664728004346558283448724389870269691211809.P90 731 (17,43) 67872792749091946529. .223192283824457474300157944531480362369858813007.P135 733 694653525743.14399141148866077141941966959399761. .13948432601001273785699253868326270649.P138 735 (3,5,7,15,21,35,49,105,147,245) 41161.4163041.20147473081. .2340389488711.27653710336343911.P51 737 (11,67) 4423.12148690313.5157050159173695487.17904041241938148871927. .1963672214729590922916323781834466879.P108 739 184603056517613273120809.48050683584092004380805463790111. .2561503388753170490897052206621137620938856555180343258504238\ 260072282185111994663.P87 741 (3,13,19,39,57,247) 83352127.2665675660861389884202429169.P95 743 1487.1219280833.14904366017.118722715461092305629361. .4721525455401597740684262559. .4977047949106985392753791512048265888682003683833.P102 745 (5,149) P178 747 (3,9,83,249) 324965201690131831.P131 749 (7,107) 46439.120618551047.227444841245238451591. .963644196044828188869351734353847. .4143416085716681490838653625856664863812512904964849.P71 751 227640245125324450927745881868402667694620457976381782672549806487. .6493500319937011450007704218333851757321824602859305748523089149897.P94 753 (3,251) 4519.12049.220116640729.180797717027593.P117 755 (5,151) 1511.15073467791.286621334502631.P153 757 9815263.561595591.572213702200206782424822797509585774915131\ 2827809388406962346253182128916964593.P134 759 (3,11,23,33,69,253) 1633369.46025761.P119 761 4567.6089.738686421813192728921171408273447.2802302669186082\ 39805810556544655376723809198780890337110755962385407.P121 763 (7,109) 20920873186456548596636141110060241427023578051534495\ 58384836836073.P129 765 (3,5,9,15,17,45,51,85,153,255) 16831.3696481.2109936092650831. .24710462787135943791475548268920478656481.P50 767 (13,59) 38351.297205245433279.6616963204951529.6329588309789019577199. .756450142211646020278834399577.714106625397559765944265428336645929.P87 769 1591805393.6123566623856435977170641.P198 771 (3,257) 1543.P151 773 6864241.9461521.1165626988664823792549971253972697. .101625278121114813541046756104385520302531369. .3102804258869848876949115800490112967822146918598407.P91 775 (5,25,31,155) 3064351.2168815801.1113614148551.P153 777 (3,7,21,37,111,259) 4663.6433561.4750535347861726648681. .96786396648673403672115546439.P70 779 (19,41) 1559.3142487.21726311.104003232119.164597693569197241. .202664437974567925010435751833. .539043252861508730639718553683237826728217905315243065969.P86 781 (11,71) 6511616671913.66232837958133438967.79034734517219615663. .370549646190282993458807249710605687589893787382049438311221836912017.P90 783 (3,9,27,29,87,261) 1567.602999957032279571271592229136193. .1345967414522954303164296915490846371433.P77 785 (5,157) 5393364481.135732250385154376731523201. .2167731870412324810536209829271. .14488318273595902692706536553684238317387680182551817911.P67 787 9951597611230279.96512008100928793. .171124793552074153093621463907993111755630713094272377046079303.P142 789 (3,263) 5609685181351.274473195338134592222791.585608533119706764820561. .748093847626791888666559.20389292512407050043445124186439967.P40 791 (7,113) 1583.7920714887.2549280727345379556480596752292189634\ 269829765250993670402549042422649.P120 793 (13,61) 4759.31721.145211798447.579981948313.5574629969448636\ 61915154471811685102632550568013283044249936559839102852607.P111 795 (3,5,15,53,159,265) P126 797 2006858753.54573369937.104757762864135516671. .747609928190821086986322983.21023711323746974956423747989180911. .2896793131110864597734842177399739433374955784567182457.P85 799 (17,47) 2957111053582540504996549489605401. .58661611895317888463459159306494372182834314694165224297.P133 801 (3,9,89,267) 3344977.16960539007.1790799748670521. .138732415594618114488007.2326974010504075618187561564812777.P71 803 (11,73) 1607.78366377.1384018681.1533745237729. .2762339998302448893880313142073.P154 805 (5,7,23,35,115,161) 13816619111. .368807221314046570921624935038049174011736160751.P102 807 (3,269) 2771239.502502761.P146 809 4148386731260605647525186547488842396461625774241327567978137.P183 811 326023. .120561845344829717145833822890964664477289164454661659494292322521. .2311981238730869511054219546672357314999967143730457809047390\ 1521408187760986228863.P92 813 (3,271) 24391.2248759.36936217.152948738791.49322756803485314471713.P111 815 (5,163) 180883807440027655212532885072379634915469957001205875201. .6309875796859222682628258124466792652955476368011894066158361980151.P72 817 (19,43) 81278478804329.1527890378338261467896809. .503836749763922905688176944079261201. .7911922734932819371233930194607936241219971448463.P105 819 (3,7,9,13,21,39,63,91,117,273) 2681001528674743. .219516331727145697249308031.P89 821 419273207.109840721427977.286121480219517473. .25348330589061322436059499894718930577798031880081867566547223.P146 823 1460915248436556406607.1534086200463688788034864584049. .143184637761572731326463181795041575633874874096385750942600\ 74593259322339364163972504114136247.P103 825 (3,5,11,15,25,33,55,75,165,275) 702948566745151.9115784422509601. .4108316654247271397904922852177568560929751.P48 827 66161.1637241673.1656489332706171370072190422631. .2550707823005230793212015514781257.13394595223843413901037846\ 777300844745495137348727969920754613220161097793251799.P93 829 72953.89654239955972104838901500177.P216 831 (3,277) 1663.3772542223.502746492223.660284006953.679758314119.P118 833 (7,17,49,119) 14821647473599.2394594520709878135254356190088519028761. .794769178865803830796254438307018567389833. .16248173432447880508878672460681334430321473.P65 835 (5,167) 18144551.44596548025921.819048171793389082617855311.P152 837 (3,9,27,31,93,279) 1127316245518063.P148 839 26849.138561000316919.377801626929390823. .113910681722635191781067775764311.P185 841 (29) 15839701019198785115846577757132209619279562784734684607\ 539770282665784201.P172 843 (3,281) 1390916281.2475486361.P150 845 (5,13,65,169) 4493034001.53928095661079461754990292241379839311.P141 847 (7,11,77,121) 42262784685026262370553.P177 849 (3,283) 18679.147727.353712117583777.29940168528270618887118001.P121 851 (23,37) 1530328553290391228929969.11862938913865507127049391.P189 853 2065711807.513740645819473.4727997228805279065233.1844945010698291\ 1477871034430148217716695646282266064204205488745738888010789289.P132 855 (3,5,9,15,19,45,57,95,171,285) 709018264240844065111. .158362232618940822526398920291451047671.P72 857 6857.289306374721106633650693738754461144023818395644402718227527. .6625204725332257664000926110446984170426466714233852759\ 08496091789616072191.P120 859 7215601.13183242101527799620391251382520507315529510625017. .58609898712737781434024027899110611446341212502589792599097337.P141 861 (3,7,21,41,123,287) 5167. .209530011998277670096922500900062393290897233.P97 863 8258911.169382737.175642891399.292859999667062206866727168104518\ 8567041998240666598148242087562523669795539013858277310234855201.P137 865 (5,173) 526769431.P199 867 (3,17,51,289) 5266159.P158 869 (11,79) 361592639.239506881856626095535121.P203 871 (13,67) 15679.95860519.12708237958354187384010097. .791926693391795441127294795391450663. .137403482726882442386895575645854007713.P127 873 (3,9,97,291) 132697.9449353.7969524463.P152 875 (5,7,25,35,125,175) 725688486718330087751.P160 877 35081.1436527.1839699736969340949026772071177. .4478527345975241075738524755872079528958635991. .913834579627257571067678951068591568485439681866895999518011\ 67598113823.P107 879 (3,293) 1759.288313.142891999.4010077111.12760970401. .4703954662078801.94031095460270951212691599.P98 881 26431.P261 883 8831.63577.258777491057348926546569104663.P228 885 (3,5,15,59,177,295) 2756788662198217256191.P119 887 16173559.139714099995626040378049.2382154297313396649423300881.1958905\ 756610480165414360798708208617177953881053051177851547528988145879.P137 889 (7,127) 127*.P226 891 (3,9,11,27,33,81,99,297) 1783.12430037668834128259094186647.P132 893 (19,47) 6705767506519. .1542338292002409373550628606652924602059467660039183.P185 895 (5,179) 21481.6917353530526492681.78961972629651529859281. .380175443574763153088777745842279962515778711. .1696067654151459074824290253436397570222341162468471.P73 897 (3,13,23,39,69,299) P160 899 (29,31) 460289.110521633444549751. .796968797719178740820037379973406834314737633.81084249853229481126520\ 50655268837686882616590590466226649600910045900760018177829156763489.P95 901 (17,53) 114684958103.5033986097724889062887.P218 903 (3,7,21,43,129,301) 514711.P147 905 (5,181) 121271.1163487911. .50620094494730690929551913249948101083228214631.P156 907 1170031.3256645177.131895016205024767.P241 909 (3,9,101,303) P181 911 1823.26129303.201955048939840841121786425435009.P232 913 (11,83) 35913067887863.15022975209558247116635814042325164919\ 4496147467096134816937630966207476089227936427945235886321.P138 915 (3,5,15,61,183,305) 360511.95805951836468022966692945378791. .8013930086014783164580302226587271.P74 917 (7,131) 5503.229268017217.57193908443040877545241. .161226249164751695652113.573472334735477809996357383167. 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.159831430413177182293087531819541498868490095317005530584441.P121 937 28111.2419437071. .348131628285692590860028784957527660987485049321208797343. .46654722984595033623595915319018639089714063407438899506169.P154 939 (3,313) 1879.995114641.147859967407. .20155798822017245111102019714324599882897299149847.P115 941 7529.2919837555537648713423753933899463272168605397100436468\ 03168061464937.P211 943 (23,41) 9431.39607.21698431.62209711.138325941036565103. .9280993516297855054039457.57644473457648767005697802783.P171 945 (3,5,7,9,15,21,27,35,45,63,105,135,189,315) 124339521078546949914304521499392241.P95 947 295130657.25749931927.4621646208862937. .11892980076500863942962129100776937. .424738513405261472668265099933196280931949222901926679264408\ 70920964574700349265985080009020182263507473.P113 949 (13,73) 22777.78341849.427960745238703.705900082312653909721. .377725045152842556276329.33983040640336090041816253930273656135559781521. 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2184761.204948631.86710817849281.44894058474254631045721.P180 967 23209.549257.1438495818172960049. .73214830052905408299354903681341531907328727.P219 969 (3,17,19,51,57,323) 11726744977.540538609159. .78161016568215708061327.432185728407904618000990086610965513529.P91 971 23917104973173909566916321016011885041962486321502513.P240 973 (7,139) 2356070859382001284653313.2166176541500493808960173319. .2587308365024554442155425741275338196287468408002970427422103.P137 975 (3,5,13,15,25,39,65,75,195,325) 1951.8837728285481551. .26155966684789722885001.1663763381192308635718252801.P76 977 867577.1813313.2069655374719577273.49858990580788843054012690078841. .23830405750609887318420248635858165476368020607396633699141951.P171 979 (11,89) 89*.13815649.7883576248112389199.P237 981 (3,9,109,327) 10341703.499601719.9727892263.128014683020611040553769. .8290249522204489310786895351990721. .206372514331790653651181848993175421190047559657.P65 983 1808226257914551209964473260866417929207023.P254 985 (5,197) 70921.7263391.73518775918537446144887630711. .97986021556246722936038962043373484819973369725772350910249974593881.P128 987 (3,7,21,47,141,329) 9585228595374769.512512927677384344303149537.P124 989 (23,43) 31649.36706221574691349767448834021945679. .1844138946953172296553312102102187271.P203 991 8218291649.41473350001.231620367206687. .6721885469050382920298612421830968178768028093133627640714502537\ 112053019071272802490029644416444090606146146238871876925423959.P137 993 (3,331) 23833.55609.857491387188810516016046647. .921777666286057213147728970951.P133 995 (5,199) 14369791.41735340671.114443156761. .2949578944598743237863911.32308603398271777835967540631.P157 997 167560816514084819488737767976263150405095191554732902607.P244 999 (3,9,27,37,111,333) 7993.473589937. .610750585993378533918571366551132613003293697.P138 1001 (7,11,13,77,91,143) 6007.6952744694636960851412179090394909207. .20200567342579527631370455849751729349809657695513.P128 1003 (17,59) 605829388649921.1629239097907113911209. .2252765682876603539639635308408558411526609.P201 1005 (3,5,15,67,201,335) 68626625145959029951. .663636889167401354279502795531186216903001.P98 1007 (19,53) 37430191.183802578728708044103. .456648335230526285864952133714425117400753719511824784488197\ 85894752763553620148815526546415896369.P156 1009 3454817.198582684439.20649907789079.21624641697047. .30850253615723594284324529.1134327302421596486779379019599. .328016293993162203862559385660775410788362383458683411815672\ 56008155638984594836583203447.P116 1011 (3,337) 39147943.6853410184776097.P179 1013 6079.71486759597273. .41120912566813018675472321435609728349473493582225344661873.P229 1015 (5,7,29,35,145,203) 2154593281.P194 1017 (3,9,113,339) 54919.72386347544037768298632733630815274606848381343.P151 1019 2039.75407.82433230679411141627745147311847388925656728692144689. .114035687775867905605686994484554082640285464189592821829801\ 3381554156431441.P171 1021 40841.795808241.51731968308257. 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.647463932206559821122945033207524451183068970139360141681.P65 1037 (17,61) 3202454929367827107369500863166382153574440123642592390083279423113. .264663433575904067756146573592831453787445089681178190073417\ 60083534582332276992306679.P137 1039 5080711.5585366661993629126074920465831594496864652701848863\ 7648010052346319853288374753.P227 1041 (3,347) 24769991104728312891937.P186 1043 (7,149) 2087.100129.3256247.7346919119.106176200291258634359340843950954\ 3822254622816882458239681481029190247468769225265309538618766660313.P144 1045 (5,11,19,55,95,209) 6271.5972377728166033731379524138706997651075303681. .2591359432094537078074951131139791193021859439188185801.P114 1047 (3,349) 18063321433.P200 1049 33569.459463.1059099980653317121.P288 1051 3575503.215738012818441827932337543036174144558274385301234576636299249. .305017906063256842921494808558019733856326299412534951989303\ 214657199.P180 1053 (3,9,13,27,39,81,117,351) 44207047.24295813738965169951447.P166 1055 (5,211) 2111.29257554834707791. .22798505814116334119485271455401054495620094271. .307289980970606234686867138691001349037525535679593763081.P130 1057 (7,151) 5318798633.117801297041.6645418768842321985721.P229 1059 (3,353) 18861552481.4067055143413119297753219773293999460854231105692799. .6327019834650802405813498384839000872342691100400396876643368617.P86 1061 468172263510722656207776706750069723016189792142528328750689\ 7630383940041368231392116815446515176847242098004471574585\ 8522803980473207943564433.P177 1063 1485761479.P311 1065 (3,5,15,71,213,355) 14139262262808175798602566204793985440361. .6252200505559391265660834611730277041893919359311.P80 1067 (11,97) 4884727.32805679003831689475103. .243371615286359074030086018570330283599480031300958764654249\ 16230567.P193 1069 17481727674576239.37473613084215372416028665821312617743022228898297. .55570361679448925026662858219518716008035810191930741829420\ 21552512721.P187 1071 (3,7,9,17,21,51,63,119,153,357) 10711.861229657.52877551231. 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.23864222009193938317456687011256092421563991. .2664797814058212286560533454960446792210016180875809243599817.P131 1089 (3,9,11,33,99,121,363) 141641296831.27306046411338223. .6148629656539349648850688099941128013039964611990754521512906071.P108 1091 87281.551978359.791343585595817.97535130364653673535422113471207017. .496474000537225566899310934393330825097522839.P221 1093 43721.111487.42565880168703357316051447. .4611633294343645255154057631569698529799025986941131181322230\ 3231047196444160418969946791520558378694863913363980328293449.P173 1095 (3,5,15,73,219,365) 702595801. .12687370311710932103729819887748340216531751.P122 1097 980719.4666639.22926719175799.1734492765338661710171833. .36079584237927411511333522577.205295973898620029528272537868263.P220 1099 (7,157) 11302318217.28617130498420804403756708531447.P240 1101 (3,367) 79273.258977744356523549983.883533090360873723903538281367.P165 1103 2207.4126110275598714647074087.P305 1105 (5,13,17,65,85,221) 7555991.115812024214750631. .155137816977180947152785562601502526330318743274151.36623786615\ 448792528228651753874770336757984952740798581899844047499677232721.P81 1107 (3,9,27,41,123,369) 7675195491326802969559.472897006006202784083089.P172 1109 30963501968569.85608965982066833903.24616019211889325200869055\ 21818107058796864006122032851020804339917742231488935126958023\ 8737955397055519355385591659502001884424804253804809798519.P156 1111 (11,101) 457892136759270759480793. .94016992174261011260856274005378816886689234303060299026659472401\ 12085572850557654128039535064932539432952669653208185411260693457.P148 1113 (3,7,21,53,159,371) 15583.51199.2363026390394916673046830675466863.P146 1115 (5,223) 7866820287217429790532545104013632296537532272087818471.P213 1117 53617.520973969756320610191611683062985619298001156192232208\ 204963188406964166233609.P254 1119 (3,373) 2239.20143.154565233.1100558881.P199 1121 (19,59) 8969.P311 1123 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365106542520646053873234125869250449257912961.P235 1167 (3,389) 60459128773735346116971161647.1510465779473273611561431058793939\ 2907720927949013372316086220189370366144748468367769414132535609663.P105 1169 (7,167) 514361.6020351.7322617.8932786385279.P268 1171 153606920351.12348670962833258442807675383265838347627997587\ 940117506190420273604620443843301292612106209291538933323931\ 056186142998412331913.P215 1173 (3,17,23,51,69,391) 428417137.18228580446571609.403906782348344599. .515878737178649880676177. .920854434270162822283216457951519800254804780099567201431071.P86 1175 (5,25,47,235) 10009431316533167951.1094883804311836270751. .5170712852551602215753262223559516152087046351.9615801571101\ 87684257205548226336434195920860869822021364930979042561801.P120 1177 (11,107) 3775817.5960329. .355693251295001123842782330386351058608227381732783. .201566078754892345466259020562112388697008576143602159294285\ 9847523108465523348455927947279783179798610711213193.P144 1179 (3,9,131,393) 28297.10909426047235017667998633478885601105094202777.P185 1181 4742897.196834168670106625096599487.199668911054466914791190422986407. .180842235317734956454651203551253000127948125985424886045434\ 8989451026887.P218 1183 (7,13,91,169) 28393.46655969015605951.6782788827593836595057461524237525\ 59959082381905409424240215735957129262394986213437565297105701895143.P159 1185 (3,5,15,79,237,395) 115150116391.21792652855138681.P161 1187 256393.113603023.1761533117965696212626325049982897. .766302834531296176581826196660125454171041129. .153327833285998453874202767942570343649971393640068204571694369.P204 1189 (29,41) 600619547820455607135590639621491727. .10276876497295959142374278224747317922211821032760703.P250 1191 (3,397) 274404635931475033688839.10712613085162141902489577. .31012907533549270862130471636936345708864774418056106790748\ 3529331484160990453225414159.P104 1193 121687.85227326201314361823893776605433636670217425388311906\ 457714409016049961507516230416822145599757462472729.P251 1195 (5,239) 270071.10602041.150885481.502862692004168161. .4925687525543853241.2004186363732465633272613168051655374493121.P187 1197 (3,7,9,19,21,57,63,133,171,399) 122899168808744663588141025320026245511852609957212433417. .68539098502476500342849178765232476276974878815092900810113.P81 1199 (11,109) 2399.174181129.4218108040611917562429786369962714155\ 026225684343947313001103389074302369031.P238 1201 57649.1967239.8510287.2830858618432184648159211485423. .9303484663199459234574876772320860861459293591098445572165959.P253 1203 (3,401) 19249.6036176514733205313599139320239. .428209191776225441650116035809142521. .157563584396809246533896922588809084010469249304497.P120 1205 (5,241) 29837535806497801678478605948471. .73060016932187138115133589215300761121.P220 1207 (17,71) C337 1209 (3,13,31,39,93,403) 1187239.32572879.505052497.4889979739596199. .10083495373751671.66393706906151652073358618281.P135 1211 (7,173) 2423.428811722403419167.P290 1213 327511. .715079841864486572798550389025242773233223013545064445043124471.C297 1215 (3,5,9,15,27,45,81,135,243,405) 49677578641. .660657672518832002413997900375962405769331474918483722521.P128 1217 1045741327.6116773272167843384976777858063213917010557325918356879. .22053390021902056444354293154701006674049109757797668799.C248 1219 (23,53) 7865380519.4209688612273. .112114237626279005145204233646457328838633247887176899247572680743.P257 1221 (3,11,33,37,111,407) 9769.564103.3357751.10832713. .5083469670561297247.P175 1223 2447.31799.439191833149903.P346 1225 (5,7,25,35,49,175,245) 1036351.113366401.21821503201.37747185231001. .13094876492852351.113591256042443401951. .826879209501691466620175201. .43577956560659729250250688550974383201.P115 1227 (3,409) 120247.P241 1229 36871.46703.10543179280661916121033. .9536289355314392579996071515160583098298616686033085857.C284 1231 531793.5684759.18207494497.63919078363121681207. C329 1233 (3,9,137,411) 187417.188994241.P233 1235 (5,13,19,65,95,247) 20187566881.11961374462243472872450821823618071.P216 1237 2538207129840687799335203259492870476186248896616401346500027311795983.C303 1239 (3,7,21,59,177,413) 263483263.1102272524932426318899113975892645895609. .1670878037781006851372822152562306836870689490944244928322111\ 88268061451903148929.P83 1241 (17,73) 188633.23837129.43901617.446793066948847. .902008166240890406559452647366945961. .388907900553908175742503046457025658927. .223871889690953298798962632633387601188053845278270076876769\ 796234447.P169 1243 (11,113) C337 1245 (3,5,15,83,249,415) 26286854948597786907115336739126588990310\ 3683620908031985454238816270819685799271.P118 1247 (29,43) 276699163508776968689. .161391234598523464727026956609522103493838535717217.P284 1249 97423.52358081.2379005273.9345276045907272726364012481. C326 1251 (3,9,139,417) 2503.4141765665149841884868090281058439. .18711855488494977389826847656083384790098295888337. .79701589763805892252138133063189365254379704685545583.P111 1253 (7,179) 90217.98192205861121.19660952720704289.3313809623975157007.C268 1255 (5,251) 2944231.119398292924910437369037130939601. .2035458130820062395619374650792440118558881.C220 1257 (3,419) 27531920567858260417749539986643662128683528445675900\ 15364783530001198571176312822543.P167 1259 875965965904153. .12837801903260418659222502180271368969172790209999210831.C309 1261 (13,97) 50441.2392608791.9817518023.10011860164738779613596795713. .1011475887230582795346080875236878564683110543141027818703968639.P232 1263 (3,421) 1313310230653921.1160237874387344563207. .96394828074288003368359.P194 1265 (5,11,23,55,115,253) 121441.533831.136149590957161.556590676780973231.C223 1267 (7,181) 170300267537.302174566303.P303 1269 (3,9,27,47,141,423) 13409665391953.980230389772951. .2000007978762572383159. .4054639296059452870934086739488655609338850043863103127.P146 1271 (31,41) 2543.134617656926451412410507151831401552071. .157490884005526743543036209681491790528847864761144839.P267 1273 (19,67) 7639.272423.P349 1275 (3,5,15,17,25,51,75,85,255,425) 2551.41355657751.4780601420529202899151. .10443388337470493382395059803087717465056821801.P111 1277 C385 1279 P386 1281 (3,7,21,61,183,427) 360770593.59852053865074950059030679473230729. .5026638059744684898569644215486557551. .32599161877302789289075576911955243092385921174258348134509220487.P73 1283 4824675346114250541198242904214396192319. C347 1285 (5,257) 3708511.9497339911.53721781932548291303600309351. .1920007072772443930489755386645317544614236001. .428744540698389267520963609661194324138479737735791445178847\ 38168843512041630684462005624604887927820871.P114 1287 (3,9,11,13,33,39,99,117,143,429) 216217.71477407.141968533929529744009. .5421243831056685352970617400882224189523156449.P138 1289 15856636079.108817410937.827446666316953.9580889333063599. .16055826953448199975207.P314 1291 998943080897.84051400422953302189544581841. C348 1293 (3,431) 2612439750169. .73475684245644536575389673549407942112577575745833.P197 1295 (5,7,35,37,185,259) 2591.287458921.589131872988751.P234 1297 12097392013313.64873964199444497. .80025868895687041966359471596981171570268166357936741924913.C302 1299 (3,433) 93529.12220578919.184466950111.2143492370401. .138656761760615247768856163952417631. .220210503364712569635004208751191654890379852983345014424326\ 67521208159.P116 1301 161317830296866767945829203107381353. .3172016620920990460580749619964431858642380903.P311 1303 10444849.1140690503.P377 1305 (3,5,9,15,29,45,87,145,261,435) 2647790191.P193 1307 101286184577.141196558805510033914433414063. .161633497146742177992711798481.P325 1309 (7,11,17,77,119,187) 83777. .182851909830134390903646706254500631010641061703.P238 1311 (3,19,23,57,69,437) 23599.46304798398041343033486090745029851\ 7610234647462968200247768280368542511482597295122309061900337.P139 1313 (13,101) 2602367.17428919561.730270072559. .74021178254286399569538165006691287501249903223.P286 1315 (5,263) 20821711.6564920264482202699756113871095601. C275 1317 (3,439) 18439.5275903.176601657325935576973876149519188287138063. C212 1319 712292734142687.4561015525367423385817952015799767. .528143874978418020442958250948319387628471.C307 1321 7927.1394977.4848071. .15514776584693313272539134504494867053743089873.P335 1323 (3,7,9,21,27,49,63,147,189,441) 2647.5887351.17072111071. .1105196924013081302593. .1105597066741955572358787642214880896705389887364638307697.P130 1325 (5,25,53,265) 71551.1067951.2594351.16289551.19525201. C282 1327 2730967.6363071161.P384 1329 (3,443) 5271670883383.14749160056100581173587085971612876148889. .24710423239051120660271179307312048226282449719.P167 1331 (11,121) 2663.80497247099660420588857.69474230349847530551244234511. .131437248032743119455503505737464640742780068008121338081647.C250 1333 (31,43) 29327. .185449330937317252200083167190588857112028090982541623319.P319 1335 (3,5,15,89,267,445) 486967951.1358103969241.68592177919591. .119850770411474610841.3192423430636078166119279321. .7281043041842781395260853247903560898126191181044290101875066161.P67 1337 (7,191) 267401.298197665489705956620265817. .2200183105419689505664913641945935202551071.P269 1339 (13,103) 2436553406461804657. C350 1341 (3,9,149,447) 93871.19779751.34029217.87980329.400482858239983. .77360147414126613793604276000882862826456964681059491988849.P167 1343 (17,79) 41216671.548748884195638359847. .525281795214043482559587344519773159.C312 1345 (5,269) 2427739777657193401.119136832329401379240227791. C278 1347 (3,449) 278476007488759. C256 1349 (19,71) 40471.95905807. C367 1351 (7,193) 2023171960111.2812474579951. C322 1353 (3,11,33,41,123,451) 40591.17057505207007.15515986997325774196249. C202 1355 (5,271) 2711.179756860951.112728018316091351. .627280852621176806510456483612781740231.P255 1357 (23,59) 21713.445097. C374 1359 (3,9,151,453) 2719.41707711.6675969767113.2744233598061589004329591.C223 1361 8167.3397057.137450113.30322542339673.15459763525875943. .856450061281312036458486309832227737.P326 1363 (29,47) 32713.22563103.139914008013123780038639969.P350 1365 (3,5,7,13,15,21,35,39,65,91,105,195,273,455) 469561.52393016292934591. .2224981001722824694441.P130 1367 10937.65617.232391.2561759.29769631481404601. C375 1369 (37) 2105741041.6337549872222510181433065176903666450905719.P349 1371 (3,457) 21323707394608154472021019927704769. C240 1373 1957392737.4540035943.95805718487.416034935039. .142203959478768454375479374259330640346359070988407.P322 1375 (5,11,25,55,125,275) 13751.6943751.P291 1377 (3,9,17,27,51,81,153,459) 246083671. C252 1379 (7,197) 4274004212633. C342 1381 8287.462853283623.20314602484365657521. .324347780588879609356756802551. .5717943157553181705211179112739301167905781641204356084154399.C291 1383 (3,461) 734448037017694655904560352073450673640369439. .3137686192033052035820020693967612860763683311604928377.P178 1385 (5,277) 132961.61604801.4853240164236570447629807637019724521. .8763532688272014806854185427939951951.C246 1387 (19,73) C390 1389 (3,463) 8969259151.1582530534046275752761. .22335531850512049331378221292233833562609.P207 1391 (13,107) 11087986287758644708471.123824903846208671573681137705208233. .22558896208633105394366595301980131378137. .919002663875888501974619475546657058672009.P244 1393 (7,199) 5246157799.6600454687.10444147481014434605310124285369.1940\ 38896022637781283943529202525374330942645948410515792534794865319.P239 1395 (3,5,9,15,31,45,93,155,279,465) 91669438116041671. .69762899759932452389350875226831. .2330800364274713909258340938080474401901550802637796459656309887361.P102 1397 (11,127) 11177.108967.618242351.1624926851105431039.P343 1399 28875361.4320651071020341609502042221583629017824960697. .9729831901051958663829453004687723271026191923786080297556081.P308 1401 (3,467) 142903. C276 1403 (23,61) 7365751.50363887381959227167658519. .184974108671317434008988391371809. .707964508185716596099485802562115938162908630127.C285 1405 (5,281) 368111.4349881.4383601.125323853452241.1653932839153471. .49909553545967496391.P270 1407 (3,7,21,67,201,469) 11257.14071.340096374452647.1005128735010289. .10463508604369759.94379978353227424201.53088206848780310639460631. .185869395380605416228548143.P113 1409 264136919719.34649857787874317478304238154673687249. .1484993916000134361209645994489796858702347953214405357561157943.P313 1411 (17,83) 1156444313.1622988641.2276704117157670362417622964159.P347 1413 (3,9,157,471) 128217222737641.32334725460268711. .314657297435668730788373264911.P222 1415 (5,283) 79241.815425615801.39826723601148990271. .1478507524858138362374651451547163263681391. .217324465815675834842001173711247406035110681.C217 1417 (13,109) 111835228649.33105879921837807137. .196224694354792350070473041621399. .56671901892032592171296689668028440676501169.C284 1419 (3,11,33,43,129,473) 116359.18449839. C241 1421 (7,29,49,203) 15699209.25652284247188456525842519940799. C316 1423 1699063.104904621559. C412 1425 (3,5,15,19,25,57,75,95,285,475) 634760551.10657302892385206201. .8463634936210536760201. .41663891569995213211790678603293227079435201.P124 1427 19054580564725546974193126830978590503.P393 1429 1757766958557127850108708353. C403 1431 (3,9,27,53,159,477) 25759.973081.1691845504865603430675449959.P245 1433 20063.53101249.86576129.16532942303.7653556173496897. C386 1435 (5,7,35,41,205,287) 7832620321.41060309512111. .109140463485895651174151021931545925141431.P225 1437 (3,479) 36329495383.133800079034660627402599. .117166794471137237993098469105117594115732235942418044032585601. .287031409597396291529341460872951621315514329092527118344752\ 584974790426307673535303439.P106 1439 2879.46049.172681.802732845007.70570366382050360064160741167. C380 1441 (11,131) 67265881.1881621039583314078479. .14493033727005345040798406653136458967643857252029297. .18272128521238688082094126256665335881447596262755566899519.P252 1443 (3,13,37,39,111,481) 2887.14431.346321. C248 1445 (5,17,85,289) 19206165481.3901904004579951728041. .11080165440414323358018601.16389114576700781882128607285877237631. .38276471029600993563428443865883777077195561. .483541227708936784200571521201548282516556268091841246101740\ 6004489922461453093111.P109 1447 57881.1754380423.135870799392023187135247. .329476003535938830704093614193630509247.C360 1449 (3,7,9,21,23,63,69,161,207,483) 217351. .528396292136087290962410143062727207.P198 1451 2903.174121.696481.17009142910813751. C407 1453 8719.6479507883338993. C418 1455 (3,5,15,97,291,485) 47372699863851391. .2149606353897549683602246872237292351.P179 1457 (31,47) 11657.20399.361337.711017.130509319.32629120387007205904673. .2651271658682823532549291409. .5222765655190372513782632007419694049123831433.P292 1459 14591.93377.P431 1461 (3,487) 716638033.P284 1463 (7,11,19,77,133,209) 2927.1478815031. .8612055962441945623327451972844118959199682536269165337730366471.C249 1465 (5,293) 867281. 273540531464313955314852499316612415349762230038482231.C292 1467 (3,9,163,489) 26407.165836909377. .7272744319188731968367956634511312340302967193497.C229 1469 (13,113) 44071.470081.8807637077851602578537.P373 1471 652662073639.241722486510605423.6149161897754904267815515354\ 0458255504752992030160252118535699943713.P346 1473 (3,491) 58921.2672023.8955841.P277 1475 (5,25,59,295) 11801.142673801.3316236275736001. C322 1477 (7,211) 8863.35449.2065461814637063313713705681. .19236737976418728476595440431.C315 1479 (3,17,29,51,87,493) 251431.21340609321.980233931161. .140257800488185952294547625370047. .903737970511516342986925655196046632123272863.P166 1481 71089.3915278233.12787706913743.3993419580376129303010329. .8268138870080189511875976090034105337. .8348981870260729786758008817506660899281935231.C311 1483 910188101009715972185070554697411008108729. C405 1485 (3,5,9,11,15,27,33,45,55,99,135,165,297,495) 19694071. .106638643913461155414345241. .3307778274605860019775884877775856144362368451681. .3745535208623794897677784427764312686722433921155541307576231.P75 1487 24464753918382797416777.P426 1489 71473.27201739919.51028917464688167.13822844053570368983. .122163266112900081138309323835006063277267764895871. .95909518295775374166321292697000685895150503357477127. .430768120877571983358263339450368443038134995818878229278591.P235 1491 (3,7,21,71,213,497) 47713.116751779887.67270991092499094308622649. .28790402469049403855325089400559. .22641688411979072442059478103675602523680474909121.P131 1493 3788526319.9128086063638824541964831110329768544223. C400 1495 (5,13,23,65,115,299) 71761.9191423582708116751.P295 1497 (3,499) 862273.4634713.1381735298979140653677620036279638470695617.C245 1499 2999.400453196195527405748338277279809339221225225247. C401 Table 2+(odd) Factorizations of 2^n+1, n odd, n<1500 n Prime Factors 1 3 3 (1) 3* 5 (1) 11 7 (1) 43 9 (1,3) 3*.19 11 (1) 683 13 (1) 2731 15 (1,3,5) 331 17 (1) 43691 19 (1) 174763 21 (1,3,7) 5419 23 (1) 2796203 25 (1,5) 251.4051 27 (1,3,9) 3*.87211 29 (1) 59.3033169 31 (1) 715827883 33 (1,3,11) 67.20857 35 (1,5,7) 281.86171 37 (1) 1777.25781083 39 (1,3,13) 22366891 41 (1) 83.8831418697 43 (1) 2932031007403 45 (1,3,5,9,15) 18837001 47 (1) 283.165768537521 49 (1,7) 4363953127297 51 (1,3,17) 307.2857.6529 53 (1) 107.28059810762433 55 (1,5,11) 11*.2971.48912491 57 (1,3,19) 571.160465489 59 (1) 2833.37171.1824726041 61 (1) 768614336404564651 63 (1,3,7,9,21) 77158673929 65 (1,5,13) 131.409891.7623851 67 (1) 7327657.6713103182899 69 (1,3,23) 139.168749965921 71 (1) 56409643.13952598148481 73 (1) 1753.1795918038741070627 75 (1,3,5,15,25) 1133836730401 77 (1,7,11) 617.78233.35532364099 79 (1) 201487636602438195784363 81 (1,3,9,27) 3*.163.135433.272010961 83 (1) 499.1163.2657.155377.13455809771 85 (1,5,17) 26831423036065352611 87 (1,3,29) 96076791871613611 89 (1) 179.62020897.18584774046020617 91 (1,7,13) 224771.1210483.25829691707 93 (1,3,31) 529510939.2903110321 95 (1,5,19) 2281.3011347479614249131 97 (1) 971.1553.31817.1100876018364883721 99 (1,3,9,11,33) 5347.242099935645987 101 (1) 845100400152152934331135470251 103 (1) 415141630193.8142767081771726171 105 (1,3,5,7,15,21,35) 211.664441.1564921 107 (1) 643.84115747449047881488635567801 109 (1) 104124649.2077756847362348863128179 111 (1,3,37) 3331.17539.107775231312019 113 (1) 227.48817.636190001.491003369344660409 115 (1,5,23) 691.1884103651.345767385170491 117 (1,3,9,13,39) 5302306226370307681801 119 (1,7,17) 823679683.143162553165560959297 121 (1,11) 117371.11054184582797800455736061107 123 (1,3,41) 739.165313.13194317913029593 125 (1,5,25) 229668251.5519485418336288303251 127 (1) 56713727820156410577229101238628035243 129 (1,3,43) 1033.1591582393.15686603697451 131 (1) 1049.4744297.182331128681207781784391813611 133 (1,7,19) 4523.106788290443848295284382097033 135 (1,3,5,9,15,27,45) 811.15121.385838642647891 137 (1) 1097.15619.32127963626435681.105498212027592977 139 (1) 4506937.51542639524661795300074174250365699 141 (1,3,47) 1681003.35273039401.111349165273 143 (1,11,13) 2003.6156182033.10425285443.15500487753323 145 (1,5,29) 7553921.999802854724715300883845411 147 (1,3,7,21,49) 748819.26032885845392093851 149 (1) 1193.650833.38369587.7984559573504259856359124657 151 (1) 18717738334417.50834050824100779677306460621499 153 (1,3,9,17,51) 123931.26159806891.27439122228481 155 (1,5,31) 11161.5947603221397891.29126056043168521 157 (1) 15073.2350291.17751783757817897.96833299198971305921 159 (1,3,53) 6043.4475130366518102084427698737 161 (1,7,23) 8103467492759792327149800361564410265219 163 (1) 11281292593.1023398150341859.337570547050390415041769 165 (1,3,5,11,15,33,55) 415365721.2252127523412251 167 (1) 62357403192785191176690552862561408838653121833643 169 (1,13) 4929910764223610387.18526238646011086732742614043 171 (1,3,9,19,57) 19*.19177458387940268116349766612211 173 (1) 347.4153.35374479827.47635010587.1643464247728189221623609 175 (1,5,7,25,35) 1051.110251.347833278451.34010032331525251 177 (1,3,59) 13099.4453762543897.1898685496465999273 179 (1) 58745093521.4347868190665879373495950562775707707143803 181 (1) 1811.31675363.17810163630112624579342811733978085990447907 183 (1,3,61) 1772303994379887829769795077302561451 185 (1,5,37) 1481.28136651.778429365397887608540618330873281 187 (1,11,17) 2191165825376888084750157716424579062015865776131 189 (1,3,7,9,21,27,63) 379.119827.127391413339.56202143607667 191 (1) 1046183622564446793972631570534611069350392574077339085483 193 (1) 6563.35679139.1871670769.7455099975844049.1280761337388845898643 195 (1,3,5,13,15,39,65) 107251.571403921126076957182161 197 (1) 197002597249.1348959352853811313.251951573867253012259144010843 199 (1) 267823007376498379256993682056860433753700498963798805883563 201 (1,3,67) 2011.9649.6324667.59151549118532676874448563 203 (1,7,29) 596834617.3692022713.252715814615565962418688965855731 205 (1,5,41) 2125820563389437533390243893834597846757304863651 207 (1,3,9,23,69) 6113142872404227834840443898241613032969 209 (1,11,19) 419.3410623284654639440707.1607792018780394024095514317003 211 (1) 4643.9878177.5344743097.199061567251.22481127512575175864234185190299 213 (1,3,71) 5113.17467.102241.203525545766301306933226271929 215 (1,5,43) 9084611.59904608378705661377430182608711698924130721 217 (1,7,31) 16233337.140508608590164280225934233098866842745808905947 219 (1,3,73) 9070197542196643.3278244690156222434135906137 221 (1,13,17) 443.4714692062809.4507513575406446515845401458366741487526913 223 (1) 219256122131.20493495920905043950407650450918171260318303154708405513 225 (1,3,5,9,15,25,45,75) 4714696801.281941472953710177758647201 227 (1) 297371.3454631579714210387.P44 229 (1) 18754643.P62 231 (1,3,7,11,21,33,77) 14323.P32 233 (1) 467.27961.P63 235 (1,5,47) 328006342451.461797907949997211.P27 237 (1,3,79) 647011.13664473.P35 239 (1) 340337.32605142983704221670173899.P41 241 (1) 2411.10411181203.15059828108442641.P43 243 (1,3,9,27,81) 3*.1459.139483.10429407431911334611.918125051602568899753 245 (1,5,7,35,49) 491.15162868758218274451.P29 247 (1,13,19) 207481.10049443.355011619.P45 249 (1,3,83) 9202419446683.P37 251 (1) 238451.P70 253 (1,11,23) 4049.85009.31797547.81776791273.P40 255 (1,3,5,15,17,51,85) 12241.418562986357561.51366149455494753931 257 (1) 37239639534523.518144156602508243009.P43 259 (1,7,37) 1456235596904319041738812533139.P36 261 (1,3,9,29,87) 523.6929826139.3453412901832690553.33563856450515702761 263 (1) 1579.92051.29261114397558193.P55 265 (1,5,53) 593783678966863030035641.P40 267 (1,3,89) 3739.4273.P46 269 (1) 424255915796187428893811.P57 271 (1) 1627.115417966565804897.4635260015873357770993.P40 273 (1,3,7,13,21,39,91) 547.105310750819.P30 275 (1,5,11,25,55) P61 277 (1) 25792643401363.P70 279 (1,3,9,31,93) 26227.119232435043.85384915399027.6444365376140611199022187 281 (1) 563.5203536083.P72 283 (1) 1699.62827.2486265371.67535788803713.P54 285 (1,3,5,15,19,57,95) 1101811.P38 287 (1,7,41) 1723.84413238703660609.4336790831080504259.P34 289 (1,17) 72251.79187.1077971.18360250452977.197766803208315851.P36 291 (1,3,97) 25609.5636963037465601.581546606903256979.99695503427255026561 293 (1) 587.26371.33403.13453890779540632945331892129844577.P42 295 (1,5,59) P71 297 (1,3,9,11,27,33,99) 23761.694387.6215074747201.P32 299 (1,13,23) 2393.834490119087067.P62 301 (1,7,43) 43*.P75 303 (1,3,101) 112102729.P53 305 (1,5,61) 331841.31347559232075126851.P48 307 (1) 1249678499.4315199443523.210708825063558235331.P50 309 (1,3,103) 619.2473.15451.89620507.2400744384937.98277023988499. .68545852036177507 311 (1) 64067.P89 313 (1) P94 315 (1,3,5,7,9,15,21,35,45,63,105) 1765891.P38 317 (1) 326330579.491981122308467411.P69 319 (1,11,29) 121333341977.169523514238420211.25925516494438382632167017.P31 321 (1,3,107) 154723.20636399209.480625710015394052365153.P25 323 (1,17,19) 17795830908608814443.3211586054639813621611. .6319957642033539607139.2065255878519475622261353 325 (1,5,13,25,65) 3251.5840251.7812610577851.9860942209386451.P34 327 (1,3,109) 666427.6927735019.P50 329 (1,7,47) 659.762394321774681.P66 331 (1) 5297.2983001129.7520796641.8530674250842274717434530683.P49 333 (1,3,9,37,111) 304363.9853387597819.31031320083857011.P31 335 (1,5,67) 93131.P75 337 (1) 21569.5333388961.964094242760707.P72 339 (1,3,113) 156619.28448881.P55 341 (1,11,31) 647219.1434929.37368615235403.P65 343 (1,7,49) 2513690593.2883580030222424891.P61 345 (1,3,5,15,23,69,115) P53 347 (1) P104 349 (1) 131282633.P97 351 (1,3,9,13,27,39,117) 4247713303224552237738169.P41 353 (1) 3803909572078746837295094051706948091.P70 355 (1,5,71) 15524635883992211.P69 357 (1,3,7,17,21,51,119) 428401.P53 359 (1) 3536450843.1110671633637523.194193974563158088483.P63 361 (1,19) 6874301617534827509350575768454356245025403.P61 363 (1,3,11,33,121) 2179.19488182484739.P50 365 (1,5,73) 581874971.498386055746534779273231850742131.P46 367 (1) 2203.19819.146264881313513.20837062885084633147. .460233616861852066165180033789571.P37 369 (1,3,9,41,123) 18451.174907.26309368807003.P50 371 (1,7,53) 18351945672220987.10471846336802440580575859. .90338901802490793533882683.P27 373 (1) 60427.694579497316894264425661243659806371972188318857.P60 375 (1,3,5,15,25,75,125) 2251.19963778429046466946251.P35 377 (1,13,29) 13454377.P95 379 (1) 15012732261073.728040923721821697586308784409.P71 381 (1,3,127) 3049.38257184231365987.P56 383 (1) 1351710731785981752792617.5609122817914313723820539.P66 385 (1,5,7,11,35,55,77) 219980531.4362989211422861340320935785851.P34 387 (1,3,9,43,129) 109053678968940302364939183451.P47 389 (1) 1074456464321.1369379108017267.2742094407638203.P75 391 (1,17,23) 2347.1578859.194902553.291438334156037699. .29111948248642861801.P52 393 (1,3,131) 787.7237497065445543055003057643920459.P42 395 (1,5,79) 5531.1415681.P85 397 (1) 13499.321571.476401.17414009.P97 399 (1,3,7,19,21,57,133) 63841.11355690325205671380495907537.P33 401 (1) 18885983617.3178641606717935496778334833. .24789994689980013078275217373572023257787.P43 403 (1,13,31) 6449.18539.576759899.153633897920257.P78 405 (1,3,5,9,15,27,45,81,135) 6481.9721.74967931.2437880491. .448217524891.10360573664851.1969543281137041 407 (1,11,37) 15467.2248206137.25330067076999169. .42897689055449636582684640379732099.P44 409 (1) 176596029450915408652219208387. .18791937710720575305760721588966789412396307.P51 411 (1,3,137) 7663507.2017223347.2707079449.P57 413 (1,7,59) 827.170735974773267443.P85 415 (1,5,83) 116201.134396921.P86 417 (1,3,139) 441187.1694689.392856131525846647191238066992041449.P36 419 (1) 5867.548560489336890960473978059.P96 421 (1) 4211.32983076027612611.P107 423 (1,3,9,47,141) 85693033.6596828416459.P63 425 (1,5,17,25,85) 91362251.5046718903451.P76 427 (1,7,61) 57461778571.1340235308854811506044205739394787.P65 429 (1,3,11,13,33,39,143) 859.8340357737139637289786276330761.P39 431 (1) 1807447391779.37452571239931.P104 433 (1) 2837017.P124 435 (1,3,5,15,29,87,145) 7060051.23476081.24578371.P46 437 (1,19,23) 7867.668214452631436913.315929758125865060721. .1905976815426273605733466333451.P47 439 (1) 3740281.5612260289.78527789689. .6563213024281378912864020513717469284499.P65 441 (1,3,7,9,21,49,63,147) 883.3529.22051.311347. .1996187656530838599012839257.P33 443 (1) 48731.489333371.2036829768181123. .203369567047358792597230853956871186267775970073.P57 445 (1,5,89) 7121.131865932411.40853155149612675915761.P69 447 (1,3,149) 19687929049.P79 449 (1) 194867.4332851.179293953141823358107657.P100 451 (1,11,41) 20747.21737299.2168435713049.P97 453 (1,3,151) 907.70089067.5667228215161742851.1302216832385373385027.P40 455 (1,5,7,13,35,65,91) 131041.1185685411.39537592800161.171525190684121.P45 457 (1) 6885357560205319573060633896800918448254904729193.P89 459 (1,3,9,17,27,51,153) 3673.98227.33204917536003441.572404735191016891.P44 461 (1) 99577.110641.4776428166707.108902775905377. .1017228587161022218598932642491638987.P66 463 (1) 2356759188941953.76834966209858049526107. .88119307925269041107418404833666787.P66 465 (1,3,5,15,31,93,155) 26041.316201.364831561.P54 467 (1) 33702457.48919673417.9516375589637513.133116327626495251. .759355003952701949854003.27312390961824038384529619828691.P34 469 (1,7,67) 408335956841.362312427317443674457. .76207764956885795275897986139.P59 471 (1,3,157) 290137.31255173993464476009.117791760059111382841. .207080154684218888000497.P26 473 (1,11,43) 947.8116681.4304613491867393. .2319326790833455848494271717419.P71 475 (1,5,19,25,95) 3145393391123750039342489201. .23352531315412606928823082635851.P50 477 (1,3,9,53,159) P94 479 (1) 3833.38321.7241702191810014332930493433. .54657255048286677488033160851148008819.P70 481 (1,13,37) 1484463163.116082946165734700021832375583736205537.P83 483 (1,3,7,21,23,69,161) 245641050541016665188014626987.P50 485 (1,5,97) 11238344415062964442147243324272630868644399851.P70 487 (1) 227020551154913939039124941009.P117 489 (1,3,163) 2840113.P92 491 (1) 15395951896033322050978817. .3563269486977651154759062020950904488457.P83 493 (1,17,29) 4931.244529.408071156372794293927147176542113833.P91 495 (1,3,5,9,11,15,33,45,55,99,165) P73 497 (1,7,71) 145915152433.5213526568247671787. .8705752060803157813200086999866476019.P60 499 (1) 163673.825347.61176403.1192425792950157874662150001. .1575585587524885013687391114684244158499565933913187.P53 501 (1,3,167) 304609.223318747.1134974373913.P75 503 (1) 2049744746263568646584566175908385907415012329005298331.P97 505 (1,5,101) 8081.223211.6909226326451.46393668925691. .145130814068214641.1025698740064276331.727679956595455269121.P29 507 (1,3,13,39,169) 10030854869257.4966300248405749059.P63 509 (1) 1019.1171175995519938934637486085538049.P117 511 (1,7,73) 3191707.10435643.44523886942460772001. .22310863847225018142861783673497419.P63 513 (1,3,9,19,27,57,171) 144667.1465129.P87 515 (1,5,103) 48111154791914771769582354405627641. .1925631536827398342750945451754630611.P53 517 (1,11,47) 220243.80765938529.635152101298808699. .41941878936097554082013916913.1398877133990750181532404877513.P46 519 (1,3,173) 7348400530773377989289144129092395161857.P64 521 (1) 501203.443418473521.90268296000189649868678102552775904610963.P99 523 (1) 36667531.83207209.129175771.11694270587.58052548129. .62802266052329939.P96 525 (1,3,5,7,15,21,25,35,75,105,175) 3205651.247772800801. .7223591273619001.129266711542799251.2310141222312973778401 527 (1,17,31) 3163.4217.578189648968825099.P120 529 (1,23) 17987.6190092443.8633301049969.P126 531 (1,3,9,59,177) 47065603823663026660218883.P80 533 (1,13,41) 354979.111719734852571.P126 535 (1,5,107) 205441.10155021917057853331411. .431458267304950409618673634079545142558161.P59 537 (1,3,179) 13963.54408841.170018474935706970530240356699.P67 539 (1,7,11,49,77) 12460603.31100269092898119731.P100 541 (1) 86561.59199467.396588707.512917469041.301118908380643. .84163674336698854450433.901912542742250747662095103224539896393.P54 543 (1,3,181) 3259.P105 545 (1,5,109) 1091.861926610031728629577011.P104 547 (1) 1533926272849.11514895455487400649824422273.P124 549 (1,3,9,61,183) 2146261699.37291324871089.165963031279777.P72 551 (1,19,29) 304153.400280563.P138 553 (1,7,79) P142 555 (1,3,5,15,37,111,185) 16975554121.22933014202051.38914392714281976571.P44 557 (1) 4457.124769.P159 559 (1,13,43) 326667346721.12553986510209.101119526079159121. .16404229182321439707977.33715476283025803700130451. .637467768535882654780280209.P36 561 (1,3,11,17,33,51,187) 1123.314161.153356423089. .2056186475270066900583885539731.P47 563 (1) 522114085011580241.74906924194076922022321.P129 565 (1,5,113) 19211.P131 567 (1,3,7,9,21,27,63,81,189) 562873504411.4744655685883.P74 569 (1) 10243.223439473.2058017388830521. .820793700834095033598534000634605722059739038841.P96 571 (1) 9137.73205584889.9640632099001.90794862316027093768853899468313.P112 573 (1,3,191) 8437952161.1063307289553.390527897582929297. .29489362305514321744929966859.P47 575 (1,5,23,25,115) 21851.270332801.1567238401.2299609001. .14807776819440781028664663654371485765148925580001.P52 577 (1) 75011.2796392419.19564699409833266851.P140 579 (1,3,193) 60217.92641.1036411.3497161.769643857. .313705683072406514521.187030532513381403767944747.P38 581 (1,7,83) 18593.219619.52588634980729.P125 583 (1,11,53) 17491.339307.2611841.492915077885080895226946001921.P111 585 (1,3,5,9,13,15,39,45,65,117,195) 1171.65521.26959262851. .43725552532343303477113703251.P40 587 (1) 2769467.13119770765051463547.58304599029582814346174509784\ 805811323612591021863318902938306546239131.P80 589 (1,19,31) 95419.59512561.208431792655914668791053468894512489769379.P109 591 (1,3,197) 8588408897489780521.2054021544734875175323. .171742076613580668857212300403179.P46 593 (1) 1187.62438341552073.6975729612775483517844546731.P134 595 (1,5,7,17,35,85,119) 2087022330866411.692218280897365325531. .165609143561652962744166091.P54 597 (1,3,199) 5153543358319177. .1616721141393989482351447740066663923511303121.P59 599 (1) 366994123.P172 601 (1) 9293424294571360217.P162 603 (1,3,9,67,201) 1460467.533471689.4484273898055819958731.P83 605 (1,5,11,55,121) 11*.715726621375769988310557612811.P102 607 (1) 115331.202769117249.16780869326776069043. .1622949422129340362249.1956783675173062584155810896697.P96 609 (1,3,7,21,29,87,203) 1602776802691.175314482313096251408712577. .17396456098240082242545082771.P35 611 (1,13,47) 821546524439369.36753316833775394448156716611. .38954799470098707550322754822902552371643630493051193.P71 613 (1) 628825424396562847763602356101542430347123271238646163429\ 2714267317577.P115 615 (1,3,5,15,41,123,205) P97 617 (1) 4937.2549322536147. .27507403322030377199658665104409171465823376047109547.P117 619 (1) 1257388159910804265763446600825278256318012249697661907431\ 303034629811311740864601663325811.P96 621 (1,3,9,23,27,69,207) 31051.25069771.1159185064537.5521094269128307. .185541553091188485307.55128155016097727617011127633.P31 623 (1,7,89) 59809.333929.390863971.P141 625 (1,5,25,125) 619324035675566251.232983411264923603130001. .983262166270913562877993411320001.P77 627 (1,3,11,19,33,57,209) 52711923798002218687534164008761. .97816902852991765949068317084025791019.P39 629 (1,17,37) 1259.2998322233.31438035163.1614575158577.335199740796521.P124 631 (1) 8309009.2530111867.4882057097.83188534509828089497. .18715723417348972017502670850275415068812403108132161.P92 633 (1,3,211) 3126092185651464401289035764906947922212259.P85 635 (1,5,127) 85091.431801.141512291.P134 637 (1,7,13,49,91) 225499. .4865853589671044882475767995199294334748858748304194627.P92 639 (1,3,9,71,213) 69779014917427.8970948423964301024591994817.P85 641 (1) 1283.32051.139739.353833.1078163. .73819843823154749726309925820314356063695778208135055585507.P110 643 (1) 1081756861144651.P179 645 (1,3,5,15,43,129,215) 1291.P98 647 (1) 4570409.9021769.932184694939.17280335379957218924978859853\ 0203678893171252012604993715049463781995845099.P95 649 (1,11,59) 72689.5804125093339.851030708304492139579. .248958833227314618649866043. .2025620548964486290862395942912830055105112948209849.P59 651 (1,3,7,21,31,93,217) 3926243469330528571.P90 653 (1) 1307.12550478467.739629398215461986863452049897.1025036797911\ 626106395517257052900895571510278920191436836561586088140307.P82 655 (1,5,131) 104801.4235167121.52900187100851753648745461411. .17208429584639695721394569191520766721.P77 657 (1,3,9,73,219) 6571.17543368071267913387. .229746997821806461949873523193.P78 659 (1) 67219.284689.8639935454794773125522076726425284776822885649969.P139 661 (1) 206233.4611137.14330525250739.36640709883877569115302731. .47125791175530065246394954316793530931317846974648817.P96 663 (1,3,13,17,39,51,221) 8401537.1001115859537.61231726987393. .1139440451841756774164983271590070953.P47 665 (1,5,7,19,35,95,133) 7482637214297894380845818269728205334531.P91 667 (1,23,29) 2784059.25276633.77954721883.13576064376179168742588\ 336277271314106325956544275716656802613527153022519221499.P82 669 (1,3,223) 247531.4340301546362831119363.P107 671 (1,11,61) 4027.48313.150238243. .10315721541618320716857581255209347260612822368454161.P113 673 (1) 1330725593.4061132942857.P181 675 (1,3,5,9,15,25,27,45,75,135,225) 377204851.578348287651. .126274316116265155801.635558882028912657106651.P45 677 (1) 2920579.6190489.4643444189241244139. .569759973030889624117974624560195467. .222155488792293038816414342324245378243.P98 679 (1,7,97) 48372050082931.486136475589650253586227318540449. .209263101129304381417185794914874527112788657.P83 681 (1,3,227) 4419691.4010501617. .2108728466430066008721288692506415323467900073343968942243.P63 683 (1) 1676083.26955961001.P189 685 (1,5,137) 920641.472748641.226338814638851. .236564778812552300459414801. .13166248872913462314441528794261286918041120435881.P60 687 (1,3,229) 779704994617.168813603058115744761. .81514868646704507393379787.P80 689 (1,13,53) 175083169.16181916011. .11938946433963522169904424491139802212517997000669460027011.P112 691 (1) 4668478921.9633758284523287289.5456646931831786367242204139. .53568019129739502623243476233360296971.P114 693 (1,3,7,9,11,21,33,63,77,99,231) P109 695 (1,5,139) 323414081.2444719759493201. .55048545633636680923804388123967583928006647872401.P93 697 (1,17,41) 107339.246739.234292369. .995911976881150379710251245959795777578773753. .1374033378873353068146291032500691255100117563.P84 699 (1,3,233) 9551137.373746913.53590752072775417.P108 701 (1) P211 703 (1,19,37) 151849.9621259.9137976433.P174 705 (1,3,5,15,47,141,235) 29611.2708611.3059396467891.6830705352239611. .421803155659906892289931.667295426465706396181651.P24 707 (1,7,101) 1463491.16729032587.P165 709 (1) 340321.5045586197318561. .1829040306801321759939909767617476342912326200121.P144 711 (1,3,9,79,237) 711001.377460666468258956042387138512734907. .2784647313277751541285980573724799363.P64 713 (1,23,31) 1427.1993292747.22816032820817. .1012570175762265527687179491024662141651.P135 715 (1,5,11,13,55,65,143) 519091.176510711521.166850044395914881. .6918033884710380409642384916290854761.P74 717 (1,3,239) 542487937.4633076102837130131059. .21719294766013521423128159168260255839743617.P70 719 (1) 34513.3138112889.4900402101963269918180361130213343099. .292593798953297307928929576997679978620437591321998775029453439650027.P97 721 (1,7,103) 8248287587. .76648826221799156068752387867047280732512230435080665839048571.P113 723 (1,3,241) 4339.153500131.5957570611.13423215628953313. .985424889624923045657501064259.P77 725 (1,5,25,29,145) 1451.372933190718801.49461103762004289880601. .1161722671658351672809136367089201. .1576422053186621557751857821413401.P62 727 (1) 11633.52068472442119144511578580563. .59803996769241650545074361210286131.P151 729 (1,3,9,27,81,243) 3*.227862073.3110690934667. .216892513252489863991753.1102099161075964924744009.P78 731 (1,17,43) 15316934231051174801. .15797542906128411931089923981198031035849.P144 733 (1) 396485324677401403.6032100214690846655623731769. .15044222650915986784475012020785853019343366205331.P126 735 (1,3,5,7,15,21,35,49,105,147,245) 5881.P98 737 (1,11,67) 3556355492892313.4992970772475256746973191595676275\ 1258933207272739486748238351859309991348433.P107 739 (1) 33407751111787921302306812882603339179.P185 741 (1,3,13,19,39,57,247) 1483.19267.P123 743 (1) 22291.4343579.6562222067.P203 745 (1,5,149) 2639421761.2113854074762921.8022560553172024220348389258622531. .51383124543331398511394411970333527291.P83 747 (1,3,9,83,249) 354854881.30495765703115017. .29004089048751837082775014755957683255977.P83 749 (1,7,107) 1499. .1067740385407532831676124118528135895750892746743123583547.P132 751 (1) 274867.1904313481544215427026507238828703275939640783750698129. .122269977610153309000355351658957538156537442215013457649.P110 753 (1,3,251) 1307209.10212446539.95741909371.P124 755 (1,5,151) 54361.28992001.33673001.204764382884291.P147 757 (1) 417817067.P219 759 (1,3,11,23,33,69,253) 10627.4036363.44261191624217967508561. .83730859983591586460452561.P74 761 (1) 1523.1485778288798957523.32888267877547582651. .59133619649645058522941873. .1891134139996867428902217085790800258704289.P120 763 (1,7,109) 17958105295747.747090793047295291603.P162 765 (1,3,5,9,15,17,45,51,85,153,255) 1531.6121. .33141833204828142196706150379164851.P75 767 (1,13,59) 10739.42953.1103294219. .66213049032039895442657530073798459769131.P152 769 (1) 36913.77836643.86369467.9401836358059.602141772875227166401.P177 771 (1,3,257) 831139.158530119801167697937. .10414600656781734361640396674583500992745231074293966400432773827.P65 773 (1) 533371.1737639742639254060437861521344464381695829802369522859.23206\ 316220078396404383777135534261928387046186611079662143434527093563.P102 775 (1,5,25,31,155) 4651.282519050251.2641147407325991861958417450\ 80394055656413965435249440593413845572793896725379051.P86 777 (1,3,7,21,37,111,259) P130 779 (1,19,41) 384827.17315878129048863927974905480696448369723747\ 093035498799994851681384411684778961025249.P127 781 (1,11,71) P211 783 (1,3,9,27,29,87,261) 12745935523. .44367700674110561467213850972770293767462491307345678065875601.P80 785 (1,5,157) 1571.25121.6412853401.P171 787 (1) 942827.5405369360996178738798259049. .44773841130192799148039136997839721.17290649624589612553204\ 17417955691339162974743882218922830411737050563040937.P93 789 (1,3,263) 255944062723386721566481.P135 791 (1,7,113) 54112378027. .1621080768750408973059704415815994507256956989913429764153.P135 793 (1,13,61) 50753.2864285210191809465583254126794859170149406203.P167 795 (1,3,5,15,53,159,265) 8088331.381199321.107814999632867521. .746485083287310097651.P72 797 (1) 875107.105670649433473243107529297593. .3716911716373158932595690775277458436562439413950537497. .721081346319803014103048601140804555897014469307122160867977.P91 799 (1,17,47) 119851.16993492187603.81778526159866851701654313293617. .8448107186210108056552572445522236629028051871109419691994271\ 732195271255522257.P93 801 (1,3,9,89,267) 264331.3441291221723107683457. .36045123652756854086648245551969409.P98 803 (1,11,73) 11243.214863145125509028597735617.P187 805 (1,5,7,23,35,115,161) 33035981768945891. .18883360229126539123965611847358657506356995001231479438139229721.P78 807 (1,3,269) 11299.369345192417701052571. .18630342702315826557199328264881.466047024627224480211076768171369.P73 809 (1) 1619.14563.19417.601897.39595205804249.P213 811 (1) 7102927740195899.762653049249738822648895115723. .13035351601359930701387351505224798208350150169097.P149 813 (1,3,271) 450403.88760231089.897186516077633497. .11170585420277403973061107961387073788895978930714757404139.P71 815 (1,5,163) 6521.11411.148331.P183 817 (1,19,43) 15840460057.P218 819 (1,3,7,9,13,21,39,63,91,117,273) 11467.13503673.P119 821 (1) 6569.1037866321911576169081957409.P216 823 (1) 316033.13615553872073.16550408839468877734177795421330292670601\ 1776596326713780562632126238280022902380359311132880309166125996273.P122 825 (1,3,5,11,15,25,33,55,75,165,275) 10006979401. .65966684197384718027476767451.P82 827 (1) 69787377067722881486602094502761253930262932578924438539.P193 829 (1) 131147801.3154069493397876555121.2751096190869286949881816932924433. .7446182219444384839739645725961979800147.P147 831 (1,3,277) 9710343080872158664398414924796646767744190877182055\ 80112757800346489383481.P92 833 (1,7,17,49,119) 1667.3724291295188700915891629715833142711857\ 5448479451910316141843224837062312908422864387566510155203.P102 835 (1,5,167) P201 837 (1,3,9,27,31,93,279) 258451922773648099179883.P140 839 (1) 1377062372371126895706481139.P225 841 (1,29) 114377.2492918387059.26042075463217140565804312036553.P196 843 (1,3,281) 28383811.7317767583121. .1165121220595973490028272789835616165757454893337.P101 845 (1,5,13,65,169) 6761.103091.108161.367082334680413807808582241279931. .42156379589779912226383108151000450094080783333678881.P89 847 (1,7,11,77,121) 59359043484951383441635753. .1629399896606002450068005313617654570814500081.P128 849 (1,3,283) 6793. .125247878746743543692481610705995992666697711316774071921529.P107 851 (1,23,37) 542939.12985283780501700403. .604367679922143570622653720534643264325088703722918681771377\ 012408526538323960466739317375681.P121 853 (1) 2465171.7155452470451.14343826193517763. .353820133707093639564050227200635816139539208825409146646160\ 09343887731347839468592930021200199529033.P121 855 (1,3,5,9,15,19,45,57,95,171,285) 6841.198098371. .23241389572585939528171.1175622349673189452424511749302390882321.P57 857 (1) 252182368360125289180898199073630970779. .553004924366546858573851495377436601050694641.P175 859 (1) 4045891.267946153.72068132891.136341146513223571362444340\ 00510378993646341182529301330876828151332807560015763251.P151 861 (1,3,7,21,41,123,287) 10388827.20958338017.78390786811. .4423364633142650480377.11306831838018220372427161. .32215327209835441806959889495947251.P35 863 (1) 535070645969.176177196937327118084628312251. .605471410378222574753949751873375051. .1020169266060477773800580920702507013464523497.P138 865 (1,5,173) 29923811.60313752055701307811411.3205853408074298683\ 566650869570798974094347365546830062745393897406012552557721.P99 867 (1,3,17,51,289) 679015215511191577.5913950382316342222561.P125 869 (1,11,79) 15643.27809.140779.13412539689160203716832768498829\ 5528535837335675424728712327063077028670312366648778721.P136 871 (1,13,67) 9168220907.2085976638755288150171.57604499880518482364227. .136202831651126186404748956578551589361900494227.P138 873 (1,3,9,97,291) 1747.22699.921446320166308603. .435350962502860533102854399065360163787224236964302573321.P92 875 (1,5,7,25,35,125,175) 558251.10022251. .511937190014372102141784257057292201840312001.P124 877 (1) 29819.42355831233323.18969179136276645172100272388219. .5493451945310865752349090299716764102827. .210871403712301056076129015652067535919402324273.P128 879 (1,3,293) 42193.P172 881 (1) 22907.58147.70481.149771.42295049. .2045616510088708944258113057143343272186985194817. .1174806445233057737347738680015012445081063982168447003222031523.P127 883 (1) 21193.294923.4675171089162696937.P237 885 (1,3,5,15,59,177,295) 516266521.873791632531.2354488203481.P107 887 (1) 5323.2607411387302489.118667786561338086904896542913501309901939. .499816891503601098167567459797810918801392823017537640227814\ 06685533122634863077113.P124 889 (1,7,127) 19901547974019072445900746812468273. .23105068079006744574164595960708060074392947703954994281.P139 891 (1,3,9,11,27,33,81,99,297) 7129.352246478761.620617419930817. .1409033313878253109224688819.236552624101029630306294196057.P76 893 (1,19,47) 1787.1513038588606647037924377544619001786660891.P204 895 (1,5,179) 14321.121721.145560017652641.10430557104202241. .5070463106922154841.1678434450877307861649130441. .298360269108491443679449696455011.P97 897 (1,3,13,23,39,69,299) 21529.258337.66354530124557299. .31735484991529375057.8437649245385270023387.P91 899 (1,29,31) 21577.69948188740643.127802493095470979. .575087607870890436346963910799123377.P182 901 (1,17,53) 105108859.P243 903 (1,3,7,21,43,129,301) 5757529.7243867. .378717376673487267097266291431316313.P103 905 (1,5,181) 127002291721.225290221737294291262043529758363468748214801. .2048815180215513463388335576071214168229077677858641809231081.P102 907 (1) 8156908781432775187914049.292694927386576695497498001026561.P216 909 (1,3,9,101,303) 9091.11312395373674587455280184557176229738187. .7566725580973124820814763156483276883350707.P94 911 (1) 830833.346637323.P260 913 (1,11,83) 2389059505456889.8731063958440403558435843670164528\ 7298311883547857842552027735626889821792854421963.P149 915 (1,3,5,15,61,183,305) 19895761.3015049441.288842216366491. .68207639734963563361372213456131836731.P76 917 (1,7,131) P235 919 (1) 14968673.2014093267.4317704341862180531. .185245489299285834957735107.P215 921 (1,3,307) 24365977.31992843313.2695130084238939067916140102205\ 3934190564918041065033739735051719011989829339.P91 923 (1,13,71) 434284416496884393040841315444206695459788549436182\ 739707934576370088748201819201184526862364134150497353667.P146 925 (1,5,25,37,185) 19129880176716856111400208466987206311982190690\ 2329171022067040679355100505963917404335406035751995698400401.P110 927 (1,3,9,103,309) 61339736467.395125276559977.11372732144384815780057.P137 929 (1) 8243947.3706175321483.389593452245969.489624750530873. .152118805170622193260551601681.8082308165748527072282228058900817.P168 931 (1,7,19,49,133) 5684313601.420502918802525203. .5714479757812584606479198276300869021129. .283339363176938747172116939877499444692266312387.P113 933 (1,3,311) 1867.121291.194897580917406265505585947535435763750785971. .12343567541333276505756188308377528186062869621904858161.P80 935 (1,5,11,17,55,85,187) 7481.22441.192611.4942411.96162881.P165 937 (1) 1431737.20795779.40172939.1961075885814321323. .2007828853899141769868082345131291.P209 939 (1,3,313) 35534561977.2492985246309625270804406373331.P148 941 (1) 1738969.5062155107501579.1053336016261649316809.P240 943 (1,23,41) 1484493554507.28554501136089979495033. .1112321273705537423158810077602360080577. .18216825757346323511608206491538778004307592723.P146 945 (1,3,5,7,9,15,21,27,35,45,63,105,135,189,315) 69931. .535027074087349862035936711342201.P93 947 (1) 7577.13259.91254170041.212341461377.881206290008086216099. .23016485461806757328483. .22975205222554546114010145307351411496025395212488281695009106987.P147 949 (1,13,73) 182209.42598203337. .148981801408086220612250112121769028190033463041602172331.25887227\ 540110145470037301654397281295032383902862252725338537413646289417.P115 951 (1,3,317) 1480727923.40740225338758415715380694619267076907012248419. .23485336884993035537508465029538304720630597755230435218099.P77 953 (1) 1907.425796183929.1624700279478894385598779655842584377. .3802306738549441324432139091271828121. .128064886830166671444802576129115872060027.338849583746672139\ 4368393204672181522815830368604993048084925840555281177.P86 955 (1,5,191) 2766037497160081. .19354275048153085260502985763801078164890953285078303467480611. .389587965550275961948342205696835219385141732512376219939998\ 66030334910251.P79 957 (1,3,11,29,33,87,319) 246907.2398243.143241922561. .3106925099920735897.P128 959 (1,7,137) 1726201.14590250979416323.29446854121733451929.P204 961 (1,31) 12787096753.845740940776943899258211.22340510647512915642585947. .173358852321881774082560487367455990875736173100402581895739236563. .5093162625592280955742647104714519124174227701950032852997184\ 21722649.P87 963 (1,3,9,107,321) 3156148413859611691.P174 965 (1,5,193) 1931.30881.37420771.5725218872819272688156683843001.P186 967 (1) 440953.103340834172163133609939997710360109744851837737.P238 969 (1,3,17,19,51,57,323) 1932620113.79573173764374544116669686940\ 8579753808434853619248646462116510258956449467.P90 971 (1) 495211.3019967621847401.745797773625002825025979. .2491229639091384610638595922517649613788649.P205 973 (1,7,139) 15569.490393.1738265567571623156365340866047578896250851.P198 975 (1,3,5,13,15,25,39,65,75,195,325) 386263879315103401. .136676778088193015037036862018432177034334500891572775415001.P68 977 (1) 7817.728843.7128193.9524716048809932689.P259 979 (1,11,89) 39161.585443.3828171544278297271775556079821758549779\ 5172169893828456847577035633016304956490069518329961563502131.P155 981 (1,3,9,109,327) 17659.295188787.96761365841467. .7033152327596719250318908599746971900855487469187.P120 983 (1) 880060241.6692446515577.450533013876830977899721147965761959561. .329276132908821678528577196635914994570945533667966264584925\ 0000278679100602318030777.P151 985 (1,5,197) 1512961.42136857550241.259101467678452891. .1212008606838635171.5004132468697940487346607403971.P151 987 (1,3,7,21,47,141,329) 5135123689810129.51548005944477448439636\ 19802983305243869440153396482199500404535444787331.P78 989 (1,23,43) 1979.49451.14407753.197443880998681. .2170889903172149784433591904243422267029143271211852851697320\ 633141555998779.333575229705691461627499256575785607633057660\ 0797223086186301588124373064443403.P96 991 (1) 3060209.5819153.3122895040527689387017. .7785692962749707974896202971851600869561. .117629529942758313311719273856832197673938841177863540264141\ 636175964038817.P150 993 (1,3,331) 1987.25819.75904445347. .65967064596937923731173645567055969095918106670911362489824961.P119 995 (1,5,199) P239 997 (1) 614153.27557081.531600259812123283363670434553975990301742\ 4645419351309189390398619467386821680502554654552190638909683.P184 999 (1,3,9,27,37,111,333) 23977.5814899281.97377658867. .241947707873451279499.P150 1001 (1,7,11,13,77,91,143) 66067. .331883508195873627260832855090645610599917875793. .60529516200616105171088617241489496035731520539907.P115 1003 (1,17,59) 21014857.P273 1005 (1,3,5,15,67,201,335) 14908171.P152 1007 (1,19,53) 169177.37531047483598542373552845362558526956969699.P234 1009 (1) 962587.39865023275343572161.9950355017715631542984016422092411. .897737413129878491558669073093664931129644710928191312540354\ 532326425133547133152959937943844040075121657347.P136 1011 (1,3,337) 37760873163247728235828372169734753939.156328003631315\ 433775143682027215046287257098236131785117207420819974245386219.P88 1013 (1) 2027.14284942415590523.2022033791466488360947.P264 1015 (1,5,7,29,35,145,203) 6091.316681.395851.4936961. .118310908116219234147550210872300654121. .134148838212903456989907164771379816790203241.P99 1017 (1,3,9,113,339) 146449.457651.28876407885213594067.32970289831896516\ 515377359350891813314051432116962729751027253442614469329074028387.P90 1019 (1) 31309721343425737972332358633. .25635519446772000001672716581008683772756347784565439577. .185753031137449464964458189283915511966460303037518072473610\ 12829098628485113.P147 1021 (1) 10211.18379.441073.63145268487193.2116429105836954764874673. .695060280235636196787387625147. .128282030910562421027269444708594948489455456059.P178 1023 (1,3,11,31,33,93,341) 6679688731. .809412655973078797084604039087771314939.P132 1025 (1,5,25,41,205) 4036451.142958801.1243595348645401. .26815123266670488105926669652266381711401. .17126056102276085634179513584247448901133853840451.P122 1027 (1,13,79) 6163.16433.14983931.23908561.419502198233. .6500198488452063592176409. .841892514867338002160398496020953232282846916283952780815948\ 7707104885851.P151 1029 (1,3,7,21,49,147,343) 8233.36892437056956699. .17008283446306740920401868978031815852569.P117 1031 (1) 79445908023117847711350146066567930257.P272 1033 (1) 24651922299337.12366664051937762461361289279871201655390521. .238132890471076527482146856632147796013432762707487534686\ 9097098713143166668320618736388741839374771.P155 1035 (1,3,5,9,15,23,45,69,115,207,345) 211104810001. .697174543237430742710277767082091045949449114019397091.P94 1037 (1,17,61) 23889800393.615240811219. .10248563168155938511565636891320807996797917433834229566763. .576904946787881315789206960481293072280918923178098376489576\ 703807883.P141 1039 (1) 155851.762642847088874611.15029302019723991462779685090903481.P256 1041 (1,3,347) 2083.14865481.7791024427430986498793899.10202290352\ 1696172102859278404984457883972697707674972945944479058403.P106 1043 (1,7,149) 17747689. .344415631298605320882953207779152104402244124702979210591304547.P198 1045 (1,5,11,19,55,95,209) 6613335467116613731.21654734961841342681. .302830601299346947201.P158 1047 (1,3,349) 24474001921.P200 1049 (1) 2099.1779522099931.24132756641778030091. .767749587188080891246822731496641644423848612695929371145177219. .262005883892527771477955853704993008279480748371752330510357\ 88338368468743990037732513623794905331698179.P115 1051 (1) 26015176530521.234166918021181298229848923411137491270809. .2985705340255877974384457755217875800152021182151468875486121347.P198 1053 (1,3,9,13,27,39,81,117,351) 10166476786129.93961711110587347.P166 1055 (1,5,211) 101281.348172262235082314625724718585320038392641. .3900999267245732823560868781735451333653187761.P161 1057 (1,7,151) 3295470541240024674475168432175459422963. .4543644491752924043185978130604407410476457.P189 1059 (1,3,353) 3286329043.117598477011619. .83787479610878510956478965630065403939.P151 1061 (1) 3428736325987808713.P301 1063 (1) 114584129081.26210488518118323164267329859. .17741533157924995125899275101326305383306635886833319913902\ 54645758278991890748315142078623195802744233104331.P172 1065 (1,3,5,15,71,213,355) 2131.67531050720249264044979244321. .160525888079920212258843748245804191445670399750291.P87 1067 (1,11,97) 8537.25705142292017.4282346827889826334464447699353. .124509068177730497137955074932069263215796834147290774388201\ 28846251329594583361100445492666170068269073831242059691963.P124 1069 (1) 7681945177.27793430506131075606692275603032027848987.P271 1071 (1,3,7,9,17,21,51,63,119,153,357) 6427.17137.119953.1340000929. .49697164752429114523. .1078825191548640568143407841173742460493739682993.P84 1073 (1,29,37) 34149299.723179476352802400636953428399129.P264 1075 (1,5,25,43,215) 6451.32251.1377607797987845739996109415156901605851. .295956655933104379149886667823386447502604395021652806928264\ 85106182235243621108846098278924201.P111 1077 (1,3,359) 25742490619.61965231619.489719099073327823465690986241.P165 1079 (1,13,83) 110059.28066418320592174976920728908193. .205183258648060416868923029306545601244648400434625944325351\ 863083008476846405914448131.P174 1081 (1,23,47) 1399100926820497.1729444049094495656521.P269 1083 (1,3,19,57,361) 2062835090323897.P191 1085 (1,5,7,31,35,155,217) 8661202066255932951384006504098700443470054187488056580001. .153324493619416764902227532669212014081062899163967552854225491.P97 1087 (1) 121398914459.59015046142680340633.144288053938906556201. .1096221689473668741885320079498807903080025340837128557919390251.P213 1089 (1,3,9,11,33,99,121,363) 2779129.P193 1091 (1) 4176767728322304092689. C307 1093 (1) 306041.149076457.P315 1095 (1,3,5,15,73,219,365) 3241201.5665531.1005823201.24375654323161. .75585758834018224531. .8395287354754937404878748093233887467947014370925681.P66 1097 (1) 1237417.993889927170673797197063676220796827. C288 1099 (1,7,157) 116615439604018153.719246910720211929911689. .186347963875290244607785015115115186185151460498163342326993.148065\ 68375728710096623707890651810091015219665579650500660012329525041.P112 1101 (1,3,367) 28627. .790733219452662288382621159905246080699151689474115231936204\ 86700648001.P146 1103 (1) 227219.20354222567550187.23531055927158473. .172634405376546547951628091436445763552227. .3340501686106326394219512125837051888087730290345881. .13520591921723351390517614914853244718598372616482921. .2743174108485910757889889842155126774297492294034389387804606\ 7425448793.P79 1105 (1,5,13,17,65,85,221) 44201. .653182304411316461972398177939790632491565608971.P179 1107 (1,3,9,27,41,123,369) 369560523547. .750910719017526169366384570149938609387931210817.P158 1109 (1) 314468041.4498094107721.114707191763959751382208987. .112985563755005263987526248018869431962485492728920337098962673.C225 1111 (1,11,101) 15120619254845707358936819. .359846976075630863007498752386627.P244 1113 (1,3,7,21,53,159,371) 90972169.7400606817397019353. .141071637344220059145065488837648909131968604721.P114 1115 (1,5,223) 382557003061241.31614634268217232957104662728817202\ 39483479402846095145474459949190169764413700807058659632361.P160 1117 (1) 70533063399945787.P319 1119 (1,3,373) 326208643.30155506036528513.2004012469328558425127565863902\ 7356795005997983166503259002925748843101252000415087461577089005691.P102 1121 (1,19,59) 2243.6088599401.58142098448088409. .359071640268582342735956401.P258 1123 (1) C338 1125 (1,3,5,9,15,25,45,75,125,225,375) 9001.11251.130147868251. .2104496060760001.1911491848228371127909236272251. .19939338707834433467107535745725657572743352610488782001.P61 1127 (1,7,23,49,161) 7736786575986931. .19322013444181029485042759893019522147. .47617582389002276776695575579779608028732467346177427237400427.P164 1129 (1) 5297035427. C330 1131 (1,3,13,29,39,87,377) 61318393206415264609. .862129909267689232423274352672765463729913497. .97969783896578766950463988989150801833252065245907311942438154123.P73 1133 (1,11,103) 2267.12945659.180611154488432693831795119603606124267. .222303826658577113353781003441443593559006324096917107954423\ 77261577.P192 1135 (1,5,227) 7025651.685467361.1046622091.6156694758084075792273361. .417175025408198479194142506235824722338320481947446263039558\ 99162057891381791481.P144 1137 (1,3,379) 36967896067692174895186731445885654925399550043.564114666698\ 255235115889687610418969645397536395150976531625094017243548780441.P104 1139 (1,17,67) 195090954822051707. .67287821449693070372895357014126417403959115084746851.C248 1141 (1,7,163) 18257.301870128784337.1200893348906161. .722526146028558523.17060613539298460913312913761.P213 1143 (1,3,9,127,381) 2576323.2061165716371. .9403580927289288953072692831494040201. .6535371089593651808167292821036140071174282019283.P124 1145 (1,5,229) 406225165149481.73563032256320682421346570851. .3762270397244577165640826633613851.P198 1147 (1,31,37) 305771849. C317 1149 (1,3,383) P231 1151 (1) 9209.264731.7183639052011.8057089084163503088491. .3043392259206870967482500082233986390424278957322258801584514334307.C236 1153 (1) 27673.3772896236651.1815221738378898021554747. C306 1155 (1,3,5,7,11,15,21,33,35,55,77,105,165,231,385) 9241.18481. .113571560808091. .928267859145048237228203439064060384235841167452667731.P69 1157 (1,13,89) 6202223372363094929452168980151819917315301830721. .2180008318627749177958475122877459942097368668735292520114598633345\ 908414653401720690084471032887791572936263634345643106246594978513.P137 1159 (1,19,61) 117466969. C318 1161 (1,3,9,27,43,129,387) 2779191397441.2871028850691129078587978917059\ 17880320362291211398518571239342998599690848163865371401808988833.P120 1163 (1) 59301371.10534255862017.116877740332519011737292886104457. C297 1165 (1,5,233) 179411.9813961. .583249810553621464231615722549327708629068174660691. .516984841825342421683264151608720182193150487231588398646839\ 94806674255960601.P140 1167 (1,3,389) 9337.97484277202003.45908592787319236096963. .936622732283266044834451024147. .3938368118355873575102129530416312021153911608699.P115 1169 (1,7,167) 2339.37409.161323.14608351671572807850092203. .8414160072705585053393085689. .23740978495305899888391704714669253618912353.P191 1171 (1) 25763.84313.P343 1173 (1,3,17,23,51,69,391) 236947.647674297.4080494539544536849. .15477225584568935651447216741685456162338995027. .352820376398397979265099331984513647290394257293220676543507835019.P68 1175 (1,5,25,47,235) 185651. .5153918554170795319759034290830504069736767291196886851. .4650384055791287715318612314019533732871786340821784227432051601.P154 1177 (1,11,107) 49504078597120643.166419727156424727241892848411. .18086003974039700834773047458500121168169812493765139.P222 1179 (1,3,9,131,393) 25939.82531. .358481631294404888613030634349490904280996785041660793. .175639552585373358307268617903286656284026269783398738412720155379.P107 1181 (1) 49603.59051.11403737.67685946763. .9186599509882727262279760862379532536049.P288 1183 (1,7,13,91,169) 18256533429955747955939. .267627241354177936155295311412461883212860098720373553358351\ 65168735371346267111892557776252075837003.P160 1185 (1,3,5,15,79,237,395) 2371.18859377449506801.P169 1187 (1) 626523937064728884681163. C334 1189 (1,29,41) 28537.306763.9758744379744403.P312 1191 (1,3,397) 1819849.43247593.64339323043.427329609001. .66809564696120553953329. .37021310507568514045709078753457472746397308843224255251382376361.P115 1193 (1) 324497.6132176836553. .3830133035529809005604118596180719845719114907654979.P289 1195 (1,5,239) 184087361.1476292474364321072638637843510554375995931. .5007861129737749849013925511829197666405121545507799101441.20042\ 71471420615598848683888548534424549010888354230261495981227043481.P110 1197 (1,3,7,9,19,21,57,63,133,171,399) 778051.1697347.P183 1199 (1,11,109) 447252559596639611.298257415638476586139. .794144907494779140961.1996742176615621275047178653063503969.P230 1201 (1) 1924003.2983620281.12227544337.107117096323. .710910143031679452050648532487518850677152269136533878913283.P265 1203 (1,3,401) P241 1205 (1,5,241) 23049241. .249131275404729139275839472969899930024630479961641.C232 1207 (1,17,71) 1015135159838323.3850085253314696881. .19386715163145854741507626199579.P273 1209 (1,3,13,31,39,93,403) 29017.43139539.77803987. .606420756938919036293334377580837334241954547365081690675900\ 71525369.P129 1211 (1,7,173) 58780455620284414376363105246593. .2723152052646845975712782486855365259098683521. .450883186269134249964766015681562947901093411513.P186 1213 (1) 1809697712203883.4827522415574830043.3777892251034479160417. .4927122961739010211937166971.C282 1215 (1,3,5,9,15,27,45,81,135,243,405) 54595521268291.7317109576021321. .4118408687411658054091.508921134248025317532282604291.P115 1217 (1) 41556581584859030984269154611961743619460332939.P320 1219 (1,23,53) 2186437897728086451778484714057.P315 1221 (1,3,11,33,37,111,407) 158731.989011.25631233. .482645325313503025981502216185653048991666620039628706089414\ 415640986221463013553.P118 1223 (1) 594379.7309035684842414944321. .68985116517993086161521463731317536484675563. .14284698176007813051039186143044751965811053936987756845816446201699.C230 1225 (1,5,7,25,35,49,175,245) 5387708103524891201. .27874420794178105304819717062001.P203 1227 (1,3,409) 2422099.36083859815030113. .2177633069850626664151734850035450616186796885814091783969604377. .1307879417126412826192929340241678921311511558317618436861609\ 87542840998049.P86 1229 (1) 2459.14921458432448378147396639454902301142300229903851.P317 1231 (1) 5680156935617. C358 1233 (1,3,9,137,411) 2467.453759531730831495724142631449950368405723. .271838690363933210241084381681447888858375859. .15044791318037026238169386216404775315987652932738833.P105 1235 (1,5,13,19,65,95,247) 7261801.444017081. .860228271135820240631552893481411. .8408151819993901660322569030307566961351971.P169 1237 (1) 19793.20100446998287218674699817095771. .10051655137687975879415699639722354859.P300 1239 (1,3,7,21,59,177,413) .359931645741056789631351742091222797125100809698191524292297. .616118417295048578293181955408006300135730334724584315102344777.P88 1241 (1,17,73) 69497.7353977369.200409698947654675332283. .1587270753424607766885764505731.C279 1243 (1,11,113) 2095699.1847201975664739.8162288746998299. .54422452078335550357549271959156307009. .99149420989103955160104612344769640777. .1427190154348758577463048684519738593219.P185 1245 (1,3,5,15,83,249,415) 52291.23491533621481. .70816756557871433816484601.P154 1247 (1,29,43) 77369128473070697.244677788770544273.12659727766698640577. .26748155488299460055590417618630601.P267 1249 (1) 42467.42456043268907753482642746969704178387. C334 1251 (1,3,9,139,417) .104550704372792883541043569577081727068987699486120393537587.P191 1253 (1,7,179) 32579.12479881.4480918457.4059601388172111433.P282 1255 (1,5,251) 143499211.1330129321. .1677043099910557077945803381443326364651.P245 1257 (1,3,419) 20113.5501285641.2155087459317166459. .292428094739132929741513244710611083563101534177825755897027\ 537501772075738091.P142 1259 (1) C379 1261 (1,13,97) 25571706135457.73763414723376088026310008245531. C302 1263 (1,3,421) 334639213291.1157691342224455071488341309913851. .239225235836952866057924877133502443434512337253336555372669\ 048486051772478758864009435466688009729.P111 1265 (1,5,11,23,55,115,253) 2531.16123691.P255 1267 (1,7,181) 33560297.28839634749383740426523.P296 1269 (1,3,9,27,47,141,423) 2539.8919953281. .12411417364574583679997770272311296704971577433. .231040241459039762810316977965440508233433892245267.P140 1271 (1,31,41) 411057250299010549488282116052932379073775618969. C314 1273 (1,19,67) 1326467.165613358312950064754563. C329 1275 (1,3,5,15,17,25,51,75,85,255,425) 93748201.155245018683330451. .4229815106556286351075051.4308204827941820023589554231419463051.P107 1277 (1) 888793.3432577.179945878564767547.2113601438322189019.P336 1279 (1) 706009.3107971.18970768920015252259.115217370846302143114697. .728012485667587623793883.P306 1281 (1,3,7,21,61,183,427) 23059.51241.99889819.616898857. .1157682023025313436817704340503504329. .86993214891586468024427579155688177045163877212649627.P102 1283 (1) 7699.614532189347. C371 1285 (1,5,257) 1441771.67548618131. C292 1287 (1,3,9,11,13,33,39,99,117,143,429) 7723.882883. .65851026290472988947469257924231828019269601. .5325537259736914639383576920781597593249222547570749857.P109 1289 (1) 2579.23203.30937.152189128667.2350390995481050368133101725609. C334 1291 (1) 28403.16981242584548819.40397701481598169. .20160790854725168608079143216009. .2028519999628439233287004349186690347.C284 1293 (1,3,431) 43963.33775747.2785099025023674408523. .2872188207377461771538665660896328005417433.P183 1295 (1,5,7,35,37,185,259) 390960945481.413080055666248475387722988636881. .1297011327466713096225068755289464647661446011. .21948435716309838454791940755133614083294130821081.P122 1297 (1) 155752053019.34114611149007864568966039210767469802327543299529.C330 1299 (1,3,433) 37523786929. .4822992600871742981082926534686812585706582976299874869531. .159756465177863772236815273065082317831476327207632682914291\ 1033633901606896389239980878267.P102 1301 (1) 18216252210539.15826129842694553. .871261283739006918793648516169148264947. .158538524646017900250810607995506380920082613411.C276 1303 (1) 53204563686868873577. .6198807295354576621851096919606790761126838017.C327 1305 (1,3,5,9,15,29,45,87,145,261,435) 13639037851.48864576601. .939295277281.3631552852976685500491. .158255906921112793238217616051.401397533418591922013367690331.P90 1307 (1) 10457.505997209.23667487979.1548495552766487875851817. .4875919167997703293411221963257893393. .5441659548352349760995815362340374980187801249995490417358747.P249 1309 (1,7,11,17,77,119,187) 765396162077779.8468599653787962071923.P253 1311 (1,3,19,23,57,69,437) 3904521800431950367453781323. C211 1313 (1,13,101) 244219.140577659. .9345661021690061106417607254853134479922777879784044948563.C290 1315 (1,5,263) C316 1317 (1,3,439) 13171. C260 1319 (1) 11142913.741565793503625917030973189850113. C357 1321 (1) 102725010187. C387 1323 (1,3,7,9,21,27,49,63,147,189,441) 2112396604782913. .7663270724502130178281.54449262695187486887704032213433. .272385472057700356020722534315683777.P124 1325 (1,5,25,53,265) C314 1327 (1) 7963. C396 1329 (1,3,443) 2659.116953.209982001.10922032987.280213628444768563. .739958949028739597407277169403625991967546315186763299. .971067660157706610437419457041030139114830748980225784336879113.P106 1331 (1,11,121) 1064801.P359 1333 (1,31,43) 1597199693194341332199398401.387882887153753354785052164073. .113934357751155814648904597492884718274847307.P279 1335 (1,3,5,15,89,267,445) 8011.7911205809612159841.486548992201880277\ 217833963724620318785338475627986456933701844986335126278640131.P109 1337 (1,7,191) 6545953.21976358411681597603.6158177809630705149646380131. .47209878926634886145808261378167884931. .177154622571860747467737151767010340250646836072137. .68782964345849210316656365543393286774395091861425819.P149 1339 (1,13,103) 7709177347. .8162180074270503321335519514675588347763269562159249504179.P301 1341 (1,3,9,149,447) 2683.369515233.5517444206275621757281.P234 1343 (1,17,79) 8059.18803. C368 1345 (1,5,269) 2679241. C317 1347 (1,3,449) C270 1349 (1,19,71) 2699.13689459054475670977741385063031707. .229255396247029955050947439811944013696396843.C298 1351 (1,7,193) 242396463233. C336 1353 (1,3,11,33,41,123,451) 2707.292249.295151539.1853547763. .52330372958162093186633571859. .5496307170451271548550041724892688009120029972254637091.P131 1355 (1,5,271) 1225482800739172641891601. .99154551628565107821346226327642742190364891.C258 1357 (1,23,59) 781633.18316787.41383073.24110014570655700403. .39545919851678025221192750465371. .34963123856135244678143953310498486257.C275 1359 (1,3,9,151,453) 29301273076611979. .8206895416798339210492228818633778567626761003105899135855291. .248747590248775635621689301885566289902894629667169263884874\ 761556011.P126 1361 (1) 10889.1276619.510799633.47547456507398171003. .333274607480679903990927142361666942714809. .2475841403501249120394990947990782147180417. .273063954218055265333034936479363611974302732876184897.C234 1363 (1,29,47) 19332793.1919221219.7964481353230123.187617535068488069953.C336 1365 (1,3,5,7,13,15,21,35,39,65,91,105,195,273,455) 35491.436801.2511601. .4663895387971. .307125743850143133483913160596928028514251505520546641.P91 1367 (1) 688969.83671337.12898178131.18101258329085891. C371 1369 (1,37) 547313788615883.11523488587105507. .688408207595429676061727757577539753316133668163. .42312517840752150334067623868470433911721535795659.C273 1371 (1,3,457) 65721651425737.206053451562433.27077051603318402060798923. .3469404838721564949151103171597889236998228963.P176 1373 (1) 810098767097.542204060920476295985452379. C375 1375 (1,5,11,25,55,125,275) 55001.31775887001.32592148446001. .2714019277637251.C257 1377 (1,3,9,17,27,51,81,153,459) 47601775286199731239147. .1076257311574336004425336864714385556453735643.P193 1379 (1,7,197) 4057019.159244643740412457739. C328 1381 (1) 14147533469161.113738319658736238418567892099. .2108932257668078812302329481992437152109096266553.C325 1383 (1,3,461) 266152819.46589140363.151773161107.642040844209. .22774258944240211.17013825717475216558081. .123982521747024050840923.12883657694705235752060229918961.P143 1385 (1,5,277) 3098422646515321.18954673356763044685182371. .4150752976422134998698211601561.C262 1387 (1,19,73) 14668142459117517676637603. .31468486590867461800836388667587.C334 1389 (1,3,463) 487719571.87208386525532626311037206064574878098449. C229 1391 (1,13,107) 180137367961349059.602097092517317008121572219. .617557073219231014175028802485017.C307 1393 (1,7,199) 256313.1368560238473.11330553673168339. .3289969796136070205317374419. .57163295951034451899579310266706609258494395563988575843.C241 1395 (1,3,5,9,15,31,45,93,155,279,465) 6811602936864841. .2176837988940791506441.108939274676766775151668441. .2256732484957168249162885692372088688664522871846923765621\ 571302806767247131.P79 1397 (1,11,127) 38314813592677405354365631291375300139. .33276105604005889302938997033988500026041898371.C296 1399 (1) 33577.2997043588920134984472587. C392 1401 (1,3,467) 2803.1818499.13628929.14259522003187. .169362185418201731843151010177. .2912031603565957550911594293490706267210714521. .15821607357985128488076411812222061077825609698597903502073\ 012198043651.P106 1403 (1,23,61) 8419.660533517639289904327791350546169. .4293891872287900315459210182165137.C328 1405 (1,5,281) 43667401.P330 1407 (1,3,7,21,67,201,469) 905550421700611.9187310017086827306899. .2500687075627595659723921374427793529624523075057.P153 1409 (1) 2819.121331538019146127595011121161387. C389 1411 (1,17,83) 42331.204610868107.26547728321683. .3954126775419855404772116265158369.890707048717838845674268005438314033. .3753640895282069907281579977557091889156379263323.P248 1413 (1,3,9,157,471) 405740620675382376539580253467060080179.P244 1415 (1,5,283) 11321.12324078836075554184590673081. .147760168722381548345968375756228907471260681. .360877403289367388748781954459955342833200811.C219 1417 (1,13,109) 2803463651.28889343049318360649. .506440460076644299164281057539863983172316568782153.C311 1419 (1,3,11,33,43,129,473) P253 1421 (1,7,29,49,203) 2843.2802958225638718627796887824397276031089. .293164921245346012759170161524756839839111329. .4029208313832481481143451623067247504863024402428753.C216 1423 (1) 112804057.16986794977.577678113814125809. C392 1425 (1,3,5,15,19,25,57,75,95,285,475) 2851.14251.151051. .5843517465218365487981080489788596889855399196998180292651.P147 1427 (1) 693523.5628089.731608372748801729113. .82718003338869891126095447587.C367 1429 (1) 1548733385688649.189354052714377739.2963477307064181408971. .11485943839018053479863036296614076404887447123. .290618710244745246524600481486713498170575911214462111652368\ 89497476421553.P257 1431 (1,3,9,27,53,159,477) 125929.97909761259.3711679750840771. .11338558054762111611140089.579684634422257831326927911007684052759137. .531127638527594620768675457397215229736466780735541870780510\ 913496107511516491.P106 1433 (1) C431 1435 (1,5,7,35,41,205,287) 203771.543024560681. .714908060219675989825758320025177708575041.C230 1437 (1,3,479) 152181510259.6562877964161669320933556865428491.P243 1439 (1) 20147.448969.5640881.137253021484417.63180494870190538956091. .751979368522107343300643.2408869127973305483719946359217514790113633539. .544975758281808131044300018470837520689015348998003.C260 1441 (1,11,131) 23057.5128925363.222159202911713.20480669195104009. C347 1443 (1,3,13,37,39,111,481) 507937.12453017851.139330013375598664958587.P222 1445 (1,5,17,85,289) 354429601.4715936681.302366166736211. .10245148601520066233751956853483648115748723702066388521.C240 1447 (1) 1238047460871066723939449.P412 1449 (1,3,7,9,21,23,63,69,161,207,483) 614377.14562451. .112835246823427691067335230264201.P194 1451 (1) 8707.14626081. C426 1453 (1) 52447489.P430 1455 (1,3,5,15,97,291,485) 24675197278121881.46389348212414164191076651. .9814755701787619050438447228245871433467284173653935983161219\ 8144949068356907214597037953121.P98 1457 (1,31,47) C416 1459 (1) 3538966647017366178930789720372963502043.P400 1461 (1,3,487) 1054843.P287 1463 (1,7,11,19,77,133,209) 8779.20483.43891.196043.205390571.553139819. .1388208944123.4209792311709490418051357246571485713.P241 1465 (1,5,293) 175955291.1755093252481.460582595816216641. .31062872124540581292691906293211.6762588977493594654927865733933851.C249 1467 (1,3,9,163,489) 196579.2720408869459.P275 1469 (1,13,113) 2939.4816921513.561423233684977.20194053813501320920441.C355 1471 (1) 87238974742151728369. C423 1473 (1,3,491) 583676251.153585785929.2022422312674273. C260 1475 (1,5,25,59,295) 35401.2627165860570505819131669414543051. .311395455907833141960100590679232110278209368621116805113251.C252 1477 (1,7,211) 85667.1940779.3169643.277311030109681. .890687378102544171550823070637020886520217937. .5318748637151540102530551399675619764952990608569.P254 1479 (1,3,17,29,51,87,493) 305616262027.2134763311450490207689.P237 1481 (1) 2963.145139.758273.317552480411.8830204633638259. .278646852930400784448242149780769465498850096808741459. .224047106670990562087604482083126041630763232761979826873.P294 1483 (1) 31994243.1111108114646495282502321422339. C409 1485 (1,3,5,9,11,15,27,33,45,55,99,135,165,297,495) 26731.641521. .5506106288631885091.P188 1487 (1) 321193.5112307.336634730815895563864259673163375963317776707. .764306661921531071005607460370828744036933756498403.C340 1489 (1) 12344417513.98860422229961209. C421 1491 (1,3,7,21,71,213,497) 23857.4735417.15330402361. .4406091499279396488314377129.P204 1493 (1) 14084963. .63739949319742773463257379389332588250573971146689081077662043.P381 1495 (1,5,13,23,65,115,299) 14751372316704213236801. .141998787657583801252851679089742008091.C258 1497 (1,3,499) C300 1499 (1) 44971.2143571.958241747.353669333641009. .6783744570276099702542784604601.29170128974784420528168967798403.C354 Table 2LM Factorizations of 2^n+1, n=4k-2, n<3000 n Prime Factors 2 5 6 (2) 13 10L (2) 5* M 41 14L 113 M (2) 29 18L (6) 37 M (2) 109 22L (2) 397 M 2113 26L (2) 1613 M 53.157 30L (6,10M) 61 M (2,10L) 1321 34L 137.953 M (2) 26317 38L (2) 229.457 M 525313 42L (2,14M) 14449 M (6,14L) 1429 46L 277.30269 M (2) 1013.1657 50L (10M) 101.8101 M (2,10L) 5*.268501 54L (2,18M) 246241 M (6,18L) 279073 58L (2) 107367629 M 536903681 62L 5581.384773 M (2) 8681.49477 66L (6,22M) 312709 M (2,22L) 4327489 70L (2,10L,14M) 47392381 M (10M,14L) 7416361 74L (2) 149.184481113 M 593.231769777 78L (6,26M) 13*.313.1249 M (2,26L) 3121.21841 82L 181549.12112549 M (2) 10169.43249589 86L (2) 1759217765581 M 173.101653.500177 90L (2,10L,18M,30M) 181.54001 M (6,10M,18L,30L) 29247661 94L 140737471578113 M (2) 3761.7484047069 98L (14L) 4981857697937 M (2,14M) 197.19707683773 102L (2,34M) 409.3061.13669 M (6,34L) 1326700741 106L (2) 1801439824104653 M 15358129.586477649 110L (10M,22M) 415878438361 M (2,10L,22L) 3630105520141 114L (6,38M) 131101.160969 M (2,38L) 275415303169 118L (2) 1181.3541.157649.174877 M 5521693.104399276341 122L (2) 733.1709.368140581013 M 3456749.667055378149 126L (6,14L,18L,42M) 118750098349 M (2,14M,18M,42L) 40388473189 130L (10M,26M) 108140989558681 M (2,10L,26L) 521.51481.34110701 134L (2) 269.42875177.2559066073 M 15152453.9739278030221 138L (2,46M) 70334392823809 M (6,46L) 5415624023749 142L 4999465853.472287102421 M (2) 569.148587949.5585522857 146L 9444732965601851473921 M (2) 293.9929.649301712182209 150L (2,10L,30M,50M) 63901.13334701 M (6,10M,30L,50L) 1201.1182468601 154L (2,14M,22L) 869467061.3019242689 M (14L,22M) 8317.76096559910757 158L 604462909806215075725313 M (2) 317.381364611866507317969 162L (6,18L,54M) 3618757.4977454861 M (2,18M,54L) 106979941.168410989 166L (2) 13063537.148067197374074653 M 997.46202197673.209957719973 170L (2,10L,34M) 1021.4421.550801.23650061 M (10M,34L) 7226904352843746841 174L (6,58M) 22170214192500421 M (2,58L) 349.29581.27920807689 178L 1069.579017791994999956106149 M (2) 123794003928545064364330189 182L (2,14M,26L) 1093.1093.8861085190774909 M (14L,26M) 4733.556338525912325157 186L (2,62M) 4611545283086450689 M (6,62L) 373.951088215727633 190L (10M,38M) 761.2416923620660807201 M (2,10L,38L) 54721.276696631250953741 194L 389.4657.4959325597.17637260034881 M (2) 3881.5821.3555339061.394563864677 198L (2,18M,22L,66M) 42373.15975607282273 M (6,18L,22M,66L) 235621.8463901912489 202L (2) 9491060093.53425037363873248657 M 809.5218735279937.600503817460697 206L 41201.520379897.473000157711296729 M (2) 17325013.117070097457656623005977 210L (6,10M,14L,30L,42M,70M) 1041815865690181 M (2,10L,14M,30M,42L,70L) 421.146919792181 214L (2) 857.37866809061660057264219253397 M 843589.8174912477117.23528569104401 218L (2) 74323515777853.1746518852140345553 M 5669.666184021.171857646012809566969 222L (6,74M) 1453030298001690873541 M (2,74L) 3109.1398316729.4345052821 226L 10384593717069655112945804582584321 M (2) 58309.2362153.15079116213901326178369 230L (2,10L,46M) 461.5981.359006912765190408181 M (10M,46L) 15096281.1021622741.7834788541 234L (2,18M,26L,78M) 7489.370244405487013669 M (6,18L,26M,78L) 21061.348661.1112388285061 238L (14L,34L) 2381.42841.823481.536296539263941 M (2,14M,34M) 9521.18292898984156916156396101 242L (22M) 3389.91961.4036962584010807014809213 M (2,22L) 1339272539833668386958920468400193 246L (2,82M) 802333429.6027043735173469 M (6,82L) 2953.125965976976392564317 250L (2,10L,50M) 5*.28001.96001.94291866932171243501 M (10M,50L) 7001.3775501.47970133603445383501 254L 509.26417.140385293.90133566917913517709497 M (2) 18797.72118729.2792688414613.8988357880501 258L (6,86M) 5951631966296685834686149 M (2,86L) 17029.46957.96758771543686753 262L (2) 642811237.2745098189.308544695409769427309 M 269665073.810791440841.12450751815271172041 266L (2,14M,38L) 1597.449329386292232535250647435097 M (14L,38M) 2129.126848469231149.679253585011429 270L (6,10M,18L,30L,54M,90M) 541.49681.165041853060421 M (2,10L,18M,30M,54L,90L) 30241.166242935471754241 274L 189061.921525707911840587390617330886362701 M (2) 168434085820849.206875670104957744917147613 278L (2) 1408349.15736774913.492717674609.12763660054721 M 557.1251163891299967635860272509229764287909 282L (2,94M) 1129.1768141.54865357.180846660913 M (6,94L) 5641.270097268484167653999069 286L (22M,26M) 958673.661521349351105339668937661297 M (2,22L,26L) 25741.3426853.9467173.4170165570896115649 290L (10M,58M) 168781.12004541501954811085302214141 M (2,10L,58L) 17401.244716883381.3902095192430070721 294L (2,14M,42L,98M) 540961.40544859693521152369 M (6,14L,42M,98L) 17059410504738323992180849 298L (2) 12961064789.11011808951971745915313242336927641 M 1789.14641916303149.27243386602395588437243602121 302L 2854495385411919762116496381035264358442074113 M (2) 4373689270176379261201.130530323901899210670077 306L (6,18L,34L,102M) 2582029.4260133.12458723489217613 M (2,18M,34M,102L) 613.318194713.238495197879143209 310L (2,10L,62M) 37201.87421.52597081.24865899693834809641 M (10M,62L) 8973817381.57805828745692758010628581 314L (2) 2790467761.5941035366826969.2203942033439148343973 M 182687704666362864775461208552445184771578920961 318L (6,106M) 207973.30007459254393181618012897 M (2,106L) 10177.7971862004867103303293462593 322L (14L,46L) 3221.169373.209160253.27037028118448801270021 M (2,14M,46M) 1933.298817.115927640417.179351574736387915177 326L (2) 653.9781.7807049.4826612561.9716134201585679932947173 M 11692013098647223345629483497433542615764159168513 330L (2,10L,22L,30M,66M,110M) 661.3301.8581.12127627350301 M (6,10M,22M,30L,66L,110L) 391249826881.13379250952981 334L 187072209578355573530071639244871112681892570202113 M (2) 75005713.27395325377910797.18208260781190156536114609 338L (26M) 677.615946323850313.215656329382891550920192462661 M (2,26L) 180201997.1259036730797.408946876729703992293841657 342L (2,18M,38L,114M) 4598533.41435606371227835355919073 M (6,18L,38M,114L) 25309.5675149.39291697.99463730244517 346L (2) 13625405957.175739665310505752968877740350313227534889 M 7152893721041.1673815085186574700322174232069942181681 350L (10M,14L,50L,70M) 701.2430065924693517198550322751963101 M (2,10L,14M,50M,70L) 1038213793447841940908293355871461401 354L (6,118M) 709.12037.2995240087117909078735942093 M (2,118L) 31153.5397793.94789873.20847858316750657 358L (2) 31815461.416115013830990336221.11575709336636595278866333 M 1301260549.588850381287433028279084110474400181861465037 362L (2) 9413.178925762979037.3830538323149121.95016376135553173181 M 28739737348957.106646454159157789533685339377679881781493 366L (6,122M) 5080081.4209508589941.19125556519918081 M (2,122L) 12836737570021.414194958733796530899181 370L (10M,74M) 1392776941.4964166554103541.1258710725115650761 M (2,10L,74L) 29246281.567471221.4299881834172078350686174001 374L (2,22L,34M) 26509131221.35155077044989397.4029292065629191839853 M (22M,34L) 5237.551353793.1819762572673.135322045917118601273437 378L (2,14M,18M,42L,54L,126M) 757.456376431053626339473533320957 M (6,14L,18L,42M,54M,126L) 304832756195865229284807891468769 382L 25212001.5972216269.20844252715379252090938485003447004944677 M (2) 3821.89618875387061.1833085153842665442652283234165143433597 386L 773.635283689603233836449.25564774360363212740382247547878573 M (2) 3089.148997.14402030644704405877.378791300027089635677652285973 390L (2,10L,26L,30M,78M,130M) 2341.723447661.8925278993793241 M (6,10M,26M,30L,78L,130L) 468781.720453772427518446437641 394L (2) 4729.1079423677.152874915601.51480369709170501304394118553664009 M 52009.3862163385805798697201354795194661512726441364448411929 398L 797.1008116715344410461444141839610180239223178503751442552629 M (2) 76554648784441.2099073106303095025303885460879717918033130293 402L (6,134M) 3217.192961.214473433.71848008781.175132692529 M (2,134L) 10453.132661.15704900959651293774270521395753 406L (2,14M,58L) 29*.28474083676894571496726280348891354240661831606009 M (14L,58M) 9810958633253.21597468549493958664902504331670645757 410L (2,10L,82M) 61213422340181.76401557052661070266405340180269721 M (10M,82L) 41*.821.269896441.82777720757144341.758399801407611361 414L (6,18L,46L,138M) 829.853669.26785337149.496817081109150685921 M (2,18M,46M,138L) 3313.18217.318781.6542857.25395382141805460457 418L (22M,38M) 8857714771093.3066290411598855013.27290812893120485231161 M (2,22L,38L) 6689.2039731321.149832750683283097.1937385241416564065603093 422L (2) 95110361.6920400848110359047653995057624941367485834954585997077 M 18455044087121.178325724886188112393573476458482965256782477560753 426L (2,142M) 266677.1396429.18369973.40524027877.20111008087273 M (6,142L) 853.189997.2646185328486854129693169911139349 430L (10M,86M) 129001.1131832377932535124189124787988905860893840561 M (2,10L,86L) 370661.1952201.4538991421.260125854015641.1401345270171101 434L (14L,62L) 867988564747274927163124868127898657976489313137639569 M (2,14M,62M) 31249.776729668507005203702993.139335546032913681584758997 438L (2,146M) 877.1013533.704710824913.142406868765525436670617 M (6,146L) 371335727233.18478609113710122023550126425157 442L (2,26L,34M) 6670914925963435577.2380142106509122200127345885819001687213 M (26M,34L) 1210509821.2291059412513.1118498440898880562062959177194663477 446L 95768689.52016435676012089.2705981985587527191852752325795076108854553 M (2) 11597.6530333.6912010464887165201.P37 450L (6,10M,18L,30L,50L,90M,150M) 413150254353901.3192261504216112476901 M (2,10L,18M,30M,50M,90L,150L) 695701.307116398490301.6269989892198401 454L (2) 4565795412500725128240734773.P40 M 5449.83132849.694512857.5661492593.P39 458L (2) 2749.5523481.84948746297.6211454306149.P35 M 602633653.33074236421.44185520789894155033573.P27 462L (6,14L,22M,42M,66L,154M) P37 M (2,14M,22L,42L,66M,154L) P36 466L 30757.15576974348063186977.25336594975374725568037.P25 M (2) 3108221.P63 470L (2,10L,94M) 941.894434441.3357909154141.38425816980821.722501809616926841 M (10M,94L) 87255998201.3237811125343321.P29 474L (2,158M) 151681.P43 M (6,158L) 18890331057055511701.P28 478L P72 M (2) 77852679293.P61 482L P73 M (2) 2640397.15594629.76119208744309.P45 486L (2,18M,54L,162M) 3333950193493.P37 M (6,18L,54M,162L) 2917.4861.26129603777437.P29 490L (2,10L,14M,70L,98M) 306178659371201.1372226516822701.P22 M (10M,14L,70M,98L) 7439220181.P41 494L (26M,38M) 515737.P60 M (2,26L,38L) 104729.2638949.531455155350809.P40 498L (6,166M) 136453.218166829.41732461753.5791487405427228378717709 M (2,166L) 1993.80485166514184335373.P27 502L (2) 1912621.57762875981.1972386557777.38508212572597.P32 M 5021.45063180240128066017730357.P47 506L (2,22L,46M) 6994042018866541.P51 M (22M,46L) 25301.109297.756550961.2569737193.9623862953. .156296877661.101027360307659633 510L (6,10M,30L,34L,102M,170M) 51001.2949879781.611787251461.15455023589221 M (2,10L,30M,34M,102L,170L) 15571321.P31 514L 22988734297.P68 M (2) 28564009.360197837.P61 518L (2,14M,74L) 2035259884744589189.P48 M (14L,74M) 6217.P61 522L (2,18M,58L,174M) P51 M (6,18L,58M,174L) 7309.P47 526L 43195464658778477.80181854738775471107692957.P37 M (2) 119929.731141.99972364781.P57 530L (10M,106M) 1061.3181.P56 M (2,10L,106L) 51941.24082141.31213331016701.P38 534L (2,178M) 3401264941.11221454641.P35 M (6,178L) 2137.928574737.P41 538L (2) 2153.3229.5381.4273873.1633401082697.3918695179304214327885157.P27 M 8609.122575221550682354302309961053.P48 542L 10474693.104167755499168696693743867494211841.P40 M (2) 97561.P76 546L (6,14L,26M,42M,78L,182M) 503413.467811806281.P27 M (2,14M,26L,42L,78M,182L) 1948129.P37 550L (2,10L,22L,50M,110M) 12101.35201.698617420601.18735216413769901.P24 M (10M,22M,50L,110L) 1905911178138824081520901.P37 554L (2) 1109.987879984327104437.P62 M 232681.98002601.1093620377.4343215646437.365883785511434081.P31 558L (6,18L,62L,186M) 1117.140617.P47 M (2,18M,62M,186L) 775844757937.P43 562L 91568909.P77 M (2) 3373.3827221.58381440973934522510444290213069.P43 566L (2) P85 M P86 570L (2,10L,30M,38L,114M,190M) 185821.247381.3996146881.P23 M (6,10M,30L,38M,114L,190L) 1457772869697961.P29 574L (14L,82L) 2297.16073.P65 M (2,14M,82M) 10333.3839331472313.17160693383233.P43 578L (34L) 7698961.21886549.113478990853.P57 M (2,34M) 936361.854096275589539341506608949.P49 582L (2,194M) 580837.856752889.P44 M (6,194L) 7570390327211773.69186562412120809.3687531861438052950582913 586L (2) 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.96943448874943589381509.P106 M (2,566L) 526381.2212378537.113620361303857.P142 1702L (2,46M,74L) 450395984739049729770917.P216 M (46L,74M) 3466225121.P229 1706L (2) 3413.64007056091437.1122047772459197542365557. .3670300973252073917081977.P191 M 57568727236201.937587543847010098806915822685030796385013454\ 77111757084835445364585650547909966405317.P158 1710L (6,10M,18L,30L,38M,90M,114L,190L,342M,570M) 110017981.848129221.P113 M (2,10L,18M,30M,38L,90L,114M,190M,342L,570L) P131 1714L 4702664630197.6871169125116761.8859671727690991421. .51158163991710264101.418776549422296498000441747335941365\ 220337506509873715826682868941035656862557.P114 M (2) 7490495630917903672489.1112610919806658266406382986993. .37254915681318275345339031340236801161. .1318415567213047203957952355470806576099575135763692557207429133.P105 1718L (2) 82488053.160783317963711097.952726149509730887818838732155323\ 484612668093856064167532290013159068113382035709074696638988493.P137 M 41233.18970157.161362916688885847263044877441415342126713555601. .50502611599893781608144090581941158712628324395186051374828\ 143142567262734004258455433198877.P108 1722L (2,14M,42L,82M,246L,574M) 2675989.P138 M (6,14L,42M,82L,246M,574L) 44773.82657. .11226524876408775073143033704082858121.P99 1726L 62137.7682681449.12118208029.7636302550869852997. .261898355200719007555285556541005219163157219718093295275151\ 374201626261386879153026036019757345519977621973.P109 M (2) 12268162909.4190110941193.41734812223623741861146169997. .46619255366962328167412700221.406766837212504479804114509779153. .4111798002954124877183397050601213755485272497.P101 1730L (10M,346M) 13841.94672594940509124602676510531741226575772518341.P156 M (2,10L,346L) 3461.297197052517429014237901. .155239988274216593089164596199061.P149 1734L (2,34M,102L,578M) 3469.38149.113908630435024549328114941768055\ 22322333679313892091082261899485723141.P86 M (6,34L,102M,578L) 83233.67133458080301.15286531841496313. 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9680947148544871316724730371874319205828789.P166 M (2) 9908497304929.3070352086706435689.49095821424025567310477891\ 55420015004986440007315047013238013867071758911999704295804153.P146 1766L (2) 3533.10597. .3261059187758456326028842534373884666172227240471097372442752\ 0447587686470581538316932773960545621248352363865216668947669.P137 M 9642835106981.21853773066679313.1397997900714226472761369661333. .959346768167962592178969793334891965611038761087167937. .1576370469903203279973040031491663414039828010968075560583660537453.P87 1770L (2,10L,30M,118L,354M,590M) 941641.112688376490130041. .13958078871765695340080761.P91 M (6,10M,30L,118M,354L,590L) P141 1774L 1982764321.9982363219299701755701813517. .2047754087000820349297809443743844453329. .13231286310635194760975216003886759010777.P151 M (2) 12067954321.154247171201.246306661383223563619590775949. .85857888382221611460390939427343597417208649286614911619554\ 66153791457137752011916061530957936111325777.P113 1778L (14L,254L) 394717.2901290617. .47053600640208033059241039730284317814777697416570061157789.P154 M (2,14M,254M) 3557.430277.28402945481. .399127051193796660679495799296414893620857762153.P161 1782L (2,18M,22L,54L,66M,162M,198L,594M) 120726937.212140766502632881. .126076291066677670603478850918204428036903440615477.P88 M (6,18L,22M,54M,66L,162L,198M,594L) 2170477.168518034037. .9055086119440404402246938172507702666506358169.P100 1786L (2,38L,94M) 3639869.999648574070171124601432769. .497403465856372009446461144453.111758423615256944193654963749427567569. .255421441882647036358581067782818217129321401. .1039334208152531253984710089202456757484571009.P59 M (38M,94L) 646109108522520037.55737216228051297161494379261805713.P197 1790L (10M,358M) 3581.811893881.4272700190724544357721. .682862187512541058734549287082001.P147 M (2,10L,358L) 94622981.9818823675183373550041. .671277176269260334004380493401.193681916538846719019638927\ 14982770557580416135048970358822297421560269501.P82 1794L (6,26M,46L,78L,138M,598M) 7177.P156 M (2,26L,46M,78M,138L,598L) 10684568857. .23631648482124605019194916705352421056228717976627497383497516329.P84 1798L (2,58L,62M) 7193.3617439859037.8713454341549.109097329238284141. .10037707648366959104221367390220295456323321675691617775263793.P146 M (58M,62L) 5886653.20723877457.43875868248089. .39574364572001586424595746349. .20078157941325448552726597857286724672278298773354024889. .28183159528202006640644774197553266657727056730280860177273146261.P74 1802L (2,34M,106L) 11747392973.91102528862545665457.P221 M (34L,106M) 174044748410668549457.224201551150113268933.P210 1806L (6,14L,42M,86M,258L,602M) 3613.9467360568830697495500595457. .45757320478618895747604607889547060541.P83 M (2,14M,42L,86L,258M,602L) 44619686161. .1340323540048991459950036430548177848438612466385636277313.P84 1810L (10M,362M) 1422661.10371301.62984381.2841546437106680644141. .100673282665910769164456015319401.P142 M (2,10L,362L) 4779887821.284960538160486454165307301. .1486018607888551051882493975787406621.P145 1814L (2) 36684968468392674349.267301538121080056247956934369.P224 M 2856279634519890658989627576084877545889. .150363045435340850101124199800576704201622268478219656542817\ 66712685048209161956773047433686967961.P137 1818L (2,18M,202L,606M) 938089.215403913.54459411697.P156 M (6,18L,202M,606L) 3637.11239182354817.89718779799289.P151 1822L 109321.42514235518096149015446235113. .89978339781600142665771163471628742033256933.474942339376\ 967475871960321762614254290810243038880418971061342256529.P128 M (2) 29153.1916488563293658474734971283197920626016404111748763973. .329091793708460842702539959507807954770541370427958294973972\ 8413840230442675105647517.P131 1826L (22M,166M) 10957.457905185813813.9118425814963735020084050069. .758984045239765414366290480154514089. .34334644886182446546273008924242084634327089789559771215864092254849.P97 M (2,22L,166L) 437342857760433461.31722291643604475850861201188341. .2440105053710133005468894317569383122715715757.P153 1830L (2,10L,30M,122L,366M,610M) 1712881. .209286094074580318288344692937218868614221.P97 M (6,10M,30L,122M,366L,610L) 61*.358681.602914116781. .2397096504835438921.89135366684453039762936076301.P79 1834L (2,14M,262L) 18341.73361.106373.337457.602481460214341. .6274647569487659758609838486398097882441.P161 M (14L,262M) 55021.11142479091341921.96578697208818436822981. .730039745374219638260113.37447027901314381254512721318017. .639745584291728863751658159947413.P103 1838L 15174529.1508449364353.2550464750317206279127335468202671973\ 7706843601365012267412584539895809.P187 M (2) 3677.169097.2703022685717.1071847300685268733. .2456774736627079417449898904657.P207 1842L (6,614M) 2903157652807014132222997.P160 M (2,614L) 14737.202621.670489.1924167937.20277440672157064961857.P138 1846L (2,26L,142M) 38286041. .115348882808768103727966010464756713847867950693181. .847283519989720607062916820262627951738307864893708962563963\ 505727965829307811179121799293289.P103 M (26M,142L) 13837693811900871607717600062424369. .1064448662217171715112211943132259502103349.P177 1850L (2,10L,50M,74L,370M) 3701.133886258536001.590663067860911343898701. .866200444503307218246408516520037907601.P137 M (10M,50L,74M,370L) 3760458001.9312718358338301.P192 1854L (6,18L,206L,618M) 401841732395629.10017165502306460200391243108137.P139 M (2,18M,206M,618L) 3709.7417.93097809073. .15697920117275073486338469567634384633.P129 1858L 11149.319577.551019709753.4609832458707079151039619761. .1020789673987483714669438485415945837.P195 M (2) 7433.85469.858397.P265 1862L (2,14M,38L,98M,266L) 4639388993.22772885633.114089637061.157174\ 865300767843375890901132435882321373073606235638707142302548601.P129 M (14L,38M,98L,266M) 11173.305308285699010909667092737518511389\ 9385295772199261164849220870247146206163484209.P142 1866L (2,622M) 3733.17962117.204082834247639533. .2867134239058725077444870925351109. .171787846178241745388291751687545359135893624733.P79 M (6,622L) 14929.31582002281292084633680717617.P154 1870L (10M,22M,34L,110L,170M,374M) 706960763753201.1401057665370661\ 25746313600841958315665446964121520594965672179547776243001.P105 M (2,10L,22L,34M,110M,170L,374L) 621939445387014541452289913176\ 1458777613670215064545164232042823638688079791503414057101.P105 1874L 546289747242387833.102338449889938893229. .22617049281426900090402043630190397588751804536661. .951768280390198849437937441741045105223893751904359405793181\ 164094516800710581484437.P111 M (2) 802073.30214971197129.524704862656309.108215387436410988313.P228 1878L (2,626M) 3651421693.153204659721481575760771776889.P150 M (6,626L) 120193.23208500533.484894051077157.479542202751565609741. .21514288711632793647440840947984309.P103 1882L (2) 3383837.25359946237.20793657827081209534512961080066477973.P229 M 1070913479895698609.6960982604145481063390741994425851833890468577.P220 1886L (46L,82L) 112410858169.36368413831997333.P237 M (2,46M,82M) 2784254414828346243382561. .234355755109811973087400958676098128093617121853664147218053.P182 1890L (6,10M,14L,18L,30L,42M,54M,70M,90M,126L,210L,270L,378M,630M) 7561. .457381.2143261.596526861195233662750200340726624395569101.P73 M (2,10L,14M,18M,30M,42L,54L,70L,90L,126M,210M,270M,378L,630L) 43887888187572165151544641.53557082595126165043094157045628806518641.P64 1894L (2) 189401.1440383213.8204616582857089246514152381.P243 M 6522937.272279643245537.8211191052325823017421025141068065597. .655341555405650612626073800652021748125098494390741048073748370101. .2531565034117848702019541217816904577156867272261301642375052\ 4674576379201.P88 1898L (2,26L,146M) 10390402230053.185571869124044164853371079021. .173877200781227262398070456350934785465483296270434727066645\ 8148244905882718982615243630813765301702039726469.P110 M (26M,146L) 3797.42986079427420364272922707125401632867398311590467\ 2752759934946637902289195084453935770289753315761645531011443281.P143 1902L (6,634M) 2892776771209447770340654201.P163 M (2,634L) 15217.31877128189.778680603097.3488331309973. .27069571592372896954201.P130 1906L 20405494957.P277 M (2) 2809306768001. .4578126188307204994619025825781999498172935052056303961035393495045\ 1990074990279258034704799907168753403494722916566061747810395209597.P141 1910L (2,10L,382M) 1443961.92459281.P216 M (10M,382L) 57301.864189637596221.301039635955941955416398544601. .326398981556503075347304776946455039476016705049583268175841.P120 1914L (2,22L,58L,66M,174M,638M) 840440400036193222729. .1085449968759125093329919224369. .1585333835462829231438151788148865056453.P78 M (6,22M,58M,66L,174L,638L) 15313.128702300026396839312134788487\ 540516275576912037945715656114023588618314007407601.P85 1918L (14L,274L) 7673.609014465221.5055546728233. .13143270612909056636088570135286832260591916100581.P168 M (2,14M,274M) 168388835672177.85143663903559418012479935784296\ 6372517930496405920800298104669795974262532867778670086801.P142 1922L (62L) 1137450670721.2184269724947805073. .1208889346570157870280450820286251695464031997.P205 M (2,62M) 252792973.864219613.948729953.37541358506075478258236735332361. .64570584168627945448109624328792927541. .172172545512925790802497530112596705980073.P144 1926L (2,18M,214L,642M) P192 M (6,18L,214M,642L) 3853.40087784364999735271516000990223904435\ 7801832970765839337907513540064872417.P114 1930L (2,10L,386M) 1246781.1608921341.3568553151401081. .5955623568140770033895876543735621.P168 M (10M,386L) 232492081623941.8392710322562681.33204775580652808331192\ 547762225872772387856364639830983746266203935325902374656582399581.P112 1934L 328781.12056557.P279 M (2) 47054221. .42396868586636966702183526209689128167397708948769403704697. .139738207874855695977570801372531414365776297457766995595845\ 304657737604850816108844083792144857340697.P123 1938L (6,34L,38M,102M,114L,646M) 3877.19381.1279081. .12774353393983945521795713234563738297. .16750182073211230556310395420299476529.P86 M (2,34M,38L,102L,114M,646L) 926282517007889243128982867521. .3648011488087216916950150682966398143704581.P101 1942L (2) 5877612181049269.6917838004568007880938360151147285081.P239 M 19421.2297056072966211443783453841711264148118601231493081743861. .16607171956665075111068728726736021321605538143765712369658881. .6180690167170075559902788794529340099720410500986413317631662\ 70749930649988915817.P89 1946L (2,14M,278L) 38921.87632273.92220941.44849676017189. .2684356809244885929794686184069. .4046624378398002211307594382075047504065028449. .907147414295234719242629807565546337688011292303997378516999456233.P74 M (14L,278M) 218561316364553.5970040190584505056822221383735565\ 626854005594779498873876095314397744521005855810197.P150 1950L (6,10M,26M,30L,50L,78L,130L,150M,390M,650M) 24457095001.P134 M (2,10L,26L,30M,50M,78M,130M,150L,390L,650L) 45984901. .1131816004801.108792457407671701.P108 1954L 36716449417.415313933724293297909.P263 M (2) 639290688796013570647966059083967057010003673137. .355888005084964948682956905273633375230381246915047451599454\ 53522748980652438417.P167 1958L (2,22L,178M) 10984381.1749046157.12769069589. .8540463790853686106162888141.P211 M (22M,178L) 3917.4135297.21467513.57717951413.290857646356157.P222 1962L (2,18M,218L,654M) 109*.17951056093.669657070334773.P168 M (6,18L,218M,654L) 49346313013.1388612680921. .561070572288256277136602810062157316007570131157641589.P119 1966L 43644426217789.1431746688753709.P268 M (2) 155837128987432356781.1366175048897551662825186361. .1323103760614147332897213698137697413.P212 1970L (10M,394M) 15761.35461.2214281.464568607149275146234181. .581887899470864922007450289381.560059099594809870298212276\ 7082360646452452022320819501080021874378141.P98 M (2,10L,394L) P237 1974L (2,14M,42L,94M,282L,658M) 57174937.28860857283150817.P142 M (6,14L,42M,94L,282M,658L) 61706836445096809.P150 1978L (2,46M,86L) 7876397. .2566447003922918738251749244586951049379997165853621152456210701.P209 M (46L,86M) 439771371096041.35049840713898433. .46336564105264156931219140569625359563486333. .11369308667009289972811369899416497441702608089.P157 1982L 47569.702972273668806189.24108966487910875313. .44229415926893141209.113447996363645096441.P217 M (2) 27749.63488677307778109.16825619625747922745475011329. .137232949773414165157899958850047768180405868649152096213159\ 20708241487922289153309232433334016888421.P149 1986L (6,662M) 13302229.25430936011753.31614476989231029379232557. .68905970337561183437462555868709.3973921258176323056321508940165661. .1314098716175595483898139799716487493.P51 M (2,662L) 183625814209.1018768450523377.74519189014953913. .18989372631177034732892899753.465177286996430226160539394957. .617680057559525522778680709413533.P66 1990L (2,10L,398M) 250741.319615746499777361243372158059093611895932550\ 1324570526400274738986155572480635187898763713197906567258456681.P126 M (10M,398L) 23198204725672081034655436981. .36016148355139711248940080869144201. .51913169750493963694908106795607369470833233378003772874313441.P114 1994L (2) 3989.23929.1316041.7905228953.450516200430246120721. .149156643181299310192264307577506850757.P217 M P301 1998L (6,18L,54M,74M,222L,666M) 72354413161.1222553230560433. .5735551460378502198796512243143473. .5497368458116180193233404694623299228824873.P93 M (2,18M,54L,74L,222M,666L) 10126001691430741.382598228266336189. .799915581937561681389258889697499905881. .49801579402999682758116547403787291213389808169.P76 2002L (14L,22M,26M,154M,182M,286L) 20021.1849849.690545857. .41080280592351540541.9215194846651389888428137. .3969862289663363742872134096701517. .13628840986604456625675621031891749568696694946387077.P68 M (2,14M,22L,26L,154L,182L,286M) 8009.12039884736627749. .41636988047270830322971733927822632217478358515946454949740\ 3163906905405115093829688640802010933.P101 2006L (2,34M,118L) 13868109346932001493749981709288184217585361.P237 M (34L,118M) 4013. .807476644894045961070719672444963420767289734419381656839660\ 7257403958619007953734583427507987430864649678033392732713.P158 2010L (2,10L,30M,134L,402M,670M) 1161781.43714589671758035101. .7202139206809052400714203227736498330521.P93 M (6,10M,30L,134M,402L,670L) 4021.655261.13154273408381894504101.P129 2014L (38M,106M) 23704361089.2345207504177.44598149829737613346817.P237 M (2,38L,106L) 2211373.2743400324920929934072747900058453.P243 2018L 12109.1291942943772106529500099325194662891337468227487983754043873. .827263279310402907822197687118025843556513383068776273960213\ 8175797184758615420805231424676072580342225956599281.P128 M (2) 242161.952957298276617. .1816911194189728629517731150999807102074709889. .2438761703367040254939792237710514481803568093234395807837721.P178 2022L (2,674M) 8089.3546589.2922737792281.3181075216261429729586653.P156 M (6,674L) 737267931919513717708801. .397490855733113630613348630003685291009. .170970754136725722159939805266417998571170101.P96 2026L (2) 33449261.264484004729713012553.399321186049288505641. .956936627523697040100248003877237301005401.P214 M 564156533186297737660008857018073337721. .164541393411625402362219413683832040344060443782361993578322\ 0753011122321.P194 2030L (10M,14L,58M,70M,290L,406M) 613061.85597365805801531151405792561041. .87678355175652250615083617929401084618044201.P121 M (2,10L,14M,58L,70L,290M,406L) 36541.357281.P192 2034L (6,18L,226L,678M) 4077850171122577. .31069150378873790895208046895771360949463293546412105951449429.P126 M (2,18M,226M,678L) 856216369.318132015893843401. .21147271559400204090224749.454399800958030464217761866249437. .1065856403671528263525870130273753.P85 2038L (2) 61141.207877.7150897365985729.223030353552686687144432969.P254 M 1862909934566184008482398847661045112399809958601.P259 2042L (2) .672016780070293290346024426318491658292297223554825720302450\ 66489386602930740136941318680402182278080214741.P200 M 88557457. .975085324963132614235287022359292686345429798435891963303585\ 74428188118349081171097421619786116315501.P199 2046L (6,22M,62L,66L,186M,682M) 4093.10308836566117.909262501760934950641. .241186415860665003411865101707998523680990567422853.P94 M (2,22L,62M,66M,186L,682L) 431919189109.45982033644093624122893.P146 2050L (10M,50L,82L,410M) 656400720309944201. .39701639943363232352915408020280101. .77717544350108411855476312332047319800951948082211484798801.P130 M (2,10L,50M,82M,410L) 3527365301.P232 2054L (2,26L,158M) 308101.24775349.105748241031224273. .24187837105009092776233550365107217.P218 M (26M,158L) 4828050703567261.P266 2058L (2,14M,42L,98M,294L,686M) 127597.7687554960386019181. .52003770991385964409.2258564379815977498898119074673. .359714423380600478940340236904806333157.P65 M (6,14L,42M,98L,294M,686L) 3346309.5417007821989854721.P152 2062L 181457.21832972170562783667409313815601848142855493763552538\ 718227165724291311620998115375711693469.P214 M (2) 32993.99370848761184288276203230691281696940392048973. .582237741388176844682736097695363585972908566605341889727297.P199 2066L 622097393.1606410037.2302309768953616705880653781. .45517419766433926393156993688590165332738044647314049681507\ 14035767163251260953795297189.P178 M (2) 4133.78509.764610073.119567616206597388593595587565413062223773. .803380233659856585566025001165615159747411892984338601319122\ 4649005528518305199101195643459094048473827432841721562227893.P131 2070L (2,10L,18M,30M,46M,90L,138L,230L,414M,690M) 1899703744314142469016395838361964239321612519501. .5946756064141975321802721152617946012331105353723221.P60 M (6,10M,18L,30L,46L,90M,138M,230M,414L,690L) 12421.45541. .284746766418697641868038011821394285860323158881.P103 2074L (2,34M,122L) 8297.4674797.14475794101.9515330527620650472517. .423082350292474675079511971763937.P215 M (34L,122M) 24889.67591661.19245413381. .28507675395016426209379265459437.108418776698113814016172668034087889. .29372667805516620161464001230063579445161.2379087623493826349\ 515745289386828551177970787122205156170504291507059373.P87 2078L 4157.47577889.25782331522951529761073.507644488024787734242019373. .144881493240241900269232403148013. .179264656762286536508977497989939355504743846331169.P170 M (2) 142133049913536832788937080594590754168045045704604784705\ 74556284589105381751127558576315390947835944546659913772334\ 7545508429457120269.P178 2082L (6,694M) 6071113.42288273231097.920711247257749.56229065675693116237. .23384866763414531770204088484887647243643341. .6212208498791522443680860464057886551642074217423393.P58 M (2,694L) 8329.112429.1557337.592686737569.6867574890898053457.P164 2086L (2,14M,298L) 12517.33377.198857827144683169. .1926620590033512371166117610796118373573. .1095231941923151040523302496212941131502792751422952913.P149 M (14L,298M) 20080858786741161561964999694927220590075478191838\ 48459023861088803452687057655722305860757903893.P171 2090L (2,10L,22L,38L,110M,190M,418M) 6029645821.P207 M (10M,22M,38M,110L,190L,418L) 1414585500587719775570810281. .252337225468275098346192473731351429835936385305691576776761\ 8815531110061.P118 2094L (6,698M) 2065299637.40562442707197.9617687207378317.P171 M (2,698L) 1965768116596960355721918724300332174927345580260159\ 8904262946663319721006141051366816994929.P119 2098L 4640777.83011968817. .374386191211579883530009072555086286507214381011256503367656\ 203188103896066772009066447235343317.P203 M (2) 12590854756648551516684021495487769. .1372098406910139347411473978297737029649599583843164650153. .237192716367319808525419681995440718925568206987372271548097. .17679965542446252663098049357830072817243994078460361117900163969.P101 2102L (2) 92489.2030533.207619855320079870004881. .9428534294343494947194510234734091242364814824057913282008223948\ 2940266029599405731418042749579581752853023894754659625008912541.P154 M 1513441.77933753.120003217560112501.P286 2106L (2,18M,26L,54L,78M,162M,234L,702M) 511421041. .1786056393133579120301535471349560928117009051711813909085892347953.P121 M (6,18L,26M,54M,78L,162L,234M,702L) 150937180544593. .23640543396721742414157469.P156 2110L (10M,422M) 7313261.1060955698661.8207774689941937459483922881.P206 M (2,10L,422L) 274301.163031261.3518920881831461. .7798241026129503827660037110146961. .111715180352426255717925792801717907641082234891700846009615\ 527511253647864321.P114 2114L (14L,302L) 3646092601989001186525363589. .46407610276467440780784332348683797989.P206 M (2,14M,302M) 4229.9817417.13093972249.252329098404058364830457653. .1063976134790213153556087433.115156277124838748001785108973\ 2941825401794650223201634913905229186261489.P126 2118L (2,706M) 1559123581453.80422923777405534042337. .6389510827587980645340633853527175669983842839060657.P126 M (6,706L) 27503548942141.2885299533969327285608778291701629.P165 2122L (2) 49459577.2308766446154677.P296 M 43497479736983828850647753.P294 2126L 4253.119057.2351357.118640804957.P294 M (2) 6262064969.51799226966893295289509.51114358532758153182876066459473. .1603777152900827521607976402498110749. .925670022446110396008291405761618232237295686334594116914906\ 19084137789567395278755210519550250512461.P118 2130L (6,10M,30L,142L,426M,710M) 4261.46861.149101.775548522986795641. .14434789001414900976541.P116 M (2,10L,30M,142M,426L,710L) 8521.9883201. .935670834191020341514842275817603083341. .805863337960228852951520597182877664103305518701.P71 2134L (2,22L,194M) 819457.P284 M (22M,194L) 115237.8670835642148979210715595043749314093.P247 2138L (2) 25657.120995596673449.39769515373402823701741. .25628302455269700936935750561.P252 M 9900693519731369541341.59623715903776666409686137682448042581.P263 2142L (6,14L,18L,34L,42M,102M,126L,238L,306L,714M) 94655375162339953175243922917053.1678012401109759349697111520625113. .108843028104327227902725329813334696855127583727517.P58 M (2,14M,18M,34M,42L,102L,126M,238M,306M,714L) 4198321. 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18241890517.28221633169.4792343120992181.6215871883210370333. .77093647531280886261895218878026714548868599954623848018218623360\ 980429624113850906610007804328686595403945892843224741745082093.P145 M (2) 4349.182617.887735509. .1944660552338008947746884006390903413472671243168594079430933828000\ 0168439435175492560992306551025052324865358247610907279211375954373.P176 2178L (6,18L,22M,66L,198M,242L,726M) 7692697.158914152241813. .755084486042964623053695739861.P148 M (2,18M,22L,66M,198L,242M,726L) 4357.1028017.21366181. .1057452633848904633973879093.P155 2182L (2) 13093.2305837815915297883997398826188721.P291 M 2070456161.1206850555657249.475989046121563895183917. .115258068376444832585305884399965414081. .26967610488143366631571497125562690595234994227486819287081041. .1440062995862605427243191028936298569737980702173934749501866\ 0778647042803798300412735237.P93 2186L (2) 13155349.8937940500670340895772341530892104386801. .7382602259305831427170481228432877375865567099206873553. 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C340 M (2,58L,86L) 32397061.260293793.1365338648031806893. .14015092861678945577467193163309833422440329. .209274240124717471245904118687826696450175732071912105901.C221 2498L 874301.111870433.534681373776302338436724283434249944185265621. C318 M (2) 529577.5205642570488111720493819683480805334720301. .341204018509113159482346004141300962381374625870169185233.C271 2502L (2,18M,278L,834M) 4863764737558873. .101505879853053634405061915849443418748025854970103452115579\ 651957144223490161478844647280526477038452554901.P127 M (6,18L,278M,834L) 749574181. .140288056149621992057161658267534838223007507383620555427094\ 502400636503868749630355529014081.P149 2506L (2,14M,358L) 13331921.1947424340237624081367500098637. .605837775118376522158628976445055501. .833206828587059005322704145140483137181.P210 M (14L,358M) 11854394022829. C309 2510L (10M,502M) 1706801. C295 M (2,10L,502L) 821317181. C293 2514L (6,838M) 45107337546613. .372541902004548758064287983975387722094906339050408099501986\ 508348587524216881618268060714903125804422351147626897.P124 M (2,838L) 82770937.47833179109.261451249703273053. .69133215155408551830340249799739061.P182 2518L (2) 28277141. C371 M 673384251448453.28932982279329329.70532085985808417. .4062195650688283357.630738843232051221097373.P289 2522L (2,26L,194M) 20177.1079417.46977717697.353653416214697. C312 M (26M,194L) 792204360221.842008940624751093837169897189. .13671952555295832626353363640415707341. .272510260655943466650157933840294501649. .2503897690431483944359083926376145505447879789788189412060502137.P166 2526L (6,842M) 1763149.7565386628831140673686418791551742571448587851033. .768684712544097553801414960240331355018149807641508827156968898981.P132 M (2,842L) 95989.2761554553.4441165187433636077485984727677. .992068065829481105861516942344288335965507094590380065684394\ 62505912456736400381373.P126 2530L (10M,22M,46L,110L,230M,506M) 116381.11045981.14576686081. .135207200917625782661.76642981318592684340181. .10701841425575442089475043297541.85872110762953806878751991476541.P138 M (2,10L,22L,46M,110M,230L,506L) 3149951201.11796409566450173281. .22445866985422163663609416740829299897061. .912398890950029653701212383188436690297531415640532851882204\ 015346852830161.P121 2534L (2,14M,362L) 1460451084121. C314 M (14L,362M) 2706313.27249477437498965993. .37966464389701496755439976305009509.C265 2538L (2,18M,54L,94M,282L,846M) 5077.2536451821.11665485520556050019449. .2467218162172630582705161861131144715621495699488695934586469.P154 M (6,18L,54M,94L,282M,846L) 2569815668817958430702606975739643\ 94491698079911473395140718506345668294524033.P172 2542L (62L,82L) 12379541. C354 M (2,62M,82M) 84948557.82543932965499101.13863074300688628796569. .2985066048816935182870333.185151286978029128974632301.C264 2546L (38M,134M) 1234788191657789227862141. .2301736698010972028864866222285479748161532407004740672155855821.C270 M (2,38L,134L) 15277.20369.6359909.3555234401. C334 2550L (2,10L,30M,34M,50M,102L,150L,170L,510M,850M) 107101.746935801. .1299193767601.4196653464309949222501. .410377611401622696951457485328489022234972109538831995301.P89 M (6,10M,30L,34L,50L,102M,150M,170M,510L,850L) P193 2554L (2) 61297. C379 M 858916543349369.31028012425558037.1227156720026097481648213. C329 2558L 4290691997.197233010954448024794514062981009. C344 M (2) 1146568796702009883941. C364 2562L (6,14L,42M,122M,366L,854M) 2633737.769473600224029. .6703506663290389516520614108342858000438594456161004584828714\ 903303956207332913176549.P112 M (2,14M,42L,122L,366M,854L) 271573.910355050081. .17293476930223056800729483751229. .29899969036060916905067447295641189014385018982618060815846500153.P104 2566L (2) 1944100257569.1150663963695481.16136173156682022513360583795369. .172832457171531096895685201319888371063970437. .82246854728142924005776121999404351754306984763883228668451697.C221 M 35564761.790966569629.P367 2570L (2,10L,514M) 31543975240498973141. C290 M (10M,514L) 221021.365189182922988243760331205103896866270939308603661. .1162316224302205204133633045083472251018288020441503062949918912461.P186 2574L (6,18L,22M,26M,66L,78L,198M,234M,286L,858M) 35343000167505171372480351118744485759866437.11236382173292790556\ 314455599021730714539437914391148357586567897419168773228187918249.P88 M (2,18M,22L,26L,66M,78M,198L,234L,286M,858L) 4243524044761.P205 2578L 10313.6325967088761.20648182637548916755356569830484537. C337 M (2) 2206769.47475491925544793901258456088876727741.P344 2582L (2) 15493.5024694586458429351986046167371826130316951956646312584533.C327 M 199505629454028359771143201093. C360 2586L (2,862M) 864619614553.3087933005187621528667453. .505135236186782540723068815648722268743298606324481985310257\ 1042448093897655049066522762059565728870793229.P118 M (6,862L) 99219649.827316343104530343803180395385251358053. .29561285952007560723306564063158711234257.P171 2590L (10M,14L,70M,74M,370L,518M) 839161.118361181821.29120674363726709821. .100883332638867344729644912746281. .186082019530474449254126811681086247751029553735016835590651\ 144723423009513378890483895907961.P100 M (2,10L,14M,70L,74L,370M,518L) 36917861.268992221.352240001. .271500470032541. .10158081031142365238833408555300844803575260525284856063921. .41754808378356377322654799118782913860942045466300446609566987593761.P96 2594L 5189.83009.28331669.57400033.P367 M (2) 14713427619262280164702742524136752190263346928019151705141695\ 286113.C323 2598L (2,866M) 1636741.11394829. .200230294390133849293865892207888991104831601859437.P198 M (6,866L) 316957.434136193.18228492889.P236 2602L (2) 947129. C385 M C392 2606L 578533.62643029.4977311911993209330675857. .19703069680686093788435311449159238692457283154085141.C302 M (2) 67757.4393717.44886574487867821363369914637. C352 2610L (6M,10M,18L,30L,58M,90M,174L,290L,522M,870M) 41761.77755979210761.P184 M (2,6L,10L,18M,30M,58L,90L,174M,290M,522L,870L) 109621.135721.224461. .2416861.326997328501470241.35370046927469820523012201. .10449747916429814942193347990519084354281.P98 2614L (2) 62750388539022414604134123982634397224861. C352 M 109789.684869.4883605501.6203690917373. C361 2618L (2,14M,22L,34M,154L,238M,374L) 7101252203893.73374480701677.P262 M (14L,22M,34L,154M,238L,374M) 8010451496741.5594047027317673. .6518430851483584659473.C239 2622L (6M,38M,46L,114L,138M,874M) 24180592669. C229 M (2,6L,38L,46M,114M,138L,874L) 15733.10174398313.877640733632629. .982106569102414814870997690078537560364120461085665467404382873. .31443663037237748401158464963803475289481689725873164254005\ 06752433929.P77 2626L (26M,202M) 94640239243603411326265396150921816238325588361.P314 M (2,26L,202L) 57773.73529.8613281.11386337. C339 2630L (2,10L,526M) 5261.51253441.1480644206441. C293 M (10M,526L) 371044628324641.20530283710306134901. .326738108283574454408901426293842545027521. .181139200471709613270446218531550735001540815581. .2706996639284226360223775532817947623057747222644299042085927219901.P126 2634L (2,6L,878M) 142237.145483520386890301460455024063159382281. C221 M (6M,878L) P264 2638L 71716669.639372578683784549915537. .5354859069507261587596664548398057571618254547842137513393.P308 M (2) 31657.28736963309.648976738373.3407784403254859949. .1325620864995498721373.1058360333252581913756680783979853220841. .2177004655299856954786224953419637692977326293.P246 2642L 592880653.57179215517.4461367814865647043672606216067401079709.P339 M (2) 14806963845146933.361950552101706786686496310582591769.P346 2646L (2,6L,14M,18M,42L,54L,98M,126M,294L,378L,882M) 15877.1074277. .411373621.154112736717744257682475965087425110190896212097.P162 M (6M,14L,18L,42M,54M,98L,126L,294M,378M,882L) 74410813.52112197369. .25046314062594331995504406386519745557262033.P166 2650L (2,10L,50M,106L,530M) 10601.15901.6400126301. .635893687247937156858979788301.432232039852259481789661212880505701. .39807236240383965942242748465009014683280026179770401.P177 M (10M,50L,106M,530L) 2180204703335720073601. .3730504934273889884608382514281727901.C256 2654L 100853.2011733.844828281031420753. .520196552023689611079032312673055654637. .6487848713728446825916653909723849312415356018074475449.C277 M (2) 5309.180473.541417.1554430579829967373174083538729.P354 2658L (6M,886M) P266 M (2,6L,886L) 49741941880513. C254 2662L (2,22L,242M) 92276094234809.340151643796415089.P333 M (22M,242L) 15973. C361 2666L (2,62M,86L) 4780185989.30029072189. C360 M (62L,86M) 5333.69317.149297. C366 2670L (6M,10M,30L,178L,534M,890M) 2541841.5847301. .33532645581151505088670119778789450502641. .1439542261407025288932073665783320706178852607429002817813268\ 9141296169594901.P83 M (2,6L,10L,30M,178M,534L,890L) 18422579973697261. .1026284914708335609098581.P171 2674L (14L,382L) 224617.56539057.17896550418703412798687446950913. .1006115845218491544211549747939404353211878052377662425170857.P239 M (2,14M,382M) 106961.7011229. .1622869792959437376289562550153549149494544653475669. .1486353852513121083229721182598069457243317953618190057. .4299670636899934418877274163222444090391869995799462030741. .1812872336390201519994832915887887755578803765630726241336456\ 0859837619763709.P93 2678L (2,26L,206M) 24616177.213715074509.P351 M (26M,206L) 438415381.2095394833538917. .9773691323025424993037032148618024139895729. .34004917286617480752914465318527528974515665520201.P252 2682L (2,6L,18M,298L,894M) 10729.123373.3032510581.9096576949. .3986279742675019105776799327962146233447443709.P193 M (6M,18L,298M,894L) 44290549.3031942277397070372043233039287433556629. .279018501039877302914557601648105184965225671373632544089614\ 2184620821.P151 2686L (34L,158L) 639269.10695933756029.175703918844029. .2366538538236891736396993.34253483955380507714888473.C293 M (2,34M,158M) 449336370691608213713.4712432201031931532969. .8977987418211944923397393.C309 2690L (10M,538M) 21521.242101.1309715444177501.P298 M (2,10L,538L) 32845413731366665967528955000955555907366411408441801. .445168683146154234108029106492652865406448317924850621. .3198542880450478964220185165595655491973198853184439541.P163 2694L (2,6L,898M) 381305591857.8037322924909.85996426291778053. .13894006809535238949057013.C204 M (6M,898L) 2971593240952095808995697310437. .392101437441082940885812671195057781.C204 2698L (2,38L,142M) 14650590206439277513. .1499465471981653919943011373129013158509.C322 M (38M,142L) 26981.350741.168379677619529469253. C349 2702L (14L,386L) 2450609768766509113.44060447683117907329. .48290946291345748195670137.C283 M (2,14M,386M) 64849.102677.48563472912496695457456796345673428521.P300 2706L (6M,22M,66L,82L,246M,902M) 2210378779223228839889559393339469. .11293730213056905017532119870598882067968200947920727418168917.P147 M (2,6L,22L,66M,82M,246L,902L) C241 2710L (2,10L,542M) 59621.1781114981. C312 M (10M,542L) 1084001.15851812914034491781. C300 2714L (2,46M,118L) 25587593. C378 M (46L,118M) 2356789827042977.10457862804878827549. .2792325798286747697838270202593011872166389.C307 2718L (6M,18L,302L,906M) 389155607857. C260 M (2,6L,18M,302M,906L) 377493096842300424269737. .180280074503800059302247009779051893.C212 2722L 2879669129.1638676450688990013295661. .15861801543743881789568987940258899326406910027482735839091441.P315 M (2) 157877.83490893417.47118478926572756841581029391224009717. C356 2726L (2,58L,94M) 866869.75740837926352576673918954169. .27735763126646658000990959339333.P322 M (58M,94L) 10113461. C381 2730L (2,6L,10L,14M,26L,30M,42L,70L,78M,130M,182L,210M,390L,546M,910M) 9385741.156869432603217290269125002845201. .1180461638962512244483119906711781.P102 M (6M,10M,14L,26M,30L,42M,70M,78L,130L,182M,210L,390M,546L,910L) 343139161.322813496461.325926171481.440166415328641.P127 2734L P412 M (2) 82021.35427173.10955646370897. .184778210381581846455084386672905410169.C348 2738L (74M) 5477. C398 M (2,74L) 147853.648165313419148121. C378 2742L (2,6L,914M) 4525294424689.11125015205754281087101. C241 M (6M,914L) 50594924786293.P261 2746L (2) 550952934662007267280133836297499633348052457. .651145819905070693078702714432246901569894183038417348720533.P309 M 2061411217.123906905264936191900371461. C378 2750L (10M,22M,50L,110L,250M,550M) 5501.223344001.748066001. .37475874542920115501.C261 M (2,10L,22L,50M,110M,250L,550L) 165001.87582962256256501. .879625915958476501.323863940785545194610611499564375001. .82261095178661123111229384319191974296001. .3306425990706190718745454059880186134315112893911512424160781\ 3225512323356759645078501.P99 2754L (6M,18L,34L,54M,102M,162L,306L,918M) 33049.7585314037597. .627554397100735801. C225 M (2,6L,18M,34M,54L,102L,162M,306M,918L) 225829.1918559294497. .29185236934129.426492738815025853.16059484758853382797. .12204547259362888603933. .8794040278187902272343340887688100579563422920215740633.P116 2758L (2,14M,394L) C355 M (14L,394M) 1003913.598958970620976617.P330 2762L (2) 963517740819081137.36903614150334937861. .573250078452321229204101450811574224575271149012155284669.C321 M 17036017.3600267001.6627626006377.25755415055743010446654881481. C358 2766L (6M,922M) 4846033.16270067941909.16507223620189.P244 M (2,6L,922L) 58217228233022281. C261 2770L (10M,554M) 11191680239996441. .401032854308858697341341902327825067282024477843181.P266 M (2,10L,554L) 229413076648565643763481.P310 2774L (2,38L,146M) 4199837.1528886360502043217.3379174890643311197. .1207723297756092698829719114401.C318 M (38M,146L) 8410769.4478689577. .35191330676636122248410367493025630850444200064528757.C321 2778L (2,6L,926M) 5557. C276 M (6M,926L) 75994969.479855053.55890066690395434294563191619451719697.C224 2782L (26M,214M) 57312115537.984958884052937.P357 M (2,26L,214L) 261509.3502359953.2957271113317. .26871260735530745661938727514781.1821694954041293648696551508165857. .175233583569249186371051910689505221.C256 2786L (14L,398L) 5573.4008811578254082558018461817467353. .36780957663513473878763583013674360497.C283 M (2,14M,398M) 10280341.1416644735106049. .59989493330883798274155409100717.265742755552796093409830010113684933. .353733929368268273112967822214627205435954024817913. .18079030929723990295640293502821337497340759521793530157. .20193662670331577392346423176457400209795181128394076458083037\ 29208493.P94 2790L (2,6L,10L,18M,30M,62M,90L,186L,310L,558M,930M) 52359639841. .995341892449720861. .1162557396592890801376548182666168711447381651683632151567501.P129 M (6M,10M,18L,30L,62L,90M,186M,310M,558L,930L) 16741.78121. .361733950613332764848223901. .244523795197375606916989769880558964554592562872572770754268\ 6404744357535981.P106 2794L (2,22L,254M) 8192088956647333.745408852921662152081. C343 M (22M,254L) 312929.2240789.21303392859472173126337. C345 2798L 156248693501471250345133045537061. C389 M (2) 1163969.2352267409.243374920806647320879209092678543721719173.P364 2802L (6M,934M) C281 M (2,6L,934L) 8063030100176928529.20296506864167514017773702081. .2448443305846767994128313793359444729. .7263194928768722280131504366837140369. .286527311514679556584668748697906423516648677093365187937442182866177.P93 2806L (2,46M,122L) 88440240574347787219401953.P372 M (46L,122M) 179895106033036397. C380 2810L (2,10L,562M) 522661.809957042804398661. C315 M (10M,562L) 87797303521.92774223781.2182408748770721. .66291650318541852240934507726981.886107007040378674207366312371089021. .266673602673967255932632208388963626132732065400450461. .4271913531347872661417285099994612159045193616787632359109141.P118 2814L (6M,14L,42M,134M,402L,938M) 4369224637.185655681974294470513. .9239692599294612353580374617. .9670299008184471466118384272551513698159620204075090420264165\ 42395935941061102193997.P98 M (2,6L,14M,42L,134L,402M,938L) 33769.3521644382062633. .4250587717526488748089.16836207728020565916000076536183071567713. .67733963992228418045136158162410793176249.P116 2818L 129629. C420 M (2) 11273.1970373781.201595415690989. .5735751584252908047062295122183510540141255357.P351 2822L (2,34M,166L) C396 M (34L,166M) 169321.3544433.121979694759941437849. .1953223904834244703220584993. .159424401285021433633036984212552441813954559105788158682518270641. .683802217606094509460359945174630997716878924606013194220815953901277.C202 2826L (2,6L,18M,314L,942M) 135649.34228141259605032430788858139537. C245 M (6M,18L,314M,942L) 2390797.6897644387886660332164672539874033.P242 2830L (10M,566M) 98913503441.3245256930751361. .4368671296974620160848947886641.C283 M (2,10L,566L) 426325734881.P329 2834L (26M,218M) 464777.55399033.23409169289062013333813. .8126966709524535267140981.C330 M (2,26L,218L) 56681.2882552089.124213494444989. .2162744757347531971423354118341. .10077884413548450205983758816508503105776429.C289 2838L (2,6L,22L,66M,86L,258M,946M) 55669547146201606329073412310467218342736329. .701497523444617283048002382277119572066996234425270433.P155 M (6M,22M,66L,86M,258L,946L) 11353.P250 2842L (2,14M,58L,98M,406L) 11236370553241.26345667597341. .17571511488837337415861.1687370285607494341397033719832771346781. .1729523005255659934115097361390262592642447148567678016749.P209 M (14L,58M,98L,406M) 11369.2796529.279858799529.156591681754957. .68047901813766159042200807981.C289 2846L 49800340024209893.968013196321576921. C394 M (2) 5693.44431753.125252461.17564720878420849132844869. .49106197845029009696046910971103361. .708433177621399865886043267575016512563234318603260160436379181.P286 2850L (6M,10M,30L,38M,50L,114L,150M,190L,570M,950M) 5701.1333383901. .1817285701955807346021593101.59977395648323347845211654501.P148 M (2,6L,10L,30M,38L,50M,114M,150L,190M,570L,950L) 102674630101.P206 2854L (2) 25353125799833948317.2661178508837113542049. .321616184125251662004127705172957.C356 M 713501.P424 2858L (2) 5717.11133193001929. .12595287707738514464031850154199994382434408306334255201621089.C352 M 1846023819219653272272982327949. C400 2862L (6M,18L,54M,106M,318L,954M) C282 M (2,6L,18M,54L,106L,318M,954L) 870049.309039673752125209. .667919766649324643184045313.C232 2866L 110366155999741. C418 M (2) 44461655778705001209464244077. .4029858213318790272236437245390916022006513. .424081850616649728052332545416832429062106984838386681.P306 2870L (2,10L,14M,70L,82M,410L,574M) 5741.206641.42435821.52762081. .126350616183541.1749391797174001.55033499452562899241. .499804591054134231746522178707085126206910212761.P168 M (10M,14L,70M,82L,410M,574L) 1076789490965021. .157494866191511982157045917439950817601. .10222602834019976766425922611746008098641. .106219230864472431538990895232493651335136784948763030921637\ 49359185401.P127 2874L (2,6L,958M) 11497.99526621.P277 M (6M,958L) 5749.10450335307261.191707987575977137. .186721685489931593041486513045031679178681.C212 2878L 564089.989243429.P419 M (2) 34537.58974565781.370186087088538086232557. .11717477243342608590581691612757517.C360 2882L (22M,262M) 1037692921.55713458969521.12001761680475557.P353 M (2,22L,262L) 17293.195977.2040457.2971357152852793. .210482624955369466393.P341 2886L (2,6L,26L,74L,78M,222M,962M) 718446613.1392460369. C242 M (6M,26M,74M,78L,222L,962L) 4734921673.5228819504221. .389632405802823613.2077275421191701076630630217.P194 2890L (2,10L,34M,170L,578M) 17341.1294721.18214324323329261. .2196916616605698641.P283 M (10M,34L,170M,578L) 28901.4699141.13063380682393961. .5097391230316286521.38786202699446648861. .14103156258836067265338485748532349450555667461. .2821441435109502828089638699434418614305254225831141.P165 2894L 4913817247313447742761.P414 M (2) 4946504506549.1357667334047960260755285617. .19754109616283186047512713349409. .45183206404351907249055357588786522461773116586235262049.C309 2898L (6M,14L,18L,42M,46L,126L,138M,322L,414L,966M) 1093124359916821. .85753924052761836397.279476293526447133609800680717. .361974895190262154631615760361.P145 M (2,6L,14M,18M,42L,46M,126M,138L,322M,414M,966L) 11593.P235 2902L (2) 133493.47628883469.12163104099116588429887217. C396 M 6163849.12196630073.12358509437.4258040158189.16322408591129. C384 2906L (2) 5813.251121209564108742517.P413 M 118169684594991032085819020201. C409 2910L (6M,10M,30L,194L,582M,970M) 22826284441.9519040103821.P209 M (2,6L,10L,30M,194M,582L,970L) 104761. .19511737837661707738071548043131128993164467659828405261.P171 2914L (62L,94L) 2444560429. .152554600751896772873225998690571286541274319047979770657.C350 M (2,62M,94M) 24244481.129296125866197355231194148390289351372766462081. .1406865138324436829416471348084764392581215681460049. .118608709955680235278624927772625489021018029464699288651462\ 86753404813.P241 2918L (2) 30277164043193. .2945595495338129333533236501397186031399848104960213901.P371 M 2616957249764352676829. .91040694459592197376675258809938836789105619369.C371 2922L (2,6L,974M) 11689.303889.26464312221055849505401. .75369005016617119751033790061.C233 M (6M,974L) 216596744832658029121.2369725482757554417520943641611345409. .37527666910921123479930989195029592758054163857.P189 2926L (14L,22M,38M,154M,266M,418L) 1053361.13352648849.25198861836030037.C293 M (2,14M,22L,38L,154L,266L,418M) 45453729772647704509. .70408009185675735739778537.20327201539273422028290745399275721.C245 2930L (10M,586M) 210961.10490450135441.21342998935108481321. .25760313043107318835119326319895919640581. .721310899542295645097426554540551218127909481.P229 M (2,10L,586L) 9074186120501. C340 2934L (2,6L,18M,326L,978M) 440101.19962937.148495609.4343493601. .174013460443775270386696120010337350269.P224 M (6M,18L,326M,978L) 5869.14078889145705114680610460013248149.P255 2938L (2,26L,226M) 1886197.13403114869. C389 M (26M,226L) 857897.15177709.32059457.2231687062716218797. .8085488453357293676448646411909101919668173. .336028241241072711333470864029161356611798974089. .1082217100305911746480193583659637436785019914097.P227 2942L C443 M (2) 23537.960028385432177.3918201534083147597671313. .4630528334123232961437062654211649.C365 2946L (6M,982M) 35353.117841.3273778341037.518906900840691283727816953. C246 M (2,6L,982L) C296 2950L (2,10L,50M,118L,590M) 20602333901. .48498446543744447044926973149369140229112539629291401.P287 M (10M,50L,118M,590L) 82601.116195066101. C334 2954L (2,14M,422L) 23633.107017513.30933153114557. C354 M (14L,422M) P380 2958L (6M,34L,58M,102M,174L,986M) 2257516683272341. .16938049106338252204013980008183905950175277175993. .981634138740298457237126942422079398936762856170736798851813. .2344985447268124742136793270703913195389738731670014268855216\ 333164518433.P74 M (2,6L,34M,58L,102L,174M,986L) 11833. C266 2962L 68078609.99286241.99726854400289030039273. .4424388743112395116816089328478915307741113434409. .233414974637879661924692361081186178308379240981829.C308 M (2) 3424073. .65221813646259307849177925259144124430100794460972383852316997.P377 2966L (2) 26071141.4279474271833.52050867956392800221. .23185195509248765875842619250621.C375 M 88843448429056637.302190509907340513723945290934901873. C394 2970L (2,6L,10L,18M,22L,30M,54L,66M,90L,110M,198L,270M,330L,594M,990M) 18209327394884790085078814351641. .2391036483477408028353958213264495727161.P147 M (6M,10M,18L,22M,30L,54M,66L,90M,110L,198M,270L,330M,594L,990L) 2138401.P211 2974L 11897.9378984841. .10676191814411536832074834433356771402537588329778394545613.C376 M (2) 10527961.84614116617473.24587114013921379242480085415355076673. .1180106344375528327967864196538291621678917272048461.P338 2978L 59561. C444 M (2) 42822438543769.6912307198663399085960820684529791591540749. .5940231518639818133881548617394754356089382789141290697209920297.C328 2982L (2,6L,14M,42L,142M,426L,994M) 1149948661.13181017668659540216034673. .9011964476452935613114949231159639776931249233.P173 M (6M,14L,42M,142L,426M,994L) 1699741.78428884213.P237 2986L (2) 47777.173189.1674741834350778517.3900547400342197955621. .18222546195231439072063867733. .356702983805463988148160565880819445133.C333 M 214993. C445 2990L (10M,26M,46L,130L,230M,598M) 279995561.5639806235970206263861. .2987050257924004911335237581.5636137681719921972498359341. .501515388291533934046083773716870460201. .332439249802813989051818134417348247768171690063861.P144 M (2,10L,26L,46M,130M,230L,598L) 530291659843249368481. .1888612297339126260721.P276 2994L (6M,998M) 23616673.39133076185633.769730897272442473. .4048605847546203121.86849811525459729209008153. .1242778031621547719007345267501236758837.P177 M (2,6L,998L) 1366158773223180217. .2704473086263361887611337232200335041856901.P240 2998L (2) 2473463192799863936418952436352014097575008009. C406 M 36123396542237915182866917. C426 2^2h+1=L.M, L=2^h-2^k+1, M=2^h+2^k+1, h=2k-1. Table 2+(4k) Factorizations of 2^n+1, n=4k, n<=1500 n Prime Factors 4 17 8 257 12 (4) 241 16 65537 20 (4) 61681 24 (8) 97.673 28 (4) 15790321 32 641.6700417 36 (4,12) 433.38737 40 (8) 4278255361 44 (4) 353.2931542417 48 (16) 193.22253377 52 (4) 858001.308761441 56 (8) 5153.54410972897 60 (4,12,20) 4562284561 64 274177.67280421310721 68 (4) 17*.354689.2879347902817 72 (8,24) 577.487824887233 76 (4) 1217.148961.24517014940753 80 (16) 414721.44479210368001 84 (4,12,28) 3361.88959882481 88 (8) 229153.119782433.43872038849 92 (4) 291280009243618888211558641 96 (32) 18446744069414584321 100 (4,20) 401.340801.2787601.3173389601 104 (8) 78919881726271091143763623681 108 (4,12,36) 33975937.138991501037953 112 (16) 449.2689.183076097.358429848460993 116 (4) 59393.82280195167144119832390568177 120 (8,24,40) 394783681.46908728641 124 (4) 290657.3770202641.1141629180401976895873 128 59649589127497217.5704689200685129054721 132 (4,12,44) 7393.1761345169.98618273953 136 (8) 383521.2368179743873.373200722470799764577 140 (4,20,28) 84179842077657862011867889681 144 (16,48) 1153.6337.38941695937.278452876033 148 (4) 20988936657440586486151264256610222593863921 152 (8) 27361.69394460463940481.11699557817717358904481 156 (4,12,52) 84159375948762099254554456081 160 (32) 3602561.94455684953484563055991838558081 164 (4) 13121.8562191377.12243864122465612155106392056552353 168 (8,24,56) 2017.25629623713.1538595959564161 172 (4) 3855260977.64082150767423457.1425343275103126327372769 176 (16) 5304641.275509565477848842604777623828011666349761 180 (4,12,20,36,60) 168692292721.469775495062434961 184 (8) 43717618369.549675408461419937.3970299567472902879791777 188 (4) 1198107457.23592342593.4501946625921233.181352306852476069537 192 (64) 769.442499826945303593556473164314770689 196 (4,28) 7057.273617.1007441.375327457.1405628248417.364565561997841 200 (8,40) 1601.25601.82471201.432363203127002885506543172618401 204 (4,12,68) 8161.40932193.1467129352609.737539985835313 208 (16) 928513.18558466369.23877647873.21316654212673.715668470267111297 212 (4) 1692645313.10920513604018498900801.20946001591429012199281424246257 216 (8,24,72) 209924353.4261383649.24929060818265360451708193 220 (4,20,44) 109121.148721.3404676001.11035465708081.2546717317681681 224 (32) 167773885276849215533569.37414057161322375957408148834323969 228 (4,12,76) 90289.9036489073.29034057164920993379000074993 232 (8) 929.5569.8353.39594977.P50 236 (4) 1889.11329.84961.765373489.P49 240 (16,48,80) 23041.P35 244 (4) 977.37831175201.4889940029309876547089.P37 248 (8) 8929.P69 252 (4,12,28,36,84) 1009.21169.2627857.269389009.1475204679190128571777 256 1238926361552897.P62 260 (4,20,52) 42641.5746001.2400573761.65427463921.P27 264 (8,24,88) 16875081675650881.P32 268 (4) 75041.333808138537249.P61 272 (16) 5441.335631827046798245410603730138717057.P38 276 (4,12,92) 5770338946481798744593.P32 280 (8,40,56) 4481.557761.736961.P43 284 (4) 2273.1433633.P75 288 (32,96) 3457.816769.1562985901350085709953.P28 292 (4) 19602880710043505617.P68 296 (8) 80513.P82 300 (4,12,20,60,100) P49 304 (16) 7798338113.179781388993.84885296460737.643966863870017. .27362254540091201.237157827243967596481 308 (4,28,44) 13553.74153335873.P58 312 (8,24,104) 4993.94849.P50 316 (4) 504337.994769.P83 320 (64) 286721.446960641.96645260801.3442404051886487041.P34 324 (4,12,36,108) 1297.3889.30433969.1164777409.3718266498433. .134921168163073.1174029487714513 328 (8) 12239719573537.18093927039368350337.25394524415842506913.P45 332 (4) 11953.14767689550320172808742174828062347720350769.P52 336 (16,48,112) 47886721.P51 340 (4,20,68) 1361.12717361.1392971637361.8088220746627020943841.P33 344 (8) 4129.P98 348 (4,12,116) 82129.10389476529713761.59372021171164475019217.P24 352 (32) 1409.1258753.441995541378330835457.P67 356 (4) P106 360 (8,24,40,72,120) 8369281.P51 364 (4,28,52) 593914915675537.P72 368 (16) 76392570609857.1335570346574631363954390476479681.P59 372 (4,12,124) 1489.29761.22415398357688737.P49 376 (8) 3308801.3853249.487073399939357470433. .163875530636702837695009.2673989784183378728255297.P30 380 (4,20,76) 3435950210316335724157758000789490561.P51 384 (128) 349621839326921795694385454593.P48 388 (4) 25507121.P109 392 (8,56) 3137.50177.101921.258721.P83 396 (4,12,36,44,132) 311712063697.P61 400 (16,80) 3399426377632056001.4850484222084371979240001.P54 404 (4) 4126631533969610752526181761.P93 408 (8,24,136) P78 412 (4) 454849.667441.40151873.52317884766401.142500609730433.P76 416 (32) 4940417.11342687617.P99 420 (4,12,20,28,60,84,140) 127681.1130641.755667361.P38 424 (8) 1697.P122 428 (4) 4209809.13012913.992005069953996722026755979686303668059315249.P69 432 (16,48,144) 68016300334849.P73 436 (4) 598193.35695338233523972669330604417. .576694829762330794568961139476826913.P60 440 (8,40,88) 47521.89119361.127886114126296744221796660380215073025601.P43 444 (4,12,148) 92353.126097.532801.854257.85337232196804809313.P46 448 (64) 1489153.P110 452 (4) 9041.30500013280577.P118 456 (8,24,152) 1459574594862075553.320507768196690588004609.P46 460 (4,20,92) 254697295909573204954870539927521.P74 464 (16) 748264961.2245984577.239686663718401.15929619591127520827829953. .6033312171721035031651315652130497.P44 468 (4,12,36,52,156) 1873.6440452782193.623293182848475361.P53 472 (8) 25342605037666235678081.P118 476 (4,28,68) 94994369.1580019259393.115846651946400929. .2488196881582734135904733409191377.P45 480 (32,96,160) 26881.4855681.610548481.137603804161.P47 484 (4,44) 209089.33186913.1251287137. .38608979869428210686559330362638245355335498797441.P61 488 (8) 1035817877926014488587133818491976759389034764353.P97 492 (4,12,164) 62966161.P89 496 (16) 5953.251969.19301855478655894221313.32206359010364528536290817. .15624307475317816130204755452289007981717441.P45 500 (4,20,100) 4001.1074001.2020001.22624001.1481124532001.P85 504 (8,24,56,72,168) 34273.P83 508 (4) 3108961.17664039857.357319966758824298104849. .3284305317126808646829056321.78829341974215087229120114369.P55 512 2424833.7455602825647884208337395736200454918783366342657.P99 516 (4,12,172) 328177.359137.52547670996812050561. .7277473036504760410488618498577.P40 520 (8,40,104) 2081.19868746561.3377549010888001.7580827241843270677601.P65 524 (4) 1271332666556177.36441674155824796521521. .88628235147538969385874281472055436801.P81 528 (16,48,176) 1632064897.190507963147393. .44250674269198344200898981420091393.P39 532 (4,28,76) 1692116131441.139065006256539545729.P98 536 (8) 4289.311532723090035002320027134588551176448471666435989092897.P99 540 (4,12,20,36,60,108,180) 2161.21601.201519653761.1117180440577441.P53 544 (32) 15233.143617.443069456129.P134 548 (4) 38226289.15164972751718165538717288739219937057169.P116 552 (8,24,184) 267457249.P98 556 (4) 6673.77764617112817456421627629713. .1716319040365034397790860195913303021663915471096474850983729.P74 560 (16,80,112) 16824641.86800001.40396092614384641. .40809065233184155116161.P62 564 (4,12,188) 201777278450257.4409486883238989864703786561. .38573092257178550307394862497.P41 568 (8) 14254355329.80377573236449.13425464222423304875744449. .11091113376655556595890990679482099679181989410614081.P68 572 (4,44,52) 145143857.311195251370951377. .1614501783881444871695814328568586673.P83 576 (64,192) 17047297.628582818817.P97 580 (4,20,116) 6961.9281.167859997042321.P113 584 (8) 32871186029052837857.79778881726281213651073.P131 588 (4,12,28,84,196) 84673.265549217634074770386573489863592827112366481.P52 592 (16) 31474859175390153735107856059776876864094488913562623409\ 377402922304455233.P100 596 (4) P179 600 (8,24,40,120,200) 4801.55201.P88 604 (4) 2417.4363297.730685377.775168188161.P150 608 (32) 14593.671233.620066693671553. .72957037607516225290419063617993856505649915307620690006389889.P87 612 (4,12,36,68,204) P116 616 (8,56,88) 29569.110881.P135 620 (4,20,124) 6338840521320763912823441. .8972288213208726237756413079825557066213015494366305516001.P62 624 (16,48,208) 792584833.9155841480185089.P91 628 (4) 7537.118528721.262400181553.992000324534793042722401. .20605715069815219132625364745038097331729. .277433242225210532955711783957443819730099281.P56 632 (8) 286297736737. .471211668918301561515489208246219513333426679953187468148445645729.P111 636 (4,12,212) 12721.239372593.208306541869009.971476396313002897.P81 640 (128) 3288416281349499632641.7771646317471635593256655841281.P102 644 (4,28,92) 53632321.508294185549580458441687901500833. .187348880910146760908202953046841356170561257966417.P69 648 (8,24,72,216) 10369.259201.1824045366145909775041. .524833094849624730914401.P76 652 (4) 2609.10433.1322257.28322881.P175 656 (16) 7873.47402561.591100350038949953.1668576469005068046209. .506060190832207779694850270816882633281.P104 660 (4,12,20,44,60,132,220) 14736481.514210163281. .649817602852289358605542163521.P48 664 (8) 3508428556083287152033.P176 668 (4) 482851777.670297921.375283446486344365461807838534613233.P147 672 (32,96,224) 494968321.663239809. .2925384400770993343049563645260155764299463512577.P50 676 (4,52) 210913.47925697.455986337.178077806451169.P152 680 (8,40,136) 496304801.10008321601.33910825580641. .10146032011084172688350401.18741457027056199460701768016571521.P63 684 (4,12,36,76,228) 12407761.1953842221288628908086845073520488081169.P84 688 (16) 2753.1755145793.18090206003620308180353. .3374493964203314716755629762689. .77411329907915702977897669886203158137376728020417.P87 692 (4) P208 696 (8,24,232) 75169.1185335329.2175937261441.3945720769057. .43420756732422994369.247716071005295731527406385377.P47 700 (4,20,28,100,140) 2801.P142 704 (64) 60299259845689822028046342401. .3210843755324367119258027752661239735297.P125 708 (4,12,236) 95646885844433203176775508160481.P108 712 (8) 290497.59170049.9497407873.1334056289569. .25222813432549907120203219752470337287201.P137 716 (4) 94513.10240246321.6249618890312649605712432659622854257. .22562882829685667659941188646849469227356664645922433.P111 720 (16,48,80,144,240) 37441.170251201.322029272318997936286081.P80 724 (4) 2897.304081.558786628009681.148643100302189793374401. .3289754668487801751212109418730038529.P134 728 (8,56,104) 145601.9828001.32038310825249.P148 732 (4,12,244) P145 736 (32) 3689800577.6699561451777.428895600365702401.2581126261168515842\ 568515186820240654583079937025463189245875897945938699497995409153.P88 740 (4,20,148) 174463386657191516033932614401.P145 744 (8,24,248) 91556187016478788158721. .2295529738871686782981597056268590225067747577438438859809.P65 748 (4,44,68) 738395681.16998871173904049. .199431288499235121583168837778864679060668081.P124 752 (16) 4087873.4810716907835700161.P197 756 (4,12,28,36,84,108,252) P131 760 (8,40,152) 3041.477822284525893121. .162956550683997466131743371152980332553159745243749491445921.P94 764 (4) 827467009.264476244523458034906978299417485309897059948654792106081. .2695155945030251018331662354179230226777032634005050325012294\ 828756577662449.P88 768 (256) 212780015855109121.2220842644284984664160257. .1796602923899342630768062019504577056782884736988571649.P59 772 (4) 43464340002838801.6113808521283176001208256000113096624506766\ 3049594184076112874904437731971413080237731822785297556226950049.P108 776 (8) 782209.372454540993.2125457487809.20468009784290989308737. .274544401673356635075368632379880469997576189095365919517662\ 917268897.P111 780 (4,12,20,52,60,156,260) 1928161. .166668825096179161138307580471434399036535876481.P63 784 (16,112) 689921.66308056470365249.P180 788 (4) 72497.3050841968833. .164852611306562008724829898441986398410912126396452362238874\ 09386257443385451391361.P137 792 (8,24,72,88,264) 3169.3665377.12925441.52386049.P120 796 (4) 8214796852906477415899530941807101361.P202 800 (32,160) P193 804 (4,12,268) 209898673.6925799047681.29493338799546784993. .133304540580175280319733184641.P90 808 (8) 203617.P236 812 (4,28,116) 562943995510177.15902347075274017. .116248663016701150509115828530608561.P137 816 (16,48,272) 959617.597149752187286607489.47192818771332809681089. .48734995441023943825153659548266541432641.P65 820 (4,20,164) 141041.11109333761.210085224303959163308751601. .3017866802599074997815107329034839893699457097851521650341414241.P88 824 (8) 19777.88993.38525979266360291610293571395929675314692801.1495445230\ 830109056355367701442241158261174462204772324328494218855328820961.P118 828 (4,12,36,92,276) 1523521.257952400029937.P139 832 (64) 3329.310379797028432711386895309334277387365875751630693121.7177\ 625770836221802329556076335825436096998008269681541802483819859969.P105 836 (4,44,76) 2368822395648721.3040124117151617.1128504950062383934670257. .4874817679895432896846666951961529136332446906956424\ 97294447279200078757956580209.P82 840 (8,24,40,56,120,168,280) 13441.4841172001.1586308510081.P90 844 (4) 91185761.P245 848 (16) 528209783809.3408818505565834978224383921527937.P206 852 (4,12,284) 13633.31141397544886408722636686759644216932367969.P121 856 (8) 1489441.229634869879668984791701633.371738331695243321977\ 108382044919572516026026284025337809051528873569.P155 860 (4,20,172) 557281.2692128880536332668967640948426044706987955\ 16716194332265336979146008021202787273766958767916961.P102 864 (32,96,288) 1718990209.8148919324033. .672915391135935402269916482777538049.P116 868 (4,28,124) 334853569.71153008417.15174698834406721.922626543715132033. .1042949211954459511633.P143 872 (8) 17547835073985096343806660481.P232 876 (4,12,292) 45553.52561.241378644784282665724224215269676274193.P126 880 (16,80,176) 32655041.374871146580481.36589369917525430721. .212669637382198127520411474271156481.P116 884 (4,52,68) 17681.572833.3327377.5882010302757468387457. .507503808182829478517537.1521590246367016260256977648481. .9490550620859983699756004482528532989220017. .459988434780718651547146575150088880586568119521.P49 888 (8,24,296) 1079809.1174047124321. .129887637532703885175569346500164339384596481.P112 892 (4) 267601.1391521.1345517777.P247 896 (128) 10753.48919385089.39257233394241687553. .328516339886958171419482857961643272193. .12914340854285079433782775726161803964147713. .77338582801985556033595814340666648061420033.P72 900 (4,12,20,36,60,100,180,300) 5807380901690048305970962748462547129404401.P102 904 (8) 3617.65089.10149175069282879921381147267876162392883116313876609. .18788185774027111039998143598614758953756098325463867051830\ 0213840692194351709953.P130 908 (4) 83537.102784730161695117416749782411470938087584550917384\ 90812210128381632640553809934883069084182177.P174 912 (16,48,304) 32833.299137.174535138510980012221761. .107464447084600919847454485663361.P109 916 (4) 24060283912401409. .9176027840820822557769652003161198049458738352529.P210 920 (8,40,184) 18401.66083546765982085951180190942752889927681.P167 924 (4,12,28,44,84,132,308) 3697.1027489.97374817.39522602650168177.P111 928 (32) 189546985765489533095169829108497477761. .4971141705173876156149290559555016352907777. 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30977.2555521.204452543956321.5588918964965108257. .3254976976165960099872801486011429794721.P182 972 (4,12,36,108,324) 26232337.13655624113. .1581214773543289355763694808184205062516817.P136 976 (16) 361526017.21251836487537653646842236161.P253 980 (4,20,28,140,196) 7841.35281.141121.4653041.60893281.4387897103521. .1463098735252025076064552980991019750718115268401264794574977\ 849375291943201.P87 984 (8,24,328) 349107457.628217089.30220180022953160453457856387777914721. .738313998235889565301599572531640626810525425999201.P87 988 (4,52,76) 189697.167659649.1482371489.6450973392449.9931868988289. .4645115103442161869804915570014378786825822382803505847361.P154 992 (32) 5201080300033.3085397990461441.53497190411184131713. .243889001786361258243254488269457409.P206 996 (4,12,332) P198 1000 (8,40,200) 76001.42144001.293543676001. .4728377214827208130517802311270133709042152454873053138954405100001.P151 1004 (4) P302 1008 (16,48,112,144,336) 423319681.494077391563970390335488001. 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C311 1128 (8,24,376) 1078369.7341898433044801.1382837215006958457741227\ 94906574976887904939982079412885536147948742638438410963841.P117 1132 (4) 275814838289.362073730366785443780868881.P302 1136 (16) 9168689293924594269435012699390053650369. .1131310334243254039205306375735433068430199247442881.C247 1140 (4,12,20,60,76,228,380) 4561.P170 1144 (8,88,104) 25744577.377140193. .276777703130280383457507979001481922404156098842053652904857\ 26373353875777888031723996905090723042311377424248182532641.P155 1148 (4,28,164) 30645407522290070293105505369518259537.P252 1152 (128,384) 18433.27733723987969.87706468640521797294901519524699649. .24616619374763459476215125737554777509377. .154271541316301150598792104029544235059675368229377.P88 1156 (4,68) 17*.41617.295937.83736716905921.31148444724976529. .2428691128313288513.P268 1160 (8,40,232) 977403570406117601.841464143582829714489281. .57281536092725157009193935521.P200 1164 (4,12,388) 5106360913.265523238370190187626688601808496584295502513.P178 1168 (16) 4673.1137948235396559809. C326 1172 (4) 9377.1345457.91433799750097436823339479719705770866646653617. .1019957463112831021365901895382776919153462973115503801760177.P235 1176 (8,24,56,168,392) 3040410389842561.5091542821206332688289. .21566694047156190030012960957098417375263164101421409.P113 1180 (4,20,236) 89681.141601.1250801.13083841.106827761. C249 1184 (32) 9473.1202741777537.414581855009107748596797028667339521.P296 1188 (4,12,36,44,108,132,396) 427681.59008134786334273. .277122598884572475987115421160411960915959497148103077473.P138 1192 (8) 255373980342366346612993.P334 1196 (4,52,92) 38273.14536633697.36919357139916161. .14755410932634657950998395089.1757744807679263833464910204577. .122255024596887310384016956082161. .745018840057202679212337050466123004340421006181108061275128\ 05905183882417313.P120 1200 (16,48,80,240,400) 9601.57601.17963653814841601.P168 1204 (4,28,172) 143458096872740846324792491674119024317255853251377\ 548782956597898585042428782180238586900730976613828960167089.P194 1208 (8) 53058511043237064262021661839681. C330 1212 (4,12,404) 9697.19736209.14754644078936966997167297810257009.P196 1216 (64) 36713210266033084673. .16829646106971151773253785496003719032544890827599795902421932801.C263 1220 (4,20,244) 12294601705273841.1285442435618444321. .30825434422026210881995856862005846631120241408893281.P203 1224 (8,24,72,136,408) 88129.315767521.224117436817833122635777.P195 1228 (4) P369 1232 (16,112,176) 17918209.189461892929. .35939315303631714477656355791486195918024248929618665\ 427939817638380283293352168933810182743888510535160829249.P161 1236 (4,12,412) 55089582063217729.175922724879833801876767153.P203 1240 (8,40,248) 2999613197483041. .9946503085473405360990336611997601211388886737839388711521.C216 1244 (4) 8778793553.721315994374961.913021421136907457. .496556598069752920725106299217.49913495347567462875776350270158241. .3987717750391427576949100850346153089. .3948166195504073867621862733925025361018857603794686129.P175 1248 (32,96,416) 129793.46270849.11601852289.P209 1252 (4) 5009.57363423644587057.2322175421309476510423241413989040437697.P316 1256 (8) 2024020769633129857. .4914060388472339641563884985215767969679703073.C312 1260 (4,12,20,28,36,60,84,140,180,252,420) 1325521.1626833408812908876721. .164861463278712334259867127702044401. .517496882214135484318298195143896326867475066317761.P61 1264 (16) 329206353952848706811958574981534811137.P338 1268 (4) P381 1272 (8,24,424) 20353.P247 1276 (4,44,116) 91873.5758764536429511022083665050905453386595210401. C287 1280 (256) 46454107161999112389551048616961. .272693971663300508935482867377449426442211453531320321.P224 1284 (4,12,428) 489620017.972936622655226027963598183896961. .3698721685503753021667958012760324601233457. .2350070806566007537212483298946577228993997211640202078666761\ 203863322737.P99 1288 (8,56,184) 40579022177.60249667297.9475763944193. C284 1292 (4,68,76) 1685694802571764886364908561. C320 1296 (16,48,144,432) 19232916593977294668066826822875947264358174529.P214 1300 (4,20,52,100,260) 15601.3249204401.1065641262401. C264 1304 (8) 41729.182561.551211233.2375675974817. .866699144004607044391105873409.1009265556630019597369833113200513. .9617997238102022519689487090034503489. .423106743593648082893456540426613278392147965775916968873158817.P197 1308 (4,12,436) 20734622338810273.24474386178031119073. .40290733590328136833.2331066870511508315059441. .5823175598896708439732353.P156 1312 (32) 834433.19034121981403464536723761537. .3657003460847662581700804008093645073320255617. .207341062192971854960946370685751813280155469727779633794433.P247 1316 (4,28,188) 224246401.151222684250456561. C307 1320 (8,24,40,88,120,264,440) 5281.P189 1324 (4) 15889.1085681.21389674513313.151558949287297. .321943136214091371087779100552582451645857521.P316 1328 (16) 15937.339430154689.1028919454842049. .663490630862181023420758843785056257.C329 1332 (4,12,36,148,444) 11734408513.1235389890817. C238 1336 (8) 109857033950628973150800380121227622775122904993.P353 1340 (4,20,268) 33816241.315697468705819691433121. .8379135588241068973866938677441.29344405793450716055849948712161. .54611808610264716700701431903437080334321.P184 1344 (64,192,448) 5387325834626133514293589977531031297. .385696940783544781329735534184960751617. .14626619556055952174977504851836542140514285626239233.P104 1348 (4) 847962097.5114319759089. C383 1352 (8,104) 3060929.1775181409.7567946458979297. .39381089758445222653815549931743674647246452663111774593. .224075294194274540787541346917961848561395152873262751915912673.P227 1356 (4,12,452) 2712001.10571377.296545202124959454721. .1277537788636552540982059137487496999953.P197 1360 (16,80,272) C309 1364 (4,44,124) 16369.43649.P353 1368 (8,24,72,152,456) 109441.6041089.19803169. C241 1372 (4,28,196) 120737.18159793.400190449. C334 1376 (32) 3412481.70632833.22988345528310529.30449592423592235219030401.C349 1380 (4,12,20,60,92,276,460) 5521.16561.2395681.11499390961. .79147863202801.P174 1384 (8) 166081.112392313590113.165888988402561.1130582443252921249. C363 1388 (4) 16657.38938258001.10419650035703431085434509603569. .2128624865611329552201767855218537390462844129.P326 1392 (16,48,464) 89968528708490689.44672273546342737921. C234 1396 (4) 150769.6345222049. C405 1400 (8,40,56,200,280) 93066401.360331676468322643689649236464624801.P246 1404 (4,12,36,52,108,156,468) 14927329.36926447460343894713313. .732009799939394109285121940575374755233. .426915135438219598953984172992825321563121957413655736970004\ 44731897344532925494493563827601.P100 1408 (128) 444929.1233948474881.72386545356458958441346486331202082817. C330 1412 (4) C424 1416 (8,24,472) 96289.339841.2367553.1025393569.7815096876193. C241 1420 (4,20,284) 17041. C333 1424 (16) 73464178473865711374011713. C398 1428 (4,12,28,68,84,204,476) 144598154737.55749156739155447169729. .134578544817069262026899085835531465410289. .35670942157302652690824989897487529464738030858042402149021099984593.P89 1432 (8) 6925153.493203713.3152147041.53170668669989158433. .31141417202523239066281921. .354775289898905593932150334645351022670042846079241734834753.C299 1436 (4) 8785395480624879362557878359873. C401 1440 (32,96,160,288,480) 252581761.40056698881.35884034243486024947201.P190 1444 (4,76) 196605550033. C401 1448 (8) 314001128134468111824455232504871308929. C395 1452 (4,12,44,132,484) 2366667073.5918889924569758753. .59850626154206877620401.P214 1456 (16,112,208) 19050263233.33203532563859841. C320 1460 (4,20,292) 696379121.301173880801.11407110975530515104534161. .14759145067968270674284288321. C274 1464 (8,24,488) 5857.2969311774977959129473. .6576107482805565289874247249078721.P230 1468 (4) 281857.340577.72619727988621969228350881.P404 1472 (64) 11777.264961.154152996205287066617033473. .33523098516168294853846224641.311940413960313330194586438395946497. .221201329058694006864983554072724303142401. .134933628653476835877432928792686879910590214913.C236 1476 (4,12,36,164,492) 214823440200271172402069669377. .162726884987944204692194507612497. .253639160276610397544490375560432707531550357712107617. .15434563476720136031059798009276436468876399950688480593.P119 1480 (8,40,296) 17761.1781921. .164893484452858108324961802167006983685183459002021441.C284 1484 (4,28,212) 43435558097. C366 1488 (16,48,496) 17193026944897.910741555888885464195459083203264897. C240 1492 (4) 35809.102516249275294547005951333267300657.P409 1496 (8,88,136) 11969.45849409.565883213281. .7045504041426796507803878045324031333440285921. .275120770238627380664222522110420663985709447552268075723169.P257 1500 (4,12,20,60,100,300,500) 271191084001. .1261828167347816850332890667592001. .490085601781975781872492242606604272001.P158 Table 3- Factorizations of 3^n-1, n odd, n<850 n Prime Factors 1 2 3 (1) 13 5 (1) 11.11 7 (1) 1093 9 (1,3) 757 11 (1) 23.3851 13 (1) 797161 15 (1,3,5) 4561 17 (1) 1871.34511 19 (1) 1597.363889 21 (1,3,7) 368089 23 (1) 47.1001523179 25 (1,5) 8951.391151 27 (1,3,9) 109.433.8209 29 (1) 59.28537.20381027 31 (1) 683.102673.4404047 33 (1,3,11) 2413941289 35 (1,5,7) 71.2664097031 37 (1) 13097927.17189128703 39 (1,3,13) 13*.313.6553.7333 41 (1) 83.2526913.86950696619 43 (1) 431.380808546861411923 45 (1,3,5,9,15) 181.1621.927001 47 (1) 1223.21997.5112661.96656723 49 (1,7) 491.4019.8233.51157.131713 51 (1,3,17) 12853.99810171997 53 (1) 107.24169.3747607031112307667 55 (1,5,11) 11*.1321.560088668384411 57 (1,3,19) 229.248749.1824179209 59 (1) 14425532687.489769993189671059 61 (1) 603901.105293313660391861035901 63 (1,3,7,9,21) 144542918285300809 65 (1,5,13) 131.3701101.110133112994711 67 (1) 221101.441019876741.475384700124973 69 (1,3,23) 277.2461243576713869557 71 (1) 3754733257489862401973357979128773 73 (1) 11243.20149.15768033143.9460375336977361 75 (1,3,5,15,25) 601.9601.2098303812601 77 (1,7,11) 51457561.7151459701.76831835389 79 (1) 432853009.392038110671.145171177264407947 81 (1,3,9,27) 3889.1190701.12557612956332313 83 (1) 167.12119.1036745531.950996059627210897943351 85 (1,5,17) 2663568851051.862970652262943171 87 (1,3,29) 74821.32234893.150224123975857 89 (1) 179.1611479891519807.5042939439565996049162197 91 (1,7,13) 4011586307.3745603812007166116831643 93 (1,3,31) 1117.26273701844015319144827917 95 (1,5,19) 191.78958087694609321439660131899631 97 (1) 76631.2549755542947.48845962828028421155731228333 99 (1,3,9,11,33) 3186217.12812432238302009985937 101 (1) 33034273.465092326319.50316775668019759306202964023 103 (1) 6957596529882152968992225251835887181478451547013 105 (1,3,5,7,15,21,35) 421.6301.1616161.26751945361 107 (1) 50077.229837.48965028505045123993421250406516036571557 109 (1) 1091.521402591.3499901929.239789806103.10624346875389299603 111 (1,3,37) 18702169.119779213.6962353413269964253 113 (1) 227.1583.2172539.526256453012063980796131127321354599535039 115 (1,5,23) 1975931.6273542442241.52370346649565455417091 117 (1,3,9,13,39) 4162861.1846794457.2821964307371847613 119 (1,7,17) 239.44626806191326911791.397881837642577477902049 121 (1,11) 11617.3981923614021.657890411545272648205502849240259841 123 (1,3,41) 51169.1999827817517387044561568810795329 125 (1,5,25) 251.358291751.14781691751.391632555001.989947158849251 127 (1) 5843.681229.21520151.76082653.301515315752300874236564235591357673 129 (1,3,43) 4129.2199072289.912851565662857110894244969 131 (1) 263.605199588591144003100881306574406851660288427740394885828171 133 (1,7,19) 8757948941961838067.257513776243156826379279929309507 135 (1,3,5,9,15,27,45) 541.53825041.773618132427345151923061 137 (1) 4933.217629707.108081809773839995188256800499141543684393035450350551 139 (1) 1669.5430731.P57 141 (1,3,47) 161969595577.2031161085853.165301473942399079669 143 (1,11,13) P58 145 (1,5,29) P54 147 (1,3,7,21,49) 47041.P36 149 (1) 7451.177941761.P59 151 (1) 1511.6263783.64745079361.P51 153 (1,3,9,17,51) 6213394261.35106034213.P26 155 (1,5,31) 311.3586225081.P46 157 (1) 9421.3381925092493.9891109125337566719.P40 159 (1,3,53) 712550912937217.P35 161 (1,7,23) P63 163 (1) 5227348213873.8882811705390167.P49 165 (1,3,5,11,15,33,55) 50821.P34 167 (1) 58451.88177.1767863.10063060897082377.P48 169 (1,13) 2029.163264150141.P60 171 (1,3,9,19,57) 119701.P47 173 (1) 347.762239.2125048865543.P62 175 (1,5,7,25,35) 109201.1430128198787051.P38 177 (1,3,59) 709.2224898159852613649.P34 179 (1) 359.56207.100957.19510643.291066066130451.6779963644378513811.P33 181 (1) 90863.890159.P76 183 (1,3,61) 733.97806913.2421854958301.P34 185 (1,5,37) 2221.17761.35521.146891.228082801.49804972211. .87841814842081.1654235911196704741 187 (1,11,17) 6359.1272753542934479.3411926755457243.P42 189 (1,3,7,9,21,27,63) 49888641454623789553.P32 191 (1) 383.311713.9593931911.P73 193 (1) 6563.29723.2346066378779.218246094772601642186973037.P45 195 (1,3,5,13,15,39,65) 2341.39838501.P35 197 (1) 9851.741019334164502879.11472574961994477441469621.P47 199 (1) 1360648969.293366430131930353811221418233.P57 201 (1,3,67) 1089421.P57 203 (1,7,29) 2843.735673.P71 205 (1,5,41) 6971.31981.P68 207 (1,3,9,23,69) 829.1657.4969.P54 209 (1,11,19) 419.2927.99381983898121.340838185560681043030809047.P40 211 (1) 2111.962188370639.54046656969013.5676687374958905209. .1695949409060064182746451.P29 213 (1,3,71) 5113.22716867932413.115264393627813.3613512804721129. .89665588664737776553 215 (1,5,43) 8477881.14491125481091320910774351.P48 217 (1,7,31) 20399.24040333283.20545698698839917414079969.P46 219 (1,3,73) 135781.P64 221 (1,13,17) 443.P89 223 (1) 54473097204950819531444809.P81 225 (1,3,5,9,15,25,45,75) 116101.875701.286870274711101. .515009259868501.119634969443826601 227 (1) 19907051929.86695423725589885803695742296342497463.P60 229 (1) 8047106008391.32356561399076305309.284663996630519253661. .634538541879036040523.P36 231 (1,3,7,11,21,33,77) 3697.73155606217.P43 233 (1) 467.27599172691870182517.6354979252162209284471. .38247482016765032274959.P45 235 (1,5,47) 5171.11321831.1287586151.30168205545535224185322498361.P40 237 (1,3,79) 37520893.52802131282482966001751707837.P38 239 (1) 479.17209.43301964055635533333945745533106128044213.P67 241 (1) 553788718707122198751861425724478919.P79 243 (1,3,9,27,81) 70957.6627097.21835473162448454819220238921.P38 245 (1,5,7,35,49) 32341.P76 247 (1,13,19) 14327.50427403417.85336889516918333646696709.P63 249 (1,3,83) 35882730354181.P65 251 (1) 503.5894996162509148852365257446042626007.P80 253 (1,11,23) 23*.38636905168680714294388463.P78 255 (1,3,5,15,17,51,85) P62 257 (1) 120277.1329772662933524112502310453951741137.P82 259 (1,7,37) 2591.18131.P96 261 (1,3,9,29,87) P81 263 (1) 53653.78901.2750510656513.65397307474141.153572905037740933. .352436749324038579121.P52 265 (1,5,53) 3181.18474777940736174884324451.3449313707942322494318140511.P43 267 (1,3,89) 850666273.2270061722000879968839976583683542421.P39 269 (1) 10223.262007.116075653.76305384036997.299470647963251.P83 271 (1) 3253.8916443.490543245624181.2709600825365281117.P86 273 (1,3,7,13,21,39,91) 30577.1636991658121.2148920356182437964673.P31 275 (1,5,11,25,55) 121083372541491664042201.P73 277 (1) 15801743.478803193369.P113 279 (1,3,9,31,93) P86 281 (1) 563.3373.422063.434989.1000081249.38012519036699. .124205327610431.543615007915184215523.2397212236344676495763.P38 283 (1) 133227911.1830824353.306487563493.1257602943398454563.P88 285 (1,3,5,15,19,57,95) 5731756981.P60 287 (1,7,41) P115 289 (1,17) 44507.1088953.P120 291 (1,3,97) 189733.1693621.80640757.184812684901540537.P55 293 (1) 587.64911612051881874971.P117 295 (1,5,59) 739861.311834125441.1243704975397142761851514391. .15800757982738113728531939755751.P35 297 (1,3,9,11,27,33,99) 1182737161.7899901813.370231459035769.P53 299 (1,13,23) 599.10997221.2886381073947332989.8661965714512154562493.P76 301 (1,7,43) 8127001.921928537909.31575110690775101163983809. .2954696283347370339434959009.P49 303 (1,3,101) 1213.464114346100971670261030354878981449019613.P51 305 (1,5,61) 65881.4919054377091. .46229214937048975901175732207117334435811.P57 307 (1) 10610542242923144869.1209358403350153553775181.P104 309 (1,3,103) 1237.16069.P90 311 (1) 3733.12460588823.873069502041694941443. .2241207330424850668586082361185081412667449.P72 313 (1) 2370037.3759897752153653302941126019779. .2714675534408576046409316982151068303918417599.P67 315 (1,3,5,7,9,15,21,35,45,63,105) 1571221.P63 317 (1) 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.796194432733702765888273847295538921929584539713085866730191\ 025204220333995274021244744735757.P121 595 (1,5,7,17,35,85,119) 81010441.3200519281.52864515971. .20036793671274541049376611411.115460168265259575622411758906553741.P92 597 (1,3,199) 73783203733.6630293477484412123587586871701728361. .8845057746607360101578544062042919811228803419862160327100045773.P78 599 (1) 15214538903.1666033953246993576905689.11621341565257598111021473. .463863815296317703220841922489739. .230941609196548964668124778957274786501. .116299206023397239536920319253925869667382606684529884846610766493.P90 601 (1) 6011.31857353131462393. .280046742341301374601452645724586373020825738763.P219 603 (1,3,9,67,201) 31357.33769.1702811701.963047351557. .266307354039135126408248940363638835557679301537.P112 605 (1,5,11,55,121) 11*.81071.1719364021.38532276146138797331. .16285121142249140363782108952956635196636630939017731.P123 607 (1) 208641411491236893484569888975245275945563278937764828427599\ 0116236503745140234728069.12046340825596705357813590815824534\ 7326036064518355187873832329408825869652943374488400197042063.P110 609 (1,3,7,21,29,87,203) 2947561.2138662632071226913. .50984930600938790172697.P113 611 (1,13,47) 15887.5633044847.15622035118631803488169965683. .14652399720340093144861352182330341522792941892683758508113. .148124731897154772276007161850713728099461071853774468033248\ 6194431404731.P91 613 (1) 35867857.125767661050875899711673820825004978972209227067\ 54617137551337648697116651.581189849342670845367685359961169\ 1179515668328823829098222844315911214677609956453.P130 615 (1,3,5,15,41,123,205) 1195561. .1362086797533369884718343037628515311025580176953784595301.P90 617 (1) 23447.252971.21406199. .214537793439643816124780926036091276945983139818406753860958\ 01022765877021158226660366476107170680628980781413.P168 619 (1) 13619.36443481348671.2257167262279770349.2722459891306289377. .18122224759963741448389856152540213. .102564444995826502188076778511448395487416397545958056216657\ 6116105880032424703194472669270283003.P111 621 (1,3,9,23,27,69,207) 8860429.301565425726996051177. .56037810170128607485215702998215395873753992381472041909493199033.P97 623 (1,7,89) 74761.560701.31913270330707901231027. .475552928682489844878157117590197779889392360367260432663689\ 6937028373650349418725336389852293.P125 625 (1,5,25,125) 667501.1880420669727399359827972501.257221971817\ 419112385228087519202709483833420607221254579502990135771251.P135 627 (1,3,11,19,33,57,209) 930469.1020265053327423164430942961. .30858021902523758046526993873345823027038680972853.P90 629 (1,17,37) 1259.227699.376871641.773035969. .31744304162022751798457757193.P221 631 (1) 6311.7573.22717.362915751904864153.P272 633 (1,3,211) 909618469.7850096263354171306561.89432834207930016969865153. .134038349588501254917347232008642911432722662713.P97 635 (1,5,127) 176531.321311.502921.23804881.92982698379603421. .142177842707433961.576026039706498031445759844248008573861. .20685345700832613746274200712813873539005195191158701.P92 637 (1,7,13,49,91) 1136303533.820770941835878611943. .243623717900486910364294705088687355239523600716372588911426\ 7732351631395223998169289.P127 639 (1,3,9,71,213) 2557.7669.499396023937.8141739904937449.P166 641 (1) 1283.24359.306161625407724378078632597290743103609.P260 643 (1) 7717.169954143652402656485399.5032095621171876450363150843743. .90409139288880820194533925917030434583969676709199.P199 645 (1,3,5,15,43,129,215) 59341.8871459380575801. .13433188106347598163359915928450709921. .2751196228592109040664179235751038501334842281.P58 647 (1) 9059.87531337.633889439015543. .442835641420911902056735643278356653800144245791.P235 649 (1,11,59) 989909317.673916750371782811556809634401. .423327054245128002718171385159536210624237. .3175352444333493765540976162522161114881431751. .15085422068047701255996957660890445982732633519169170463921377.P90 651 (1,3,7,21,31,93,217) 140617.4606477.103910017. .96204592550401464761305884120719794990493457611613148273892749.P91 653 (1) 1307.634717.166588056729719. .507216328436780733648194592905005673693190657627218143170902507.P226 655 (1,5,131) 144410471.41455160705149024808959921. .124776134253343847813100968236583197728589631926088904912454\ 338154751.P147 657 (1,3,9,73,219) 58791747493.2232469550996803671785172991162280\ 58686491827406406309030993178576248812126197773842306861.P106 659 (1) 1319.5825636900029.642909136700440706267.P278 661 (1) 1350527799835192133627989406820628982952430766061042016995048836527\ 4010879719287362708336006737159624171665013560405953364074451436173.P182 663 (1,3,13,17,39,51,221) 186130617349.P173 665 (1,5,7,19,35,95,133) P207 667 (1,23,29) 310823.55455709996667.25359506465081394537400918368\ 811516993503730623239065990152596258171619851.P202 669 (1,3,223) 2677.1167176831079433.3667711380899203564933. .114913570893607451412008904866479302563550673.P128 671 (1,11,61) 8053.178487.1144727. .2606324493303532053608289430528064074821722730167300919990985239623. .159359711977971169252437621024150165719389758928289445369218\ 6236411741424552809273.P124 673 (1) 1826415879755569.4989166368238892867.15964393398656515639633. .162738636085359957907179241.518665099640854360708523609062187.P206 675 (1,3,5,9,15,25,27,45,75,135,225) 78301.523801.5942701. .218043503399624494149061014280065604327642958243101. .5555502683936822447877092421751037648181820879664401.P53 677 (1) 33851.995361959.83719264139843. .13904875444170081312886859407682609699.C259 679 (1,7,97) 52744375069. .15429185464286114084387233548922359713063387872327389102407. .171880680582803196467937580463901202087996694143877438226389\ 06947567117417.P133 681 (1,3,227) 1791237612385377222291559361027754240802604827168374\ 6540522410033644069.12975992332195311515032550352808183815637\ 69714974946578770599377350713429.P74 683 (1) 1367.458977.13703228398497002085953147749859. .5909738323741694703472816799172371. .261799592113054020351183694832455820746063852477087766532721\ 6483793459.P183 685 (1,5,137) 1422061.5507401.26636505319811.661718838635930238791. .15761953912526059950422004668720291591.P176 687 (1,3,229) 104596370587621492079662718881133512822715626369034\ 4876782164668343294332064615217521.P134 689 (1,13,53) 299027. .23592166751590360527440683737835798740484621759417217676978473409577259. .665554211022426646678290670438853987603149396421139066795285\ 4822969562839982865805775365958887727.P125 691 (1) 927323.1955531.5411865319014896596957. .3971992653480423383454086803739.C265 693 (1,3,7,9,11,21,33,63,77,99,231) 8480390689.103600005401243737. .18640970977551223539934315621. .159726751678525658083898531371647932938681.P76 695 (1,5,139) 94191961.35725129090801. .1415085487923782842786280300887039057567659793736322663601.P185 697 (1,17,41) 59178594023.2959203620981339831579891. .9738355430515256541615925389673.96304834198087802152015096471381. .72974630467126217381507259737866919.17934107564634692987281\ 8144036158918210212564023529819586742149111386081.P101 699 (1,3,233) 2797.47533.9189420277. .2792368585835176722591243185969983351503354217.P158 701 (1) 25237.33228803.733483315139. .23637385035979072308469324277209913925678054439921. .14495974396253094510975132408526029375861043561244873539909249873.P197 703 (1,19,37) 388057.1923409.444045733.62000138226054796871. C269 705 (1,3,5,15,47,141,235) 16152584934361.1792516326188661389059561\ 1153971449075737880597365455065081252926739721.P93 707 (1,7,101) P287 709 (1) 354698521.4520530117.26754546073.356905407983726281. .274491592643873035641589597480400693593.P254 711 (1,3,9,79,237) 119025204703201.2343447081818929.5428379240564473. .3297217946493332412969462353064559561775620666597919718037.P121 713 (1,23,31) 1427.18539.5484397.82776117708507944145134008991. .5247548284951598026728082817296120340053. .3746121650449359706373304838111671353932176369894346189979.2018991\ 70515693330875562714316614363610229288846992326512304705165161183.P104 715 (1,5,11,13,55,65,143) 10905024958974646501. C211 717 (1,3,239) 2457614587537.4981944496429.75933466677818671998613.P179 719 (1) 1439.17257.221502813314677.1356659247133798853032285643723.P291 721 (1,7,103) 72103921318784818532825738663789543.P257 723 (1,3,241) 8677.64739815339484841937. .15779202447007574212358914303778883757. .844419612452198561310720080038799341972811718390811373415844777.P105 725 (1,5,25,29,145) 1451. .388560625903893405394183616138892653779673583851.C217 727 (1) 15720604856068681.17084413231256940122269.P309 729 (1,3,9,27,81,243) 17497.58321.1069604540569. .22042143919397906169295955942862036796712960201837095878188469841.P147 731 (1,17,43) 83409037264696307690489614635052488166993297850365365503.C265 733 (1) 7331.16127.104087.124228877555650115560077697921014551. C302 735 (1,3,5,7,15,21,35,49,105,147,245) 87459121.58770727715103776715586741. .536827955723741125410788967206335237321.P88 737 (1,11,67) 19163.204887.247633.1275011.9880223.13071433. .7762468739681282321710292584571107363763. .10133404298009476405834536689923299291429889.P197 739 (1) 9735769273.813734950283.34025089913861723. .335842527291577270615983746819.C285 741 (1,3,13,19,39,57,247) 50473626669819633853.P187 743 (1) 1487.25622686553319767. .184299732531199558664226573204873006690059.P294 745 (1,5,149) 1509371. C277 747 (1,3,9,83,249) P235 749 (1,7,107) 1499.27190199.415172831125016176415630197. .26307391311402430728807244996438212113732710366151.P217 751 (1) 3343453.166253377.178550628538635458028047. C321 753 (1,3,251) 17775396313.30059927248728405764106073. .520007425071396254516306885057657287480573719509149.P152 755 (1,5,151) 128351.996601.269285504605310607656292706151. .125233030892411130707398670330756708512594441.P202 757 (1) 2178647.2295116507.4727951545470190522572692113. .50970551620807604645290420443828540446885807.P274 759 (1,3,11,23,33,69,253) 6073.10756549.6077994827105389.P184 761 (1) 1523.785353.38103366758871952617829679.P329 763 (1,7,109) 186315167566010423435402943151338110617. .47372539533051908292098380985414473149036630999230923666194\ 209007162889039429902848314341365007150628451.P168 765 (1,3,5,9,15,17,45,51,85,153,255) 645661.10746721.1117636388614441. .154100434621689901.25628738622818419801.P119 767 (1,13,59) 2818195499922245091642848978466851. .206670308843964099321679340844065707921597.P258 769 (1) 18457.193789.25480224409. .54881494789070208618554690004702274737120782891528221.C294 771 (1,3,257) 3238955581.116965444865451934897. .2611299865258291465026074807769303661. .6349458818586896189136555241554887684748673593241.P130 773 (1) 9277.1016796969359. .51753676317054169356502097758181015861805520123259. .8011062057892989000108346044696281175092307195847153886977.C245 775 (1,5,25,31,155) 37201.10739917689782934291348634826555020368414408001. .842892156255345168709485040276035193507093677153879833802901. .109125541734620789876788035838290486275690601641331425299963\ 3936384614087001.P101 777 (1,3,7,21,37,111,259) 186786949189.2052507579193.25276528395553. .2571962138124987934147419817293123173577059740948079871281409\ 261069982357.P97 779 (1,19,41) 1559.88558709567.130573980779749846379. C310 781 (1,11,71) 17183.119231275967.20036085663335413410633417825853. .5501671635134375421799107392412853. .7780641680178781705992580957454350040047182204553.P205 783 (1,3,9,27,29,87,261) 404917489.169858473171317642672943936256\ 83460269476735735277751666822243599687323885567204561593.P147 785 (1,5,157) 1571.14864695631.42676366873743709945178446910641.P253 787 (1) 15507049.7536057013.73107419816149. .4249706276986205037627340907159.P314 789 (1,3,263) 22093.130616349214127317.81159138345801708673502600279778659\ 4389790262300032332414054489579398193937894052773397078884223596253.P127 791 (1,7,113) 28477.30059.87011.48705094117.10944936884154421. C280 793 (1,13,61) 57097.428221.74238033082234471784146014843792971. .2183282650517290924429932389219789617134601763. .16697555282285598006569362183247214662839081861. .281917997457114791804117679712996794806843175202151.P157 795 (1,3,5,15,53,159,265) 1071661.1085209497702518110561. .27761403088971444051151309071030241337789316419761. .2732127590150530354751609879787760711974002898685201.P71 797 (1) 550786660190498073424717. .263254579103211347551339254609213356427415299857034916163.C300 799 (1,17,47) 498577.5343603337.587161516717.1821157711385338283. .4341970587851670430963877293120273.P272 801 (1,3,9,89,267) 9613.20707561959708849649450349129973778946833. .3636712209590658267050316720358771765474393. .479337468384856700129542830220533158079469153.P121 803 (1,11,73) 1607.20879.155308992851. C325 805 (1,5,7,23,35,115,161) 146202491.1542547441.109263953863331. .11278228860607484309101. .888928305160400714160568240062438859169724984976952114684802\ 92798761.P131 807 (1,3,269) 3229.506797.21398413.70806348401533. .34294726714918734467346734317748796690437027460001752181.P170 809 (1) 1619.1513137421.73238445222097.157695593446805927. .326515135597401725879.2133031659325752941414443037439757.C289 811 (1) 601763.1000814022851.14313619299443.76828439544227183. .4422507277804997635333.C318 813 (1,3,271) 1939974097.33934730461823497549. .41508033675559782143165575329219407764100701. .1042774403606335073835442930974301177527151657123020368709330\ 822769249505467367390967373.P99 815 (1,5,163) 11411.1947851.240117261450671101828595941. .50695097759157169679058690449222615096542252614182711.C220 817 (1,19,43) 35916262161133.59346557047682110885478903. C322 819 (1,3,7,9,13,21,39,63,91,117,273) 42589.15110623722731585030128496057693\ 8795431700122305603092505382883434872121075258170857403261210300101.P104 821 (1) 21347.2147737.19492821175377849852264529.P356 823 (1) 974228888530699445757319146555496498314349. .4993306712740682373278028175457833409641267771297902870921089197. .1181944190217838168575602563426725286703053115907380051630816233.C224 825 (1,3,5,11,15,25,33,55,75,165,275) 9901.42901.4283401.P176 827 (1) 41351.1501511402042903676731. C369 829 (1) 4327010267.688966554873133029743.12897918757296422163419778877.C337 831 (1,3,277) 9973.30923173.319230313. .807232901286531227602895051093433509727524980513. .3131122261990047725614066743039336634526968903348045849.P141 833 (1,7,17,49,119) 1667.1321139.6147541.882502393357439. .731600836601677641719974561.P263 835 (1,5,167) 573583211.6056215202595841844608656745169717582811971. C266 837 (1,3,9,27,31,93,279) 16741.3220324021.28203521869. .668569787651590990235641. .9497711241696998009889385308110385421936694455438729.P158 839 (1) 333923.9171895546319811169. C376 841 (1,29) 4742519947946695589635026000017432593. .137749028800268059901893260035738603546333696165636274217.C295 843 (1,3,281) 7529980709303377343101.1961607248936156894207399749\ 78484659677332675000037899272468768902840697.P174 845 (1,5,13,65,169) 52391.22996301582734588067659428109043710321.P256 847 (1,7,11,77,121) 844758839.27934005037272181. .67585636091101553932390258037819591394495216143.P243 849 (1,3,283) 20964643592387707046170260467034488629. .86483147351848002945911917824786187338564603738561233898471715753. .1782481114990916299866857277299276034132781002181324568262661\ 835578218109.P95 Table 3+ Factorizations of 3^n+1, n<=850 L,M for n=6k-3<=1695 n Prime Factors 1 2.2 2 2*.5 3 (1) 7 4 2*.41 5 (1) 61 6 (2) 73 7 (1) 547 8 2*.17.193 9 (1,3) L.M L 19 M 37 10 (2) 5*.1181 11 (1) 67.661 12 (4) 6481 13 (1) 398581 14 (2) 29.16493 15 (1,5) L.M L (3) 31 M 271 16 2*.21523361 17 (1) 103.307.1021 18 (2,6) 530713 19 (1) 2851.101917 20 (4) 42521761 21 (1,7) L.M L (3) 7*.43 M 2269 22 (2) 5501.570461 23 (1) 23535794707 24 (8) 97.577.769 25 (1,5) 151.22996651 26 (2) 53.4795973261 27 (1,3,9L,9M) L.M L 19441 M 19927 28 (4) 430697.647753 29 (1) 523.6091.5385997 30 (2,6,10) 47763361 31 (1) 6883.22434744889 32 2*.926510094425921 33 (1,11) L.M L 176419 M (3) 25411 34 (2) 956353.1743831169 35 (1,5,7) 374857981681 36 (4,12) 282429005041 37 (1) 18427.107671.56737873 38 (2) 5301533.25480398173 39 (1,13) L.M L 157.10141 M (3) 79.2887 40 (8) 14401.128653413121 41 (1) 33703.270547105429567 42 (2,6,14) 2857.109688713 43 (1) 82064241848634269407 44 (4) 89.2382953.56625998353 45 (1,3,5,15L,15M) L.M L (9M) 387631 M (9L) 755551 46 (2) 12553493.70601370627701 47 (1) 16921.256057.1534179947851 48 (16) 76801.24127552321 49 (1,7) 857643277.127522693159 50 (2,10) 5*.101.394201.61070817601 51 (1,17) L.M L (3) 613.30091 M 129159847 52 (4) 2093124281.37644053098601 53 (1) 78719947.61557605176233223 54 (2,6,18) 150094634909578633 55 (1,5,11) 659671.24472341743191 56 (8) 113.19489.36214795668330833 57 (1,19) L.M L (3) 3079.53923 M 1162320517 58 (2) 12413.37945127666529000523013 59 (1) 3187.1108439448677340328268341 60 (4,12,20) 241.298801.26050081 61 (1) 367.86630432442539925437931403 62 (2) 1403808961.2860659169.9500438809 63 (1,3,7,21L,21M) L.M L (9M) 127.883.2521 M (9L) 550554229 64 2*.1716841910146256242328924544641 65 (1,5,13) 105919308797935444986721 66 (2,6,22) 13490012358249728401 67 (1) 5390821.4299412981246169975118907 68 (4) 137.6458150122561.3833564416504313 69 (1,23) L.M L 139.5107.132619 M (3) 9109.1476463 70 (2,10,14) 28596961.32839661.94373861 71 (1) 853.2131.82219.3099719989.4052490063499 72 (8,24) 1418632417.56227703611393 73 (1) 439.38488154120055537150068589763279 74 (2) 149.953861.142659759801404920771391593 75 (1,5,25) L.M L (15M) 26251.119101 M (3,15L) 2551.1530601 76 (4) 761.31769.3302353.278733912072436804273 77 (1,7,11) 56495392933101222275861053369 78 (2,6,26) 325729.271722723752757889 79 (1) 66361.327220181191.567239060331150635317 80 (16) 8194721.700984481.597747428754241 81 (1,3,9L,9M,27L,27M) L.M L 163.208657.224209 M 1297.5879415781 82 (2) 2088869.110767897.574933708017116710865237 83 (1) 499.997.2466097.813201725710097952736361977 84 (4,12,28) 337.673.1009.167329.2108826721 85 (1,5,17) 1531.224401.13271362257832586268931 86 (2) 173.470593.2641485701.55473422113.903239908009 87 (1,29) L.M L (3) 261697.37464463 M 349.142159.1383301 88 (8) 6922081.15656839738849.1363620137403810529 89 (1) 264331.1125706177.2444322641415331355533344283 90 (2,6,10,18,30) 176401.452808441334403281 91 (1,7,13) 8737.595141.2354116499281.2452788561133 92 (4) 1289.743170846305411756447828504941347481129 93 (1,31) L.M L (3) 88239050462461 M 373.541447.3058399 94 (2) 563838649753.125384283132205265785477849439329 95 (1,5,19) 39901.29574984661.25349956307509384561 96 (32) 7297.68737.96948097.70613232600577 97 (1) 459991849.503803759819.20591603926857377806745611 98 (2,14) 197.16661.251325313.426712077457.34013149495921 99 (1,3,11,33L,33M) L.M L (9L) 199.4357.337448233 M (9M) 397.378450588583 100 (4,20) 133201.18055139801.61459926512826500975801 101 (1) 379963.1017291527198723292208309354658785077827527 102 (2,6,34) 409.49637281.187668407555352123529 103 (1) 619.3661040653.1535090713229126909942383374434289901 104 (8) 1249.13729.475356961.780464337846444296785447886881 105 (1,5,7,35) L.M L (15M,21M) 24151.3369031 M (3,15L,21L) 211.1051.3454081 106 (2) 90313.609422621.1481588501.460740683381672021327601001 107 (1) 643.100153.4375617272295428356111030724847180250451293 108 (4,12,36) 2161.15121.10512289.16569793.3958044610033 109 (1) 1992772009.5933538193981.7696680097963.27866471458012723 110 (2,10,22) 177101.927319729649066047885192700193701 111 (1,37) L.M L 223.25709599.78539161 M (3) 64326272436179833 112 (16) 14561.45697.101921.643553.67765601.378369377.5685756833 113 (1) 362053.156472231.3626038130651680583578933430931295416667 114 (2,6,38) 457.2281.7753.3093009324389492947932121 115 (1,5,23) 6211.48991.4232020527831352569905247101633701 116 (4) 233.4177.277991360381003661564752468378981135693842991081 117 (1,3,13,39L,39M) L.M L (9L) 937.37441.6079786129 M (9M) 1171.2161927.43264261 118 (2) 19966781110160346782368664772328944885905284750420567849 119 (1,7,17) 7719769.1098440018152695917905622020432593239209 120 (8,24,40) 4801.13921.51383579021948491809121 121 (1,11) 727.2179.74779.256900099994436377787031292704214632407889 122 (2) 180317.262199473.39504363995133913.865923475887669700104067517 123 (1,41) L.M L (3) 40049539.130099576237 M 2337001.15606752580607 124 (4) 81516726600079249.21775844224805408923066692226998392022049 125 (1,5,25) 2251.100501.2278135721427929786778229917312351656251 126 (2,6,14,18,42) 1180369.475110761833.40226570408250073 127 (1) 22861.63247.52147471.13030796206528578864006320088875125740738871 128 2*.257.275201.138424618868737.3913786281514524929.153849834853910661121 129 (1,43) L.M L (3) 1651439941.28395735937 M 1549.27091.7822354593043 130 (2,10,26) 82669546937641.85515537811724373585467087637721 131 (1) 787.114742271896804438572098194909.881304930739946561320646289889 132 (4,12,44) 660001.11096576833.20431242370346923068097 133 (1,7,19) 11173.1084483.1256610601.295966423763788589324732476512991 134 (2) 269.1609.1877.11257.50546266229.719571227339189.P25 135 (1,3,5,9L,9M,15L,15M,45L,45M) L.M L (27M) 3511.487891.86548771 M (27L) 4591.451441.73321201 136 (8) 17*.5641553.23229617.2670091735108484737.P28 137 (1) 82093596209179.P51 138 (2,6,46) P43 139 (1) 26436515641.1113626506203380968993.P35 140 (4,20,28) 281.18481.369879560116990841.3353336738929580410561 141 (1,47) L.M L 283.93953407627827115729 M (3) 3798402051319990403467 142 (2) 3672239816477.9159751032889.P42 143 (1,11,13) 53197.P53 144 (16,48) 77826286120321.P32 145 (1,5,29) 59086051.25481953741.3159421788711031.76455796243959454561 146 (2) 293.18678646095653.86782247836514775846688349.P27 147 (1,7,49) L.M L (21M) 119471899.882757098511 M (3,21L) 7*.1471.3529.15583.200568859 148 (4) 410257.9537896093307601.31199592961514012689.P28 149 (1) 4482722618976860674653013440107317.P37 150 (2,6,10,30,50) 1201.55201.P31 151 (1) 472027.645979.135286639.P52 152 (8) P69 153 (1,3,17,51L,51M) L.M L (9M) 436357.133395235891527691 M (9L) 919.123343105382171675857 154 (2,14,22) 671352452318708161.P40 155 (1,5,31) 1861.33131555630426311.318620421994509961.121462982451478217731 156 (4,12,52) 309746737.P38 157 (1) 252457.159420524134654609.32129434337475049222622287.P27 158 (2) 317.10393819190815276250780568850989337.P38 159 (1,53) L.M L (3) 2769035095381770614187391 M 48973.395794533062864139307 160 (32) 4151768361337614527605197761.P34 161 (1,7,23) 967.1933.5468575720021.P45 162 (2,6,18,54) 82434619394313344569.P32 163 (1) 8483499631.4956470591980320134353.P46 164 (4) 41*.2297.32326369.P64 165 (1,5,11,55) L.M L (3,15L,33M) 4951.1286011.4968781621 M (15M,33L) 331.991.11123788282861 166 (2) 2591261.6956557366277.P59 167 (1) 41332144291.196098784741.P58 168 (8,24,56) 13441.P42 169 (1,13) 4057.351859.7336932438768271.P50 170 (2,10,34) 7674481.P55 171 (1,3,19,57L,57M) L.M L (9M) 25309.1676620643529235921057 M (9L) 19*.42509373931.102310358933917 172 (4) 226519873.21376165893692833.P56 173 (1) 993367.14427163.125330011023211.156026417563831897.P38 174 (2,6,58) 19437193.1388985225193.P35 175 (1,5,7,25,35) 23185675801.4260648635770037050051.P26 176 (16) 353.19009.62210098369.205188547169.P48 177 (1,59) L.M L 38926393657.363002702388730267 M (3) 76819.15743388547.1669126011067 178 (2) 1192464167514295068582330293.P57 179 (1) 3755779.47029186391731.9248363581047133.P49 180 (4,12,20,36,60) 116809201.2081711451601.P26 181 (1) 51043.715722801240612811884999961.P55 182 (2,14,26) P69 183 (1,61) L.M L 189223.6117064141.109870115206699 M (3) 279666823.64961725048119249391 184 (8) 112241.2057857.2190337.4475616001.79781171123090497.P40 185 (1,5,37) 10322251861.4183611889192231.55223513719943993551.P24 186 (2,6,62) 5853105289.1137273143641.P36 187 (1,11,17) 18177792435744585993179560027.P49 188 (4) 4513.2563193.P78 189 (1,3,7,9L,9M,21L,21M,63L,63M) L.M L (27M) P26 M (27L) 379.84673.30354157.60439117411 190 (2,10,38) 70578185345621.4975481820118441.P40 191 (1) 176349919.854888497.P74 192 (64) 280321.15687169.339601921.3167109739009.P28 193 (1) 167911.679747.7967041.32685391867.P64 194 (2) 389.1209361321548310091770485682269470852086753.P47 195 (1,5,13,65) L.M L (3,15L,39M) 54975287251.3785998525531 M (15M,39L) 419437201.56919999055921 196 (4,28) 342875768396449.P66 197 (1) 8714655511.24742960162351.49676157359100536013871955394289.P39 198 (2,6,18,22,66) 4401193897.3571691108833.P36 199 (1) 2389.5484043.P85 200 (8,40) 401.P74 201 (1,67) L.M L (3) 32563.1351123.301027886874675599533 M 275371.5931946571197.56755588835611 202 (2) 1189912513.69531972955397.96207837407260037.P56 203 (1,7,29) 398858013926743539066881263.P54 204 (4,12,68) 53958784909638588059956801.P36 205 (1,5,41) 1164811.6749930086876080531836671.P46 206 (2) 1522395676033.7625998476893.3276710054092300162911791926389341.P39 207 (1,3,23,69L,69M) L.M L (9L) 5724793.7671021268285255340377531 M (9M) P32 208 (16) 1614913.20634017.2763736726854088129.P60 209 (1,11,19) 8779.146719.227123983153149333776852194879434768181.P39 210 (2,6,10,14,30,42,70) 4201.7035101641.871383685710721.222665666643176401 211 (1) 892531.189250543.2645385196586430249915420486682565415343.P47 212 (4) 1079398849.1135214993571937.1331247175934064574966369960667813849.P40 213 (1,71) L.M L 210019.49682251.55126531.13055351529193 M (3) 12685215427.84569390002476091110121 214 (2) 582937.2827369.3096650621.481786776662041.499965737866229.P51 215 (1,5,43) P81 216 (8,24,72) 1155169.P63 217 (1,7,31) 1303.89839.174469.35258161.1023879682351. .70961158264970285776591.P31 218 (2) 2617.5233.P96 219 (1,73) L.M L 741973.P29 M (3) 877.P32 220 (4,20,44) 7481.15401.131561.P64 221 (1,13,17) 506533.278300881.P78 222 (2,6,74) 9769.4010575301861137.P50 223 (1) 19849231.249693347977.3619936401181.2784009098113351. .130559956932626998645445231983.P30 224 (32) 449.8513.31539199370561.1269624189254401.3356086147916993.P41 225 (1,3,5,15L,15M,25,75L,75M) L.M L (9L,45M) P29 M (9M,45L) 1801.16985251.697381651.1988005951 226 (2) 2713.798087896392921.P89 227 (1) 28603.31327.1533148921.28279305227149.75743328083517433389294793.P51 228 (4,12,76) 2842147681.P60 229 (1) 169003.4032176417327894814764968543.P76 230 (2,10,46) 461.5521.P78 231 (1,7,11,77) L.M L (3,21L,33M) 463.910237483.242613305580091909 M (21M,33L) 10627.1286903793030368825203123 232 (8) P107 233 (1) 1399.6991.P104 234 (2,6,18,26,78) 5589928324657.P56 235 (1,5,47) 717838945155421.1641374046359401.7061686540772491.P42 236 (4) 87793.66454972460489.79024015559441654878348076969.P64 237 (1,79) L.M L (3) 14221.2275201.P27 M P38 238 (2,14,34) 719575263747470241217.P71 239 (1) 14341.170647.42124768369936320790693.P82 240 (16,48,80) 3875067470401.P49 241 (1) 4339.281971.1837867.43195076631439.48557382169494007737217333.P60 242 (2,22) 34849.P101 243 (1,3,9L,9M,27L,27M,81L,81M) L.M L 487.59779.2051893.859270843.8638915776957163 M 572023.5062663.1319934691.116004991998176173 244 (4) 2441.123450337.740767954561.1206708060834097. .4100906420054031805880028751022497.P43 245 (1,5,7,35,49) 174931.P75 246 (2,6,82) 195817.336529.65765641.4221482364108929706493417.P34 247 (1,13,19) 8893.74154686428369.62568550770275094093451149019411003.P51 248 (8) 4002721.400317813041.P97 249 (1,83) L.M L 1993.57957241.9839624437.3511321676267937799 M (3) 6598368647023.P26 250 (2,10,50) 5*.3001.8501.124254307278001.P74 251 (1) 6936751667531821.2538098416666589323. .1037789051490064084073309914577355481.P49 252 (4,12,28,36,84) 12097.2153089.123922438035505085089.P39 253 (1,11,23) 7591.25918707093150367.P85 254 (2) 509.3049.10641077.P107 255 (1,5,17,85) L.M L (15M,51M) P31 M (3,15L,51L) 443701.214169911.94428036319693051 256 2*.12289.8972801.891206124520373602817.P90 257 (1) 1543.57039521761081.688337912506999.P91 258 (2,6,86) 1033.3496872198697.24265926794596097277813268849.P37 259 (1,7,37) 3109.44126729767.P90 260 (4,20,52) 521.10080658121.1037093029970883601. .901949427723250036534561.P37 261 (1,3,29,87L,87M) L.M L (9M) 5743.51679.2178829.16944904567.797319240844141 M (9L) 1253323.252929176627447.53670250194350899771 262 (2) 2621.P121 263 (1) 255637.2246021051782237.887168953916584879575348145255837.P72 264 (8,24,88) P77 265 (1,5,53) 436200603555041251.45023598003342782094423520012240471861.P45 266 (2,14,38) 144173.17837429.7755867337.719738936617.P69 267 (1,89) L.M L (3) 1069.2137.P36 M 59809.64995477807679.748414146903737647116457 268 (4) 3217.220876757609.3303153326731482337.9848734625069351700096193.P68 269 (1) 61333.24957410917727872704602454775227215502551784969894669367.P68 270 (2,6,10,18,30,54,90) 150612481.235234345635395687521.P41 271 (1) 220586933947.688981583287.1940450784379411. .2316988319537740538182118778939772220401.P51 272 (16) 8591440291969.30138863687125057.3016794653198205857. .6168271395328887598987777.P50 273 (1,7,13,91) L.M L (3,21L,39M) P35 M (21M,39L) 28393.14141401.18051592808807180134513 274 (2) 344693.18329390240606021.46249052722878623693. .201820452878622271249.P68 275 (1,5,11,25,55) 669901.1067981089624261919976337719009583271701.P51 276 (4,12,92) 4897293118613530475909412835121446993.P48 277 (1) 13297.43035232876181345838699618577. .101071313380773599319140923347831746047.P61 278 (2) 557.1107553.8207398122145081. .13857905391453292485606236633776204574597.P67 279 (1,3,31,93L,93M) L.M L (9M) 2791.31249.229897.259381279.6186894751.197940355003 M (9L) 6866191.P37 280 (8,40,56) 73361.4035574481.419208734084813681. .122082169547398535336209894561.P31 281 (1) P134 282 (2,6,94) 1129.79675153.194235961.1277541004894145634521793241.P42 283 (1) 542985073109767895287.1463553505369059688342594473350302719109.P75 284 (4) 569.2578667177.61625929359409.4184419330738062569. .653165498937448839705668161.P63 285 (1,5,19,95) L.M L (15M,57M) P34 M (3,15L,57L) 571.11971.79801.107919731669693201297881 286 (2,22,26) 8724847561.P105 287 (1,7,41) 2236879.63306570925501.P95 288 (32,96) 1153.64513.602627329.267037263019450369. .185901652872784317405136897.P32 289 (1,17) 3766249.179061915490699.9765621200099707.31050992819328421.P77 290 (2,10,58) 2881441.1027258301.738654079881247833101. .4942615627283111677404623687381.P40 291 (1,97) L.M L 9594160501626613625431.1989549405617260510054951 M (3) P46 292 (4) 65138399321.1047013338807636329.P109 293 (1) 1759.3517.103483820887. .2078027659694323316196007798843459853366512641843942412939027.P62 294 (2,6,14,42,98) 3663241.3355185337854292321.8240215921531652188201.P34 295 (1,5,59) 83835947865035777262546791066217463181694871.P67 296 (8) 593.635809.268282561.3891902129.P111 297 (1,3,9L,9M,11,33L,33M,99L,99M) L.M L (27L) 1783.99793.10165682236858831.4885372291761429931 M 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10781.11139181433126881.42616540594017306841. .1939897538167586914233386033412974841301862291509811887541.P64 491 (1) 608926431044827575733062235676626887409859691974652906541\ 73842691745096014633691396823.P148 492 (4,12,164) P153 493 (1,17,29) 11833.10460016289198147545294753955830327500027581.P167 494 (2,26,38) 3131049661742425528068232396297.P176 495 (1,3,5,11,15L,15M,33L,33M,55,165L,165M) L.M L (9M,45L,99M) P58 M (9L,45M,99L) 2971.650229042030120136981.P33 496 (16) 135752657940481.29572149681736256801.14697881508142957864698198881. .72829931572241882463585913265633971549921127240417.P118 497 (1,7,71) 23857.1010899. .13220422274071910215876252468819242538756902481.P145 498 (2,6,166) 15937.6623401.7160040632843551703449. .216620436604313043566475914989777. .3827781058655183126205789289853376790116016057.P46 499 (1) 502914828563245444040270933733606351210630815812168646542\ 02148086500144195079163724148106275521673861082817129401.P125 500 (4,20,100) 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.811585543251277560120467057191.3865306830584167073127171461490704904967. .10793217203542650706249328961410064151855304581.P55 512 2*.134382593.22320686081.12079910333441.100512627347897906177. .185203545384014444998415700339182963094565346115682981302539\ 679248192554448695865898272140289.P101 513 (1,3,9L,9M,19,57L,57M,171L,171M) L.M L (27M) 13339.2370225727729.18922857792733.P48 M (27L) 2053.796177.36441469.366009862219342685069818843.P34 514 (2) 149789881.13910135119037034721. .5440162865009261024414945198670366357712554963673.P169 515 (1,5,103) 3490445461. .77104115792306847773969759123947639401032809855965933396877513801.P121 516 (4,12,172) 307835856381706655023029487757335537454417933070976\ 26003633282161500251889.P87 517 (1,11,47) 101594938593498193485713234840114778164168663847714\ 149034344787245701990201570015907057074635739614123343291.P113 518 (2,14,74) 1230769.979486201.34380007061. .1223967211946315524725505592278476748023592868457900490298056129.P118 519 (1,173) L.M L 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36893309.614601335704406847014819901955802334466227429378451201.P235 623 (1,7,89) 3739.194377.5686556044639.P231 624 (16,48,208) P184 625 (1,5,25,125) 462311251.6329454609315001.P215 626 (2) 28462659967079735788297.2296458697909124947889973834588437.P242 627 (1,11,19,209) L.M L (3,33M,57L) 21319.150368908141.388863219568252900988590466647.P42 M (33L,57M) 140449.237150211.P72 628 (4) 126170538473855459870995755264812959134139669176057183246713.P239 629 (1,17,37) 71707.877960444290871.51299425811678957273668061329.P227 630 (2,6,10,14,18,30,42,70,90,126,210) 7561. .12590175379400132061492944820636383346706910611864696890158853481.P70 631 (1) 3354397.551665229921374663. .3527519602384687600760560181416106278756256864901236966389. .661744421719350417964892910308146398980799692115145399069401\ 549047107849.P147 632 (8) 210964129.11969747953699489. .594548574449554037511134980694607790101788345550302129. .337523273815744401490672882025035998834268007703157399765020\ 445521436025761.P146 633 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C262 761 (1) 82189.2301240631759921.1591359823057107299742304320433.P313 762 (2,6,254) P241 763 (1,7,109) 9157.3179463179489143934260672926181415256258497993\ 062493320803731709677756649339029629119346129.P215 764 (4) C363 765 (1,3,5,15L,15M,17,51L,51M,85,255L,255M) L.M L (9L,45M,153M) 3061.9181.42841.3246751801.40013904871.P60 M (9M,45L,153L) 279991.P87 766 (2) 656822133606644237.2102130222907676881.68749406802433157741. .2774238816790942869692104969.11913498249982150275039859349. .30386584928990666330278777161645922849. .303889341986146630791713973167874707042199651755239385807424842909. .6269436981885403156973575821142345808666112250020578256047326\ 42929274209337.P76 767 (1,13,59) 23011.483211.433402695736999. C308 768 (256) 79873.1191937.3838349202433.417640990866433. .40954545504988911659715489116607926436750337. .165456058625467287980204466925838136186989569. .91730834648442264377552298732808331695683871942657.P69 769 (1) 49354941703447993616761.147639543843549779383753. 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(9M,45L,261L) 414991.P155 1311 (1,19,23,437) L.M L (3,57L,69M) 36709.76039.5844439.25679869. .197019064534643578236470519860924797481.P128 M (57M,69L) 28843.91771.2565529198795631969709544404900654938238\ 819298341757226219744091905156200806131899.P98 1317 (1,439) L.M L (3) 263401.8466973804975764703.P185 M 197551.289741.1693663.21954697831911273125452942243018812804117559. .15625305790155774800504213544664082865394459261063.P100 1323 (1,3,7,9L,9M,21L,21M,49,63L,63M,147L,147M,441L,441M) L.M L (27L,189M) 2647.690607.179745427.6984887381669898746134586894281501.P129 M (27M,189L) 132271052961533171877807680107.P152 1329 (1,443) L.M L 2659.3194080670970886663543.P187 M (3) 3801522739921.3032400247439036377.P180 1335 (1,5,89,445) L.M L (15M,267M) 4368121. .29567379293584507904163835608008428593336167876648058522691.P103 M (3,15L,267L) 8011.15321327751.5767178386850936738521. .3204904531701877804575792123993929101. .1456709174321118298895999730143218667581.P57 1341 (1,3,149,447L,447M) L.M L (9M) 13047336215929.107309352478501. .261148385124073275472375540004076742596018447969467750479309\ 2352664077819.P113 M (9L) 2683.15146739640694405124361249723.P181 1347 (1,449) L.M L (3) 228988172224679462242791599307571660953770400768266015782\ 650669023522386399550060982667297.P125 M 1382023.5005282279.2341505365421689.681119106721331999131. .9616790564899660933918984330332787.P129 1353 (1,11,41,451) L.M L (3,33M,123L) 622169735683.111229878914327119. .83613362115293179644194965306446000845497946511165006709.P107 M (33L,123M) 2707.21649.67651.14276178392219492191614473311419643489609. .7521712640237443464210963517184508143827693. .12172762896108114166967478683637697221722581.P52 1359 (1,3,151,453L,453M) L.M L (9M) 2719.1831779200555198259643.7080130727856537225319. .21080502535525157810647.6899030887465321400524120466233864197943. .2022294677035020074854486664093028261522434362123.P58 M (9L) 8883378019.41480433559.8674184041358617.P179 1365 (1,5,7,13,35,65,91,455) L.M L (15M,21M,39L,105L,195M,273M) 2731.54601.149929041991.P119 M (3,15L,21L,39M,105M,195L,273L) 33635567483907481. .518543558494289748812885629501. .429904436524300318893386253327768167731.P53 1371 (1,457) L.M L 205651.707437.57939414217.7348195407392994367. .217554631041972451443797098558007039161.P139 M (3) 146585804684188576896625228659166818114839136744511.P168 1377 (1,3,9L,9M,17,27L,27M,51L,51M,153L,153M,459L,459M) L.M L (81M) 311203.3425977.1095862211749. .704104974521439858171605401239347119. .6225260477163439918554663122723584483.P110 M (81L) .414931834888041650427503029259917969497463164157967102504515\ 2106665845347.P134 1383 (1,461) L.M L (3) 5465617.2673259958697812507617881136246428379. .1182718958128495494468566947747280615372427102019.P128 M 2767.87751351.1493391477818131. .101230960987312031866957790447845050391.P156 1389 (1,463) L.M L (3) 52783.630607.825067.1683469.22279561.2816430853.4812656350498393. .280607880074325841. .95994604310948122947970710957774523366749829616603023.P95 M 72229.8997943.922076539.52230324397879426011825816300492539615257. .16250405219544813499287236268073691846867803.P117 1395 (1,3,5,15L,15M,31,93L,93M,155,465L,465M) L.M L (9L,45M,279M) 41851. .138313402515052772754780440245592997704574949931994882618830193511.P102 M (9M,45L,279L) 5581.33500523241.P158 1401 (1,467) L.M L 13589701.488290807399.407360415181333.26457780181284931. .598998091634640325159243603. .272274988033889335721484807373062503985916595364448604887.P90 M (3) 268993.2235997.14355102746454601.P195 1407 (1,7,67,469) L.M L (21M,201M) 14071.P185 M (3,21L,201L) 104119.1089426031.24954300042681743057851633.P150 1413 (1,3,157,471L,471M) L.M L (9L) 33992579050663847110287755066064573401486148081858312221\ 97895970158237266603378649324399.P136 M (9M) 5653.749605434294682380564938608132519.P187 1419 (1,11,43,473) L.M L (3,33M,129L) 613009.1033033. .11703406430266218978257490461953503553682840367379.P140 M (33L,129M) 39733.12848991079.14341918141. .29168058670862674378104507538208850016837.P135 1425 (1,5,19,25,95,475) L.M L (3,15L,57L,75M,285M) 148201.898131901.4696492201.8743740551851. .613904115718627651.4002655084470402928850766151.P90 M (15M,57M,75L,285L) 3730651. .794828025405915842154705640143116713586610451.P121 1431 (1,3,9L,9M,53,159L,159M,477L,477M) L.M L (27M) 95708378299969846513.1561563182708321767651. .67786171980961244577335827669. .3927892755414960353222801138344493547469.P114 M (27L) 28621.16628221.1028675654996466097.2291093083303520337883.P173 1437 (1,479) L.M L 62175121597.56487210228951949.2776488233036576576107. .246481581579886849168659931.P154 M (3) 3398498146142284897724797703967083713. .191924272471438794806592701994990140810916848276651511296313\ 69049188345174354853908858619.P103 1443 (1,13,37,481) L.M L (39L,111L) 20799403.327989896957482033146397865633925722501302373.36\ 2466230088787245203725150695608196446507416763500471557553488672973.P86 M (3,39M,111M) 194127162320689729.3558012519747676270879. .17897550933983682381524022832723680547.P131 1449 (1,3,7,21L,21M,23,69L,69M,161,483L,483M) L.M L (9M,63L,207M) 11593.55731067343800638739237.320660395810846082\ 34530436622210937908724090089606941026078750243892289807051.P86 M (9L,63M,207L) 29000287.633367524259.7482821004500437.30773809103643523. .19601985151451171363006071.122767969266755699304461743743129577. .172582549890082128784638779466950263.P42 1455 (1,5,97,485) L.M L (3,15L,291M) 39320616866697721.3639201532632397252388041. .31384221745464139339748791. .3146955858766457814647982108433483105173251986980374041.P63 M (15M,291L) 11382322846501.1565183882137144946648898538725391. .46704991494763830091439977057672231.P102 1461 (1,487) L.M L (3) 11689.37987.8889442813.499108671770210353. .4001107679969153471668159060060172149.P159 M 420769.3684643.P221 1467 (1,3,163,489L,489M) L.M L (9M) 8803.26407.92649853.1075948323481.P204 M (9L) 1467369063868139907894170198267347695043.P193 1473 (1,491) L.M L 172859938936754194133451029513749626969089626547847175322011.P176 M (3) 67759.21879943.45156289.419701010039666236565045972319840541. .101705266346881352956337022559977570781967995934890594153910\ 3899330419505921.P103 1479 (1,17,29,493) L.M L (51M,87M) 1801750339.100743241579.327582100849. .1195496928653800716779761036930067651090617. .1315924956569789619337671062640003985324619492796255289.P86 M (3,51L,87L) 1884247.56569454593.P198 1485 (1,3,5,9L,9M,11,15L,15M,33L,33M,45L,45M,55,99L,99M,165L,165M,495L,495M) L.M L (27M,135L,297M) 2704969997342143387928487901. .5474245653260990986533436821246647816715166891.P99 M (27L,135M,297L) 728533568225878800721661003585941. .408357497164678483608973463538490157762187609740820571.P86 1491 (1,7,71,497) L.M L (3,21L,213M) 32803.1234700083.12204804151.283192937712609508123. .308354416212184836239887.P134 M (21M,213L) 235938996420163. .1336666262860734148823336429211753277097394853.P141 1497 (1,499) L.M L (3) 30622633.16227428273195273317. .4325949238806739927299209368953885473640314221453. .18121221314230958534921272566638481354835724027233.P113 M 25253746291.257775783606245005632632725579014923415327180576\ 888770877561674157915898499781016981.P145 1503 (1,3,167,501L,501M) L.M L (9L) 3973933.18616805333083.17803305651886327.15682582722996886087. .202573493641436909586621348046771.P151 M (9M) 144289.P233 1509 (1,503) L.M L 138829.36274466316667.11553678517192316645158593100969. .4737233752020545884052798695412419254883. .27459510724289498116813774473856506741721424907963276819187958030449.P84 M (3) 6037.42585163478378589415814407.P210 1515 (1,5,101,505) L.M L (15M,303M) 1509557922609968251.2706127467270869932660976815677\ 7363988042527261853049427552775878973839531215357631.P90 M (3,15L,303L) 3399661.42023071.P178 1521 (1,3,13,39L,39M,169,507L,507M) L.M L (9L,117L) 167311.114910003172322436455447319908539210773. .431270705707474469926387253492102092723171.P139 M (9M,117M) 39565371457.217412353148563.41490665439293308213. .5851380513076385535484370482767823. .8002439729908294163002140206186911.P112 1527 (1,509) L.M L (3) P243 M 21379.746958920898165755935823445465202971333729069876913071\ 2039564064844959830743.P163 1533 (1,7,73,511) L.M L (3,21L,219M) 6133.3139140338963351773.54015953668213067778283. .377667606055574411584732518101496032645221.P120 M (21M,219L) 8250607.2997447307.104886107247517.675398387645824468669.P155 1539 (1,3,9L,9M,19,27L,27M,57L,57M,171L,171M,513L,513M) L.M L (81M) P232 M (81L) 161691714495465128664479087883100410975673390632829.P182 1545 (1,5,103,515) L.M L (15M,309M) 160681.3161071.47226070700056986973989716338395248861101.P142 M (3,15L,309L) 110932363449347086341421. .120827206310996826267591035767856760692282690273958361228231.P113 1551 (1,11,47,517) L.M L (33L,141L) 251732260937427449284221399869569351765747869364693. .9566060032790010874483547376656893826943127817285473.P117 M (3,33M,141M) 38302937641.120659061706327. .24323442816253703577801984883577228485909. .5210457042762754918650165277316177454890893470999329279279079799.P92 1557 (1,3,173,519L,519M) L.M L (9M) 9343.29322896865949.42004681021037076473602297. .26350935907549089150764284767335479. .108599989773642835219110454527234001. .1268413494411135671239686038243358243539607519968737801.P80 M (9L) 6229.11593423.P236 1563 (1,521) L.M L (3) 41834382085765861.34519678373151698155933989949555159. .122709649224812489003719050561751333767918697.P153 M 71899.550177.277182577267708993228633.P215 1569 (1,523) L.M L (3) 6277.P245 M 2425645759.162231794629.51138967238152227834674642227.P201 1575 (1,3,5,7,15L,15M,21L,21M,25,35,75L,75M,105L,105M,175,525L,525M) L.M L (9M,45L,63L,225M,315M) 110251.32064630002294879480214754569659\ 7591103896898277711821386517638335251.P99 M (9L,45M,63M,225L,315L) 3647701.P166 1581 (1,17,31,527) L.M L (51M,93M) 3163. .82460484027281186047102892108013807301830647372983199436523.P167 M (3,51L,93L) 230827.10677421154509.2538886045364881. .2105815853951880661039.P175 1587 (1,23,529) L.M L (69L) 12697.53646949.16901076645511.124474615237130101. .217764979183711382181338210484375843962800941959247124967413\ 9050799124524986354490901667959297641.P103 M (3,69M) 35053268773.2353514382719968087651.P210 1593 (1,3,9L,9M,59,177L,177M,531L,531M) L.M L (27L) 18307502339617.P236 M (27M) 6373.637201.10867447.827488629912847539301464625039. .651801120376464912317703961852338147792701829163. .89984026679224734202841571611513508860907497599083631.P102 1599 (1,13,41,533) L.M L (3,39M,123L) 15991.546775362312983523851969901933375522496389\ 20478666535028713591897703492219572876065612993934538246497.P125 M (39L,123M) 6397.47565493662571. .621599274392580047116718267463758813685157884389347746436663609903.P146 1605 (1,5,107,535) L.M L (3,15L,321M) 310593181. .17789260554240279829195325878385684456164749487729776549507801901.P130 M (15M,321L) 192601.68084780521.91665896341.P175 1611 (1,3,179,537L,537M) L.M L (9L) 592849.P250 M (9M) 555198338864649115917199.478249103045128318887643948068869938123. .131863149805536176483000888716939283511945973.P149 1617 (1,7,11,49,77,539) L.M L (21M,33L,147L,231M) 22639.238958551200611078500890308107077823. .39176411954757684279286049848109010550909057. .166463779642956973878860171631999409509399613.P73 M (3,21L,33M,147M,231L) 126127.4796965570769103019086848452789. .121934855918652005425425185516541065340216577. .476266745652632045310161945284909891520767955887.P73 1623 (1,541) L.M L 292141.407602903782505999153.3163401339421861679053579.P208 M (3) 13083623647871199018487. .39367486031366231721913295794603522482900132767422021176361. .4683208111782133131851743693682869861088775327355306645830944\ 2435079578606405629469.P94 1629 (1,3,181,543L,543M) L.M L (9L) 35839.29037757937334212167140607281793424249647282263515336\ 04104116940448802181562862701355990087152162175898809267548667.P139 M (9M) 3259.13033.53570303569. .467943675136108780880137098254031233748485762306956955464181\ 2367855707.P170 1635 (1,5,109,545) L.M L (3,15L,327M) 3271.712347543122958811. .56652339351190790112632283967015870471.P148 M (15M,327L) 93256712032126453021.P186 1641 (1,547) L.M L (3) 162617461969715948481703107551698534356643. .345033777394052269283494188083645960665931156007359938190503\ 097814477619.P148 M 85333.P257 1647 (1,3,9L,9M,61,183L,183M,549L,549M) L.M L (27L) 957056956057.P246 M (27M) 3027187.8989704811.180791256173167. .729811615372825638608563545422812973864852884158218893934078869.P165 1653 (1,19,29,551) L.M L (57M,87M) 26449.159431851.P228 M (3,57L,87L) 3307. .903585068916626197183996182809244068371662180583769869481143\ 45048510024468030375619044382624994939375343.P134 1659 (1,7,79,553) L.M L (21M,237M) 53419971510739.58235535551086590800251. .2016137367947688901473821902973535064854672543528607667522466\ 44402189442031223710807822465399.P95 M (3,21L,237L) 1718070111787. .606485332930911703007754621440567577861448865135977. .8370243442602533311853596673240498661034199781997282891862953\ 0787743789.P90 1665 (1,3,5,15L,15M,37,111L,111M,185,555L,555M) L.M L (9M,45L,333M) 3331.31555081.145601356442066254072961070152462\ 336112617247671710966946731975255218676686670649626981.P110 M (9L,45M,333L) 42705373476148159714265556679835954983581099281\ 9320955171672056025948618935491788761.P123 1671 (1,557) L.M L (3) 7579657.47444154913.P248 M 22952857.9502901987227131883. .896006499058441830246499144007378375869596793598810275135820\ 34927661704393603794074197168264578475656077386376770859003.P121 1677 (1,13,43,559) L.M L (3,39M,129L) 87892314589.P230 M (39L,129M) 3042079.644838232111522679335349578277194759. .623946491284066832337611657335109969863.P159 1683 (1,3,11,17,33L,33M,51L,51M,187,561L,561M) L.M L (9M,99M,153L) 104347.1908523.64694997973.10209940774213951. .57136851755325132350832361. .1062888839253785112338961138207829526172596536878504103418945\ 462955714141913.P91 M (9L,99L,153M) 124543.10813022551.14911972417. .3956528238136812637682086243.53547249629521271130544957483279. .173267370329470749751209721516081. .110995096534055033775812456877810354806490499839538741.P59 1689 (1,563) L.M L 20269.50671.327667.7645632650659. .118646464838771316087247218652828678212019443271226609714077.P183 M (3) 388015285982748829. .1257709554061888898885055328103862453400448193470307463922621\ 2114353280356370608078260653310596942148182604454548717834797.P130 1695 (1,5,113,565) L.M L (15M,339M) 3391.P210 M (3,15L,339L) P215 3^3h+1=(3^h+1)L.M, L=3^h-3^k+1, M=3^h+3^k+1, h=2k-1. Table 5- Factorizations of 5^n-1, n odd, n<550 L,M for n=10k-5<=1095 n Prime Factors 1 2.2 3 (1) 31 5 (1) L.M L 11 M 71 7 (1) 19531 9 (1,3) 19.829 11 (1) 12207031 13 (1) 305175781 15 (1,3) L.M L (5M) 181 M (5L) 1741 17 (1) 409.466344409 19 (1) 191.6271.3981071 21 (1,3,7) 379.519499 23 (1) 8971.332207361361 25 (1,5L,5M) L.M L 9384251 M 101.251.401 27 (1,3,9) 109.271.4159.31051 29 (1) 59.35671.22125996444329 31 (1) 1861.625552508473588471 33 (1,3,11) 199.386478495679 35 (1,7) L.M L (5M) 85280581 M (5L) 211.631.4201 37 (1) 149.13971969971.8737481256739 39 (1,3,13) 79.608459012088799 41 (1) 2238236249.5079304643216687969 43 (1) 1644512641.172827552198815888791 45 (1,3,9) L.M L (5L,15M) 1171.169831 M (5M,15L) 297315901 47 (1) 177635683940025046467781066894531 49 (1,7) 227376585863531112677002031251 51 (1,3,17) 90271.317731.654652168021 53 (1) 5960555749.17154094481.27145365052629449 55 (1,11) L.M L (5L) 11*.103511.190295821 M (5M) 511831.65628751 57 (1,3,19) 11735415506748076408140121 59 (1) 21180247636732981.2047572230657338751575051 61 (1) 8419.918585913061.140194179307171898833699259 63 (1,3,7,9,21) 280729.2161279.23792163643711 65 (1,13) L.M L (5M) 20986207825565581 M (5L) 131.1034150930241911 67 (1) 269.1609.26399.2454335007529.604088623657497125653141 69 (1,3,23) 139.6211.598761682261.8868050880709 71 (1) 569.18607929421228039083223253529869111644362732899 73 (1) 4853479.5729041.9519524151770349914726200576714027279 75 (1,3,5L,5M,15L,15M) L.M L (25M) 151.3301.183794551 M (25L) 1989151.49892851 77 (1,7,11) 527093491.8090594434231.162715052426691233701 79 (1) 205367807127911.58523123221688392679.344120456368919234899 81 (1,3,9,27) 4861.11419697846380955982026777206637491 83 (1) 20515111.1431185706701868962383741.88040095945103834627376781 85 (1,17) L.M L (5M) 8198241112969626815581 M (5L) 1531.34563155350221618511 87 (1,3,29) 5569.6961.28870194250662203210437116612769 89 (1) 179.9807089.14597959.834019001.8157179360521.231669654363683130095909 91 (1,7,13) 9680647790568589086355559.17499733663152976533452519 93 (1,3,31) 31*.148429.878851.172974812463239310024750410929 95 (1,19) L.M L (5L) 2851.11600321878916922053491 M (5M) 4113691.1245576402371959291 97 (1) 389.264811.P60 99 (1,3,9,11,33) 143551.1731511.22542470482159.153560376376050799 101 (1) 5937018283241.3434487311396589821473854121.P30 103 (1) 3709.28429.59117897713198738371603984809.P35 105 (1,3,7,21) L.M L (5L,15M,35M) 21226783250214361 M (5M,15L,35L) 1736701.119461537021 107 (1) 6421.5486016363791.35411885288978941.172163150940018661.P24 109 (1) 1091.1007161.1528399.P61 111 (1,3,37) 3109.P47 113 (1) 2939.6329.129499.308491.304247586761.2084303944451. .620216264269531.8237123176890810696379 115 (1,23) L.M L (5M) 689081.29028071.100062970166640331 M (5L) 461.691.2855911.824480311.17223586571 117 (1,3,9,13,39) 223963741.P42 119 (1,7,17) 239.1429.4999.7497182681291140146079.P36 121 (1,11) 12101.486179.P68 123 (1,3,41) 739.960139.1785961.9025583299.P31 125 (1,5L,5M,25L,25M) L.M L 3597751.P29 M 28707251.4032808198751.767186663625251 127 (1) P89 129 (1,3,43) 18471511.43955934961951833386625799.P26 131 (1) 2621.23928199.34720241.16815642611861.P60 133 (1,7,19) 9311.65171.281429.3257947519.152317058321.P41 135 (1,3,9,27) L.M L (5M,15L,45M) 11071.1312315694449748688331 M (5L,15M,45L) 541.26941244373060650224561 137 (1) 20551.603349.48102071.121719631478506669.7851027307722624763151.P39 139 (1) 21521602057721.6789441546024769741462601111.P56 141 (1,3,47) P65 143 (1,11,13) 24615836446631.53130566763791958299.P51 145 (1,29) L.M L (5L) 1461311.P34 M (5M) P39 147 (1,3,7,21,49) 24556351.5071357999.2035895040229.P30 149 (1) P104 151 (1) 1175989.2237519.389439261961.12799319666401. .2843809592323334251225153490677489.P35 153 (1,3,9,17,51) 4591.26481241.360143672909416579.P39 155 (1,31) L.M L (5L) 11161.257611.31473312961.21783999170235219053011 M (5M) 311.5624951.P33 157 (1) 32029.5129819.2107089779.8616314452100494153901371725720169.P55 159 (1,3,53) 1775305720077559.P58 161 (1,7,23) P93 163 (1) 4599209.40100609.675775181.6582151087844246659. .102556399583828574447011133455059.P40 165 (1,3,11,33) L.M L (5M,15L,55M) 2311.P26 M (5L,15M,55L) 331.9867165115635267180926131 167 (1) 18371.53441.P108 169 (1,13) 13859.784646826705980283039372085276899721.P70 171 (1,3,9,19,57) 19*.P75 173 (1) 1039.3461.1708272343265311.P99 175 (1,5L,5M,7,35L,35M) L.M L (25M) 28001.200201.8894201.P26 M (25L) 12601.50051.22661801.1657309151.38105263380318401 177 (1,3,59) 198241.340863370420651571324835367261.P47 179 (1) 359.3581.75539.17315029.100894073362387242965129.P84 181 (1) P126 183 (1,3,61) 38431.P80 185 (1,37) L.M L (5M) 2591.P47 M (5L) 30810641.21829321837586441.P27 187 (1,11,17) 4200769.1202338040280510524134632541097924516136661.P64 189 (1,3,7,9,21,27,63) 305921358183421.P62 191 (1) 112691.60426671.P121 193 (1) 749154725101.406875383561091922623241829.P96 195 (1,3,13,39) L.M L (5L,15M,65M) 14821.P29 M (5M,15L,65L) 933692761.P26 197 (1) 470323176131.362204827770839.P111 199 (1) 53731.P134 201 (1,3,67) 1248228732195063112609361470351.P63 203 (1,7,29) 493291.4978655062910170670969991331.P84 205 (1,41) L.M L (5L) 15991.1256950067521.P40 M (5M) P56 207 (1,3,9,23,69) 10047916621.P83 209 (1,11,19) 419.56431.P119 211 (1) 5594292675731.37973612258438259769.2047676978710884689089. .144115393066310961947385445876092809.P59 213 (1,3,71) 156309592445437909.P81 215 (1,43) L.M L (5M) 1291.P56 M (5L) 431.144982241.1273316896028212631.P31 217 (1,7,31) 8681.1828916514769.P110 219 (1,3,73) 439.429241.2183431.239701757320911389817996792709.P57 221 (1,13,17) 351391.231452141519.183276094190104631834639. .1436003589550079403417985191612889433318011249.P49 223 (1) 355909.P150 225 (1,3,5L,5M,9,15L,15M,45L,45M) L.M L (25L,75M) 1274851.1390332823651.489346511141264975761501 M (25M,75L) 1086749551.P33 227 (1) 863773591.17408515139.107857890714179.154907695140797990849. .239976686263858506551.16831369699997499687405534401.P57 229 (1) 2749.53129.63785116081353654247759.25703365361608909110896940589.P101 231 (1,3,7,11,21,33,77) 13920748381.267859557529209897722406319386619.P42 233 (1) 1318781.412500871.208771951788632309319091684496790985222571. .122893706196784651098718052024745515496783278694509.P57 235 (1,47) L.M L (5M) 20885861.68308861.P49 M (5L) 941.4231.96766610646500911.P42 237 (1,3,79) 12799.657439.447298617719114285037649.P76 239 (1) 479.40093613041379.P151 241 (1) 79531.578401.882061.464913101.128338427949683383916242111. .23296571833941039118079506609079.1054929344030207429836604785995221.P53 243 (1,3,9,27,81) 1459.14001661.P103 245 (1,7,49) L.M L (5L,35M) 491.8821.10781.P49 M (5M,35L) 16650328910366149531471.P37 247 (1,13,19) 29641.893134065430622331883159985777080426121. .73264607998188798376620748253610482190769.P67 249 (1,3,83) 499.12451.169321.64613577662440706821. .486307761332920261532701.P60 251 (1) 8325671.31005529.P161 253 (1,11,23) 215556321311.4586605887769406257148888900423581. .75458741165755163938354406143932160485170968091.P62 255 (1,3,17,51) L.M L (5L,15M,85M) 1021.1445377105917001.P27 M (5M,15L,85L) 236641.782302186051.38385602257801.263420722813531 257 (1) 10081392432072125477404185330039079.P146 259 (1,7,37) 1483253451821989.12331512430205535516641371.P111 261 (1,3,9,29,87) 6717619.81131329.420610743056505018221215111.P77 263 (1) 1523516701711.P172 265 (1,53) L.M L (5M) 488094322309591.1335618937071191.P43 M (5L) 1061.43347650492220877561107611.P45 267 (1,3,89) 1069.1133149.1652731.18484574880511.369718501929859. .92358800604937937130124908509003639071.P42 269 (1) 3229.4016171.32785719659723694619.P158 271 (1) 64993931.12987902099.P171 273 (1,3,7,13,21,39,91) 376909369155066379919582224252183771.P66 275 (1,5L,5M,11,55L,55M) L.M L (25L) 23785874550224051.29881163609373451.43877290026688801.P21 M (25M) 233201.1234133939501.354655233566701.P38 277 (1) 37095841.14075563135476669013895019180975816431.P149 279 (1,3,9,31,93) 247114592858611.P112 281 (1) 631100202961413821.P179 283 (1) 1699.451669.113334709.416742821994932569.33926661157694104397239. .1503555624642039390353881.8717585253517894966154284413195420314854559.P73 285 (1,3,19,57) L.M L (5M,15L,95M) 30211.260930841421.P35 M (5L,15M,95L) 571.P48 287 (1,7,41) 10690751.203375089.1038891585945814650631.P132 289 (1,17) 17341.81053519.27605542907603789.9027110169772242694759.P140 291 (1,3,97) 8731.15247819.65482996292971.425798685220729.P95 293 (1) 1759.520369.224108738217451.88957588316686547560127731.P155 295 (1,59) L.M L (5L) 842521.6264826343527027047964986594326671.P42 M (5M) 1448181445390051.485704102682442915241.P45 297 (1,3,9,11,27,33,99) 1049599.1730583185128108939. .101367829967676409195407966079.P73 299 (1,13,23) 599.71761.1076401.7752619982267966542535041531665354400879. .4483622187767180916663396803931609479674368941155912707479.P74 301 (1,7,43) 66221.3595452428681.453098474981964966729037498128705243871.P121 303 (1,3,101) 126463111. .897449797190508611732321830427288714681382628177991026939.P75 305 (1,61) L.M L (5L) 1884901.P78 M (5M) 1831.2441.1786560207910631.117369445599178322177831741.P36 307 (1) 30093907237519.41907329770349.370746598982672170784362177\ 5363101765344082634099897042729510565487681100579030907337171.P100 309 (1,3,103) 619.8934148519.42173111702521341940416989340041084225191.P90 311 (1) 263729.1649908341047346424876131429988519619911.3869545540\ 1981313830913060474530524458380779268946879355849020686413069.P102 313 (1) 229651231.21428622089774767159447145142284385968882142917\ 892658511907216761741.P143 315 (1,3,7,9,21,63) L.M L (5M,15L,35L,45M,105M) 11971.23311.34651.P38 M (5L,15M,35M,45L,105L) 1732501.P45 317 (1) 34871.29048967458203698934091.117326604811899693858471988\ 2501239841331337879112270918586790280760729499132694039331.P110 319 (1,11,29) 95701.533942839.10384276959815785278012327720400611\ 6809062929798301541558844883634526221.P111 321 (1,3,107) 35311.80251.3482851. .204438681420686525733014991351502624422714996979.P85 323 (1,17,19) 3247691391126251. .824025642333621472612253607491152025643258690550015151. .4520075300365525822415973296109200878340148487916084028121991.P72 325 (1,5L,5M,13,65L,65M) L.M L (25M) 1659451.142816611356873351.P61 M (25L) 1641395317366745868848220671801.P54 327 (1,3,109) 3900606421.2570834326384926058220919782123933663342371.P99 329 (1,7,47) 659.6581.15957217104409233285978673415179.3625663221570\ 350634568091041714437127962087908478575591859134630145357912199.P80 331 (1) 67440292875072467734808551587718580464816759. .141112104541733856106296850936798990544389413081573359. .36660509879767573074043387529034539467473550476763301654073761.P73 333 (1,3,9,37,111) 15319.344145511. .11071665290671449530331408923856186107268916092023773607149.P81 335 (1,67) L.M L (5M) 126631.11494162725571360186894779691.P59 M (5L) 1148552280514941389076611.P69 337 (1) 242550562936636678266163293887551.P203 339 (1,3,113) 7459.234303241.22628763748399.204867325883294509. .24528557597575188455414632667311.P83 341 (1,11,31) 109121.10161119.192446105281.609146164309.45207486995930\ 99017783616543781400678030271123301730038268744743823945263930101.P96 343 (1,7,49) 245723963580715350733457214075196517831719729.P162 345 (1,3,23,69) L.M L (5L,15M,115M) 21391.31741.1715341.27875688121.P36 M (5M,15L,115L) 37951.5347963681.2351881115374174051.P30 347 (1) 34911671.9060198312365106899848549.8515033276662925031602\ 64801368706292468844937316440842702924682291647564259.P135 349 (1) 465248728728895394653153888943818531375975270853944206732\ 179708325578302943996260672261958710669770611963071.P136 351 (1,3,9,13,27,39,117) 7655311. .6475711850365695029787483033056414199292785571. .1489161023006154219903790225805356280792802449809.P51 353 (1) 235099.5451190499.205504553260781.34785215885504832719. .8597971138069346350487920233892950696823018756984661.P146 355 (1,71) L.M L (5L) 8499626476216091.8558727566683804731617356972960527829841.P43 M (5M) 71*.17041.7484111.P85 357 (1,3,7,17,21,51,119) P135 359 (1) 719.41785692653578003162849.6677881008782967997903339939. .837248571667848555569202584041.P168 361 (1,19) 129422865652104096162599.6417463808715658282089494909.224567\ 41321661756943535202665387921991636237742965091090748406504927189.P118 363 (1,3,11,33,121) 3631.P151 365 (1,73) L.M L (5M) 1077334433621.11219338425853865221726037921.P61 M (5L) 6571.1328865721.650916499741.22354588958731.33735961890251. .560294380367699191.P32 367 (1) 1047157937929.645658411286666140609459. .52862043959452141411641760543741.P189 369 (1,3,9,41,123) 12755158004188042198855653459546433904913399274\ 4450750874579570996690409.P97 371 (1,7,53) 2969.11131.35922655704041.226578241537144915139. .11014814494800487352604755748091574916119. .22524108177157511856531387268450126765714109909640309103811550689.P73 373 (1) 2239.4350204259.1368671486390599.437284546695919489287780329. .132287615591619115060073063073355132265371. .993814769723013038733622579709248518485779. .2634696095973127246023496488851214554377085833500724085471.P65 375 (1,3,5L,5M,15L,15M,25L,25M,75L,75M) L.M L (125M) 751.317286001.527559073501.P47 M (125L) 281057814001.38033863525621501.P42 377 (1,13,29) 13076016539.1267005005969.2778318756799. .72952844755822287959.7913584118074610352277451069398306909.P144 379 (1) 15919.19709.154593500445308877590595293456916511.P221 381 (1,3,127) 17365824770202511.2146271536375625882474712607488854837881. .12882995722731844746940951540119250212241259630747509.P69 383 (1) 525692477729.2948582111117607147637161465549027541. .4260621080011732733351177066528303869.135449218000728997398882\ 7240992403128157841807978803698384041173092322450899036561238231.P96 385 (1,7,11,77) L.M L (5M,35L,55M) 33411357084712191971.P65 M (5L,35M,55L) 2471701.927476143441.134234460550630441.P49 387 (1,3,9,43,129) 27091.42571.237619.591570397114510975382037276803611. .2656120768584457773885517433083338243991.P90 389 (1) 179719.138068549.3391732755856086401282016931.938771696215104\ 2842693323146443792205381753954656905958476063709922148736350901.P152 391 (1,17,23) 2568871.74708371.311250747739.416079604348810289. .787775103387484980951811308682438561347569.5532656303850220\ 55666695438035664111456941805599247964204695144048160899.P89 393 (1,3,131) 344313589. .3275262323842759491144568903593811836020835083160675552849533185921.P107 395 (1,79) L.M L (5L) 104449388937445035371.P90 M (5M) 190391.68175421.38701052851841.6440862401422039384631.P61 397 (1) 1043801929.7768438039. .9817109164720890817702170752376314347166114272389620675501.P200 399 (1,3,7,19,21,57,133) 93174481.P144 401 (1) 58161041.P272 403 (1,13,31) 1892489.688730186119.311447631608357947354270996859. .5031770563367301370277089549186021905732092831.328973887632605\ 5626218496122253460916812420650821714159179769278548188108251.P83 405 (1,3,9,27,81) L.M L (5L,15M,45L,135M) 811.1621.6481.921737881.P57 M (5M,15L,45M,135L) 2332368714077641.279151346689444799703543961.P34 407 (1,11,37) 24421.P248 409 (1) 4909.9240875197613356058222184275052339715205781697901395\ 70308423505134963796317426081635865410787919.P186 411 (1,3,137) 1758306499.13509261751.3501243666084542114634292493431.P141 413 (1,7,59) 1677756178117368440322458992363311946171.P204 415 (1,83) L.M L (5M) 116201.90045041.167674286348441.20498545382037148227331. .84340842933027824154067061.P39 M (5L) 1209311.P109 417 (1,3,139) 5839.1446646439677126258978503447303571. .2463633633449688423900024936785360355054079.P114 419 (1) 839.3676736043047175259. .72898712900545938884496308172168836533702575641. .253223724619264984937512323106215870334054372644006216919829\ 591185855496480749.P147 421 (1) 14894981.31410466159536169.73688412163867840421869. .2510106373340528083960492234939.6226633359276226469107090691434236881. .622232758780358778126190590256749954524999505890859340251987532999.P115 423 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1571.62801.111555508872397870330826968741024532776659581\ 56925604671852423308739616133659346997785443510271.P117 795 (1,3,53,159) L.M L (5L,15M,265M) 27031.465396726961. .1759519043894301046372377642322402644556845061431561676869571.P69 M (5M,15L,265L) 6941839831.310928520390594886861. .9428867545869562874663176246654957067219281.P73 805 (1,7,23,161) L.M L (5L,35M,115M) 513476216471.3776990462491. .12488135411877004965688359260853096787381153034705344502325034244561.P93 M (5M,35L,115L) 2000144310791971. .52083866402604872103138538630779570592776194951. .884759571094733769873572106626750614848619033081.P76 815 (1,163) L.M L (5M) 21191.23230427545093989573574035606899884718671.8785531510\ 9257143338670779766109110941856976397892463693622420012151561.P111 M (5L) 33596633405529951211752346481.2835390828069919584008238108700801. .54938978785399383334196504918901015066871425911. .4978019070778465969873397393941797403128296569832548381.P64 825 (1,3,5L,5M,11,15L,15M,33,55L,55M,165L,165M) L.M L (25M,75L,275M) 1184981853909336451.1342155134288948494351. .232159617295908150401568225810555451.P66 M (25L,75M,275L) 915689343435380401052957142231951033638922949189951.P89 835 (1,167) L.M L (5M) 264278122166663495614091.56173271056427875611390781.P183 M (5L) 3329981.55690652993685370934111.P204 845 (1,13,169) L.M L (5L,65M) 54658890184991.375253243497628098828340729608671. .2158078190694169386056600385951598471.P136 M (5M,65L) 6761.633751.892321.11711701.P196 855 (1,3,9,19,57,171) L.M L (5L,15M,45L,95L,285M) 29279767389963944149986328770810652642323537932397766795544349601.P87 M (5M,15L,45M,95M,285L) 227431.9581918519281271232331. .1554246690784409607115661081503201. .9438797532811279585143365523975961.P57 865 (1,173) L.M L (5M) 445838345602031051099408504461587023312861.P199 M (5L) 418381471.446573551. .37248661684213703064761312273115067533733792708040311. .279955139266334333905779991057157842833926571066600624816588\ 67721239899952819876121.P89 875 (1,5L,5M,7,25L,25M,35L,35M,175L,175M) L.M L (125M) 199501.21987719251.3292915346586251. .714230949655553158292542550246822887001.P140 M (125L) 10885001.65201101781407160404501.21618698221031733473930251. .290420343548877552397308040001.P126 885 (1,3,59,177) L.M L (5M,15L,295M) 82837467331.440656089327907801.P135 M (5L,15M,295L) 18072629251. .282500728032914696042973568098174674481979831. .11142214628485169485922225114352330077923536391.P61 895 (1,179) L.M L (5L) 1853672814935393064677577610841. .6396469153560002935620691652371589233274012625328042902954061. .1339759112732934021471701060869862688293028160785211637880638\ 63997077518141.P84 M (5M) 8951.901665213571.3808663720051. .883309533541949415266717039218360375211.94946879076693120072\ 882072244060631442348888153192895617269416419532376359079371.P101 905 (1,181) L.M L (5L) 1811.1576511.478171613586061.10906993756490561. .1099457512072271447891187965053460964329312193641. .140890979240136855983847814451354759466274272215506415921692852111.P99 M (5M) 700931551. .20262133583930116870412046062033475219244006906591061201.P188 915 (1,3,61,183) L.M L (5M,15L,305M) 23289087777421.P155 M (5L,15M,305L) 5923711.10780641615218004138391. .121282650064473713751122581.P113 925 (1,5L,5M,37,185L,185M) L.M L (25M) 16651.8812832752110151.1141054090214696265915696729751. .2129445870585343659389924797250288351.P166 M (25L) 61051.260282051.2241821583598298389886231557501. .64749190634434101945975744448386166981309201.P165 935 (1,11,17,187) L.M L (5M,55M,85L) 1871.53289827581.1497355422751. .21989923924589782406613721. .465311585950879191191346374910156621386822710283845749791.P116 M (5L,55L,85M) 192611.920448828120750970042200015191.P189 945 (1,3,7,9,21,27,63,189) L.M L (5L,15M,35M,45L,105L,135M,315M) 4545451.P145 M (5M,15L,35L,45M,105M,135L,315L) 21025419411528634804787037331. .1325545554645456657650354760481.P93 955 (1,191) L.M L (5L) 3821.284591.1288176748081.5531619057121.77270071023861971.P216 M (5M) 2249981.P259 965 (1,193) L.M L (5M) 1931.36671.1370755481.1322945718331395498506759861. C224 M (5L) 295291.3410126538956743878028525329443955975186063381945\ 21136021.P207 975 (1,3,5L,5M,13,15L,15M,39,65L,65M,195L,195M) L.M L (25L,75M,325M) 1951.17551.1761111219840080597767580940301.P130 M (25M,75L,325L) 107251.49015201.3879644432625001. .53060066966296132594129972671398659924948384932762869920268851.P78 985 (1,197) L.M L (5M) 35461.170572300709456235387703271.P243 M (5L) 9851.11821.P267 995 (1,199) L.M L (5L) 41469611.1490619451.269644492391794455719338841735437621.P225 M (5M) 44703361.P269 1005 (1,3,67,201) L.M L (5L,15M,335M) 192009627782919356468478127051. .1068957318594859875017440746034235853026553797471939518917936\ 75552901.P87 M (5M,15L,335L) 2011.4021.5031363661.598266261966511.2040040123496522971. .394275169378753956227041.102937710806996149542349947586681.P80 1015 (1,7,29,203) L.M L (5M,35L,145M) 6091.19140871.5096476247620086786318482647376687823221.P185 M (5L,35M,145L) 389761.462841.1784386016701. .65066333936892086314580939459161154079210269584985921.P159 1025 (1,5L,5M,41,205L,205M) L.M L (25L) 12301.136335757233504893186232335217667649377931249403751.P226 M (25M) 6151.94705678601.48659779110396746051. .221635203995902074697997800309988477932320301.P201 1035 (1,3,9,23,69,207) L.M L (5M,15L,45M,115L,345M) 7699609491873825871. .23882751099104450893650818821.P138 M (5L,15M,45L,115M,345L) 16561. .48841669317052812201246639020225642893645986405811. .17734519225985123791681425282952597558927396299254911.P79 1045 (1,11,19,209) L.M L (5L,55L,95L) 1134871.61848377251. .177617502813927783533104749459766039458057456311.P188 M (5M,55M,95M) 2593691.812629159102751.47159250091473521. .4835666414138554300913159447013059491. .11487652614845151253933368941567575323232345244204261.P126 1055 (1,211) L.M L (5L) 2111.20876816861.1532829720131.4650646000871485447343041. .25430981153850245517325049011783051.P210 M (5M) C294 1065 (1,3,71,213) L.M L (5M,15L,355M) 2131.434355966402327111049381. .5737253303475429997709553409561. .649333691176324405759459277148828850841885536003482706036484429461.P73 M (5L,15M,355L) 10651.308851. .10487613799550779934554590111232978181837956503871.P137 1075 (1,5L,5M,43,215L,215M) L.M L (25M) 502376998827592712867101.2935493713182089348309759914798351. .7715049437625809874216586481366238059404651. .58476140425908996624338007360943017067876339301.P147 M (25L) 6451.752921401.1069431562145725653421501.P257 1085 (1,7,31,217) L.M L (5M,35L,155M) 151901.4832449411091642761. .1569014835697578143008796159931791. .259318528448377245063216825128086419845947229111392188460844\ 81628370691.P125 M (5L,35M,155L) 916471291.P243 1095 (1,3,73,219) L.M L (5L,15M,365M) 176413261.P193 M (5M,15L,365L) 54751.56941.22493894825881.977511916276393921.P162 5^5h-1=(5^h-1)L.M, L=T^2-T.5^k+5^h, M=T^2+T.5^k+5^h, T=5^h+1, h=2k-1. Table 5+ Factorizations of 5^n+1, n<=550 n Prime Factors 1 2.3 2 2*.13 3 (1) 3*.7 4 2*.313 5 (1) 521 6 (2) 601 7 (1) 29.449 8 2*.17.11489 9 (1,3) 3*.5167 10 (2) 41.9161 11 (1) 23.67.5281 12 (4) 390001 13 (1) 5227.38923 14 (2) 234750601 15 (1,3,5) 61.7621 16 2*.2593.29423041 17 (1) 3061.41540861 18 (2,6) 37.6597973 19 (1) 761.19609.213029 20 (4) 241.632133361 21 (1,3,7) 7*.43.127.7603 22 (2) 89.1030330938209 23 (1) 47.42272797713043 24 (8) 152587500001 25 (1,5) 1901.50150933101 26 (2) 13*.53.83181652304609 27 (1,3,9) 3*.163.487.16018507 28 (4) 59509429687890001 29 (1) 5096867.6090817323763 30 (2,6,10) 2281.69566521 31 (1) 1303.21207101.28086211607 32 2*.641.75068993.241931001601 33 (1,3,11) 595123.190771747 34 (2) 1973.20129.45289.12447002677 35 (1,5,7) 15216601.4698932281 36 (4,12) 73.543097.1503418321 37 (1) 9103.29010221.45920153384867 38 (2) 4885168129.2864226125209369 39 (1,3,13) 3121.22735632934561 40 (8) 25601.909456847814334401 41 (1) 83.43543.221401.9472026608675509 42 (2,6,14) 2521.24587411156281 43 (1) 1549.9547.7866608083.1628744948329 44 (4) 9080418348371887359375390001 45 (1,3,5,9,15) 60081451169922001 46 (2) 5465713352000770660547109750601 47 (1) 2069.15888756269.3602372010909260861 48 (16) 97.240031591394168814433 49 (1,7) 49105547.1866013003.2481357870461 50 (2,10) 239201.424256201.89620825374601 51 (1,3,17) 103.8467.528667.60119016343 52 (4) 51169.537181587281.129044008326199409 53 (1) 107.28838378869.599659003321309822423087 54 (2,6,18) 14551915228363037109375001 55 (1,5,11) 10910444855403996246103496881 56 (8) 113.337.2520917617.37007700327977836913 57 (1,3,19) 229.75649382555448580095589 58 (2) 1334402673828313149547634216455312875601 59 (1) 827.5242462229.3237765225301.2059647179472887 60 (4,12,20) 23320317172851318360001 61 (1) 367.9029.15571335384347.14008364639128540436401 62 (2) 8124604717965111529.102651353523520067851969 63 (1,3,7,9,21) 883.406729.24132781.1692416503 64 2*.769.3666499598977.96132956782643741951225664001 65 (1,5,13) 18461.15188886343541.15199221608544481 66 (2,6,22) 1453.6509387183417404924784917 67 (1) 11293772630057337854244300009061892827351888021 68 (4) 137.623017.938894988049.1361753880209.4959636586609 69 (1,3,23) 66163549.253592389.403316413944121 70 (2,10,14) 281.13148832195720299503896018648521 71 (1) 4261.5747338499820296170481.288231038713838413442281 72 (8,24) 1297.2739177855667309845605995807633 73 (1) 63554310563.777612767772190289.3570677866897550288203 74 (2) 9769.40849.510241095096183757930733363918820917976121 75 (1,3,5,15,25) 118801.20775901.24665701.149439601 76 (4) 457.21363981507860375753.21654472202540732126905077281 77 (1,7,11) 20828886541.49970061516036179615325895945741 78 (2,6,26) 157.8684521.4056854881.667929705480493 79 (1) 18251687.7897663181.511465533067.37399095525167136010188229 80 (16) 131349761.167597261761.24625444126052524088217281 81 (1,3,9,27) 3*.1783.5023.2066067271380136212224701233463 82 (2) 193357.6355001.1148205782281.56373078952722628530598981268453 83 (1) 167.4029666108840585686296627.2560787702841639767474730913969 84 (4,12,28) 6553.90217.6019022585035590658668001 85 (1,5,17) 75752681.247515241.504156421.68795069664507129341 86 (2) 173.2171388367013.132331554743163541916284364878460504933118649 87 (1,3,29) 349.210390487070809.22500358133965991972941 88 (8) 13729.929281.71225159567951317923809.91029014606406186465761 89 (1) 39387996609449861.56522267529181963.12094715786677995586454978647 90 (2,6,10,18,30) 20478961.6794091374761.25535754811081 91 (1,7,13) 15887476811320661.15994146485373751289418997754783021 92 (4) 150220315444217.214752088491462210591995581828628861192144614553 93 (1,3,31) 258065887.75005167927.53345671490722200466369 94 (2) 5077.12409.329573417220613.935213864500231208652603316429973471246089 95 (1,5,19) 4561.179763436784239734042181.309828362361188845069741 96 (32) 193.5207826497153857.539344757336151926206665601 97 (1) 29683.261707.547663.90130760102421063383.P32 98 (2,14) 197.164204573839769.74535675530760254357.21441970593484574539001 99 (1,3,9,11,33) P42 100 (4,20) 4001.132001.776401.P42 101 (1) P70 102 (2,6,34) 6733.4613053.19724557.34288117.26837241260899651321 103 (1) P72 104 (8) 247161617.825256433.2220784177.31308249137777.P27 105 (1,3,5,7,15,21,35) 421.5236141.1354224218968567573270561 106 (2) 8871726015923707071209.P51 107 (1) 643.P72 108 (4,12,36) 73009.1853281.3314953.36280398313.13012873776055827785521 109 (1) 19403.4046322895447485867367.P50 110 (2,10,22) 245521.1458601.2802204291103029121.P26 111 (1,3,37) 223.5107.668221.13844587.107903101.221746234901611997486023 112 (16) 271489.1149569.10922689.465314420407473281.P31 113 (1) 227.1387189.12249784663.P60 114 (2,6,38) 22573.53590717.2108505761893.P26 115 (1,5,23) 73141.P57 116 (4) 233.929.33409.397823386118610689.1547355341777494553.P33 117 (1,3,9,13,39) 40483.43236180703.P36 118 (2) P82 119 (1,7,17) 2381.25229.4172141.P53 120 (8,24,40) 2172116161.P36 121 (1,11) 374499841.304639362281.11449313571047243.4600715686162128721.P23 122 (2) 733.61001.19811275733.26933356951273517.P50 123 (1,3,41) 30970420211207224741561.P34 124 (4) P84 125 (1,5,25) 3001.51204738027593108331001.P44 126 (2,6,14,18,42) 4661402165281.147053007410401.308942475257273345172721 127 (1) 509.2287.2735581.P76 128 2*.257.23653200983830003298459393.P62 129 (1,3,43) 327845761.558801427.1420986601.P33 130 (2,10,26) 87881.14402441.P56 131 (1) 263.P89 132 (4,12,44) 331660297.112835047682166217.P31 133 (1,7,19) 2129.354047.P67 134 (2) 20369.P88 135 (1,3,5,9,15,27,45) 164701.31472682400981.182517282870121. .223823944168266601 136 (8) 17*.999329.P83 137 (1) 823.2741.22469.7642530702770043710321.61562630761411218787053569.P37 138 (2,6,46) 277.70942489.22600337281.66988220431117.P28 139 (1) 172694671812043.417786018853823.2459716746919477501.P50 140 (4,20,28) 514845603025661988644048801.P41 141 (1,3,47) 283.1129.24048335089.37516308093487.P35 142 (2) 853.72497533.8367932201.200771218157.554474665573. .1095832589179957.P40 143 (1,11,13) 2010581.2253938672701.567618483045329. .3028704600213534236926361.P27 144 (16,48) P68 145 (1,5,29) 98047293061.3532907090761.17149742984461.P42 146 (2) 293.27133517.84128413.772557938155429260697128053.P56 147 (1,3,7,21,49) 7*.9887502829.P48 148 (4) 3257.3542233.10044059578457.P78 149 (1) 85229.4394309.12703371381749.1084802496290323. .864203844381482464122519761.P37 150 (2,6,10,30,50) 14401.299541552154912341601.P32 151 (1) 43367201.P98 152 (8) 14897.4189729.11524380579073027969. .101284922414513827611672455293249.P39 153 (1,3,9,17,51) 307.6427.6297787.45618058027.P44 154 (2,14,22) 8009.40987409.74353801974761.P59 155 (1,5,31) 21701.108674992710961.145475949458129109023753501.P40 156 (4,12,52) 319143533738738955692755921.P41 157 (1) 1585387.223975620462535382927.P83 158 (2) 317.41081.72997.10390269663517.P85 159 (1,3,53) 5407.1725469.P63 160 (32) 46957667265666758402894952584920394200961.P49 161 (1,7,23) 116243.P88 162 (2,6,18,54) 503731168597.720314410420100602530036001.P37 163 (1) 1981740926993660561.286075553470422974507. .721493104094461397911450801.P48 164 (4) 2953.811755457273.46964872205858855033. .2211877372577215640856618933593.P47 165 (1,3,5,11,15,33,55) 661.9651181.P47 166 (2) 997.4649.99006230951147470700089.P85 167 (1) 4978061451403.50902967640396173052637279626869845515838501.P60 168 (8,24,56) 12433.44763922656823409574575008753.P35 169 (1,13) 493481.P104 170 (2,10,34) 1361.14281.14239201.87393601.1972618762904267665190337601.P40 171 (1,3,9,19,57) 60272250820183.6267476427578502461453809.P37 172 (4) 18233.30185745097.2646713294612838233.P85 173 (1) 347.42794294406607.P104 174 (2,6,58) 382801.506670253.146817720340602448117.P44 175 (1,5,7,25,35) 701.2801.6309154245455368301.P59 176 (16) 353.1827937.2704769.1800750547615213217. .609201485490930587260897.830940907997357679202561.P31 177 (1,3,59) 709.1063.347629.49987218529.130325543183670643. .504583856881942565107.1663887084465861537223 178 (2) 20365288294844141313970353677.P95 179 (1) 21320258969.12021304420747747.227138023883511049. .20324346366468227562461.9711234996179070876201114229.P31 180 (4,12,20,36,60) 8641.440641.356646293281.50735307557193841.P30 181 (1) 1087.28961.101723.P114 182 (2,14,26) 3640732369.141437955091157453.P74 183 (1,3,61) 17203.11833147.2880471241.1117197595048793563.P46 184 (8) 14966561.7323187654220815881445121. .36153673470666026958084532869022033.P57 185 (1,5,37) 2221.3701.P94 186 (2,6,62) 373.1117.1489.10269119521.P66 187 (1,11,17) 1123.12343. .17871635646349095375983368709164224334356049680569.P56 188 (4) 90617.755009.951281.12795134934601897. .4760594190627487654169124325931441.P63 189 (1,3,7,9,21,27,63) 2932903.238040587.3916103733109. .1743424593819524631667.P27 190 (2,10,38) 98041.2574645949207561.P81 191 (1) 383.17932621608157901.45343989264399047245009865403089.P83 192 (64) P90 193 (1) 69481.1046447. 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371 (1,7,53) 743.31907.171403.42073627.2340865442872909. .83529561196595406306863.4294105917163012848027061867115931367. .241881732025657819145103362017436952827107.P82 372 (4,12,124) 854099353.P159 373 (1) 16827523.855947877694729.3402270307745780791746163. .11154375543111756821332089996502714524028241938815715700967\ 871500680683519826453861993140068830879201.P114 374 (2,22,34) 36653.1833280694213.273799167334154011397. .923042449224830739177821000828273466092937049.P142 375 (1,3,5,15,25,75,125) 9001.994501.84719274001.P119 376 (8) 80637397290342655433338510282666959378353.P217 377 (1,13,29) 9049.26156261.140848709.590546419655063.658682853381229. .2892674132017489.1143735337011486830184857527605073769700916\ 831409126204412747203317982036209727.P93 378 (2,6,14,18,42,54,126) 757.20692918440938644983866317355828595289. .819438001747398504074179279584891660651265447170220801.P57 379 (1) 4549.37850067509.1343210014472411202426336065918923.P217 380 (4,20,76) 13681.P198 381 (1,3,127) 23623.88128349.2906725201.967413475393459207. .560679020564216733169.P116 382 (2) 1053557.206218283317.146292198125317.234499916148809. .1450381225491210600799800528142580736112755564637.518795406863\ 113189776769006766478178496100854556415486885838669324460646241.P97 383 (1) 122948435869537075322765443342673273970369015562377774799074688\ 62173285451004329475113416721336688277608976323156483762962209189.P140 384 (128) 11059201.11046880513.54263502654032658722910258215691970561. .39121721970474583977175915186504532678962985522839069078146049.P63 385 (1,5,7,11,35,55,77) 40420381.5394824821. .3652217646340731768196856238641110981. .7193006983512766784866963293032603060201.P74 386 (2) 773.157489.3357768242667569.29236154014192628894921.2188204970\ 175459207787323803702410481729392361313578427539575673958230643241.P147 387 (1,3,9,43,129) 711307.311491116057601. .200253796299662273123815420919014088858469902515816181549623.P97 388 (4) 2558473.8761354357601. .2263044155863595424435070827541937027775094467601.P201 389 (1) 1918549.480684942423787952315045442717762901142199887665624\ 9744151908083440952028702060283604283304272581020645686839107.P154 390 (2,6,10,26,30,78,130) 106819198985704526442073820024512172507707681.P91 391 (1,17,23) 104789.338342444887.513765906786138686731576770204403.P197 392 (8,56) 487649.31312961.119324017.3963317569.136134424591242051521.P184 393 (1,3,131) 787.5503.14149.365886952009.2346813979937685523. .31486724064290126361763951427593381. .232544166333069010693505967345270131281.P69 394 (2) 21277.52009. .168565108839546843599332960034300611817889542621431425201409954169. .73790636581458670049969687570528825724609281826017951532233\ 34695744694124049076609742477.P112 395 (1,5,79) 7901.2452107355981.2450102857830301. .106534495441595594244841.165790458765148163402161.P141 396 (4,12,36,44,132) 4352560631862697.346866834441245977. .3469311118976860338738481.P111 397 (1) 37372787.145945976031291343336358831924626830985356649410\ 4595852491932349900699487549204386483046526924066112853387.P164 398 (2) 797. .24688871653296457340343698107085412267529334706921796439672401. .439576188836585492607813158138372060197521100539793690042855\ 9139073819674326507718509772527692224009.P113 399 (1,3,7,19,21,57,133) P151 400 (16,80) 10467247667093179201.570816590874389863426712610221376823\ 983504352706521883023381652903468683124270020472964342360390401.P106 401 (1) 3209.68860956180521243.333064937028925224769589. .420717786424985136639945399052723356069431301479246714094457\ 759188729290364889658383853603.P147 402 (2,6,134) 15277.4807375693.6815632610027885089.359599502582636\ 9977659826406670547615979975895153952282217794900186926613.P80 403 (1,13,31) 142958609.50422342829.8134973129579141. .793899011193308548529. .290997650534397141563820246300495954484696648210147356023.P140 404 (4) 12873449497.176729217433.579264071033.P247 405 (1,3,5,9,15,27,45,81,135) 359683606111861. .27958214476418447045648661835559283181.P99 406 (2,14,58) 918848200649.46233876772514796806449.P201 407 (1,11,37) 488401.73108132021.706404287882271194070912641. .26337873665845235353307452756064083. .419923501988747088508592525569165716040432773229.P127 408 (8,24,136) 5530033.469036801. .3290490848983782585870394810161320136439633.P122 409 (1) 567508524694081. .179425223701718689835393837247166286352741072164031120636432233591\ 589571388940800769444701690976543908944390697369214917439022818121.P140 410 (2,10,82) 41*.583841.2896241.34167223380089694290015311471038\ 86888986064390011829175980595779171884858582418606948161.P123 411 (1,3,137) 280303. .2110554780135004202099793136762963590324098107950957883. .3852735458397598071150011401658661874155403923682368550872409.P70 412 (4) 875089.143724625337.P269 413 (1,7,59) 5783.791309.74811647.28335417881.287948481625309. .32820211095209235603211341762606041003509476839919565067488\ 24076292276237936814589.P120 414 (2,6,18,46,138) 1271333135249191801.P167 415 (1,5,83) 961347785521.55785954324461.54238669980920652116766437767923548\ 2113503370942017294492342497725064744615307084697173312788543096361.P102 416 (32) 9900401473.98759854245313.50303941887027464825562881. .4670727010078891472720277353744610046303535783924992577.2347390\ 534950637681414328340159351238530716731893251495801040097664641.P95 417 (1,3,139) 1669.7507.68389.2972602849.6231277854493137343731235\ 3901828477385743715090139973652675999660403253132274229.P92 418 (2,22,38) 31769.1680361.7201636278388333. .76891527486997630150967815266363922266871691437.72933901304723106656\ 006752127002639668273458400627707551792920762389246520686868895005797.P90 419 (1) 281595692549.79779766571538167749.18570424577878762265812169. .967380644061707817493048083600098828622392004768853039801494\ 9325161831491017698369800194461861854003.P136 420 (4,12,20,28,60,84,140) 782349962686680131171831761. .123682372689587234320272170926306609340495521.P64 421 (1) 75781.205114040909.2670138546849776123377091323. .8995624597957689187076765315194349723348112246742888198702884889831223. .105187948182876443327926736137490993577314213859000021132398\ 0722266983.P111 422 (2) 49701926718842398034917.1838688342673461699900627759697114609. .311432401581629924844904088616068036851896508487327454494715\ 4369923639426300086880269705437.P145 423 (1,3,9,47,141) 222529765609.47221880173493743.8636976339699869\ 318683821732318207901297057837683243210682129853674321.P95 424 (8) 1500134897. .60268651913201966316354616992545254403334511716998956168391459\ 6709175729823869724137674843406107143671357881937261384279217.P159 425 (1,5,17,25,85) 56101.24320833768392901.P203 426 (2,6,142) 299097157.10980344624856402438121. .33861120548112135250672625281. .1042353298371672770854199410473194161120444561.P92 427 (1,7,61) 1709.78569.2478342640892955029371216779549673912736487569. .563755283862496929168659991708057447948580426252052767.P145 428 (4) 857.881695186297.1151785652724457273. .1161803970449055432131784880415625128129.P225 429 (1,3,11,13,33,39,143) 8581.34744510854769. .18538918397035986453797788078200765174683046595921.P101 430 (2,10,86) 2383921.19138570947468281. .29523508733582324644807542345334789774261776361. .340732317219318187306456127459311407346619258419020582677053361801.P101 431 (1) 863.1319723. .1299045235662270036905137300245416244853020592140901344547400241471574661. .107347603521010806034529883914660126293686240977560226904797\ 55674553000219634801495349068959153581761.P120 432 (16,48,144) 16417.76946093484599331535592157286631660929. .1816635831076069705419094985033611385104065844528715474020035550753.P93 433 (1) 59838112849.137082542813711740361. .6241637147741740981618471273184293996262028746119554490647312140117\ 034401495008827086088786497184191229779873774610991168214097728569.P139 434 (2,14,62) 32117.26490493.339914790655637.493140571225597.P211 435 (1,3,5,15,29,87,145) 8737168800277087090205609856511041915132043207241598729973141.P96 436 (4) 464777.1942414084717961809. .308269926237154790677509621853570797581741454788321935416024\ 64749116633105005172121480382982329033.P181 437 (1,19,23) 383527035556992289388236087.P251 438 (2,6,146) 877.7032466681.1278677279155561.4725897742147117.P158 439 (1) 471487.662755721911092119744737643749343823193619423487281. .726845143491739952115155244450851409238604625439133466538561\ 56079451856750949074523.P167 440 (8,40,88) 359041.16079210384161.13901852309409971054059871521. .30705281217618182630071422092483681. .87530085823642527016184874776489974647524641.P99 441 (1,3,7,9,21,49,63,147) 63019783.177942365089147.334983841832046709. .1412763237721728611106087634318515911781756690338345284469111587.P74 442 (2,26,34) 1925383738253.938705194413297601737101686241293330600757. .27060574572993511759497340055450978609641029013. .8236443738642303027336453331644376378492747440274033886009.P110 443 (1) 887.8861.32783.58799821946580083201519815867. .67741846030242538458856732404026479281543092694582483258359\ 650991443207508407922949480467163503.P174 444 (4,12,148) 662457647768722978873.288243041871591634870747489. .2110210599897098921988264554383969. .12183357210260619534067632764355337.P87 445 (1,5,89) 414780941.74122686370301. .118105003026044634237696289344460081081. .5895518746203541920435931300822793257683987241.P140 446 (2) 16682721313249361967072668559607434769. .3754900109140529243402027156921792844356092542908932626331118\ 4809126147808341402156263293709818372455116963314974595677197.P152 447 (1,3,149) 1789.2493584477509.63998602029097150801.P172 448 (64) 2195201.3711466630036481.156991808999010049. .1214606229579135791230337. .23371863775658144623538828456854573496104607906605333794952273409.P141 449 (1) 6287.24247.248636782340798457034945031270021. .65947657789277139989109990709269229724914022322962389130611\ 8460133145942262091148064858750118672916742591021.P165 450 (2,6,10,18,30,50,90,150) 1801.2516401.5115601. .586035627698598209390491847184601.19112388231871991649234058440147001. .670159729536080076087493765952253601.P49 451 (1,11,41) 2707.9923.27061. .99727835247004201173500507893602570607105772056177313899261.P209 452 (4) 1148806388418179041.645242881466809773505201. .25254606970434754819456057. .151445975886988995098619115988854902693819562580983495230657\ 67676425622309077158667995506200103502953.P146 453 (1,3,151) 907.48418343681527938421.766492135026955437098117761. .8146766587356196823064018499336810819230244501.P115 454 (2) 27241.11968978369921.28223162330477. .379571043658013011637700285412541336658841886949428435235223\ 713741824370376909693.P205 455 (1,5,7,13,35,65,91) 7084002845921.567454610437261. .344614595608455761681.527997808645161693896110537853475614480\ 462726804663276790604591366210441.P82 456 (8,24,152) 9242209.166986765141073.266907178346502367875997124\ 6463050471518645889898176890916414860361001098151488625457.P96 457 (1) 556627.168077755969. .117220108378126490381762151218816684092066444528511689043053\ 528260965023351980155831635995424109.P207 458 (2) 58478290641569.7549416542904529. C290 459 (1,3,9,17,27,51,153) 47222237030383. .6202487812746184700505670204578844708640694244849.P139 460 (4,20,92) 263705913240553959836477326650720189605187407476536\ 4889139618399522196738398685647099556845082406779294922029921.P135 461 (1) 9221.675827.16043723.57776275545721. C291 462 (2,6,14,22,42,66,154) 8317.285517.12168544081.537684328029194809. .17757087562354803087936135241. .1373095119406080811642424383401401449810674535237.P55 463 (1) 33684664003.58350359323.64249516403.470253774218237389. .2924865435359209459542823.C249 464 (16) 974401.7099201.20581886497.24208780451201. .513682561119621544979692603182989732675937805212391169.C223 465 (1,3,5,15,31,93,155) 17392861. .65728307202655190132956107152419813447801.P120 466 (2) 402540984648503528488454011551383318201. .4101952307739917190835211386634078017943853080512921.P235 467 (1) 2803.9341.12143.5458604475996540934416287. .530481237780471205625505210196183416842092199646460837093943.C230 468 (4,12,36,52,156) 937.85873160400449918797155817.P173 469 (1,7,67) 55343.2501647.12278858047.14758952066454916741. .3571577568009293113803246365768930062975505663. .118670248524809688178093249909640852381841493324290034550005\ 451255580787.P120 470 (2,10,94) 146529848333247341528151390620613254711437023936034\ 77029400929078809518237211981943351791921.P167 471 (1,3,157) 7997581.762195685382569.2377864993956889. .44886416674333153030653350565562472802301. .2121999993860741578057840033007656075393147.P99 472 (8) 94050721. C317 473 (1,11,43) 947.11446601.99270403.85223951417067562768043.P253 474 (2,6,158) 43609.157651060477.1133101180287529.3367254562316010241. .10074918917599232092884277.58400466995304188804026921. .30967644304103854956320826397.29674700910032777583435863458273573.P55 475 (1,5,19,25,95) 5701.15859350277801. .513815858751874265528003239989981623497386326029637020932236\ 99747258701.P164 476 (4,28,68) 953.121008044805780049. .329466886273185603920929243056323831211539643728650902949159\ 094286673492784518024190831497916000648073283311761.P138 477 (1,3,9,53,159) 6207533974627497245750519718144906499412274008\ 13646116953937789726143602347247590228392984503.P126 478 (2) 267916133.96213845302733. C311 479 (1) 2356681.363424007.124567972643.200505869393705878515667139575543. .8148074372286947771897126264800254214544463885555769.C224 480 (32,96,160) 13441.15361.4385281.2796282170881.218142099567361.P138 481 (1,13,37) 1856054903.46314576101.61320012890721739181. .17400227608812312697369.486059913607710365830032115613076\ 332269305947462620375880290572017340680850278954192602546\ 886507318525244009874673153587.P121 482 (2) 28921.934844161474657373.P314 483 (1,3,7,21,23,69,161) 967.712909.98351423022563612754061645927.P147 484 (4,44) 1138369.34155242389634609.1049387990436309833. .122515116543117574751477696008576308350159849162039389265200248\ 664706810525983995317855050309136882282571227567572775657339729.P142 485 (1,5,97) 32811221.176937524794721.268392844035430518101. .122421916731890979324011172973754461. .767621265267973253254260261142097075696808078786255888812712\ 53222035762027054431076524779741.P100 486 (2,6,18,54,162) 3889.187597.5313236622013. .105404102949627434662169176477. .1479484627345517501028316896927845640086642808249703019041.P119 487 (1) 31560523.2414879462366988244737921114229. .661750709145526762982572000157367120136361. .17946993671211675804303475321060080572775145674764419504889.P202 488 (8) 977.46455649.13438797761.188732040042673. C301 489 (1,3,163) 5869.43966879003.42582482649247. .28384281575469484539729485807882589299897038184608441.P147 490 (2,10,14,70,98) 7841.90023593801.306133764161.41448356277321841. .681419962974819214441. .1697022120731335981925709877507964961107487731686306359889183940761.P105 491 (1) 983.1394441.65203052535938640122309.P311 492 (4,12,164) 19681.21649.10704937.998773951495417. .806543918439857063609041. .3328982736891469475110718092947151079706495362468067039231558\ 357955631710833214561.P88 493 (1,17,29) 146779436039839305501219694026409. C282 494 (2,26,38) 3230532761.1767659860587277814048907809. .36743992589172549688896577643923578971115369473093.P216 495 (1,3,5,9,11,15,33,45,55,99,165) 754381.1863181.50448760561.P145 496 (16) P336 497 (1,7,71) 99401.409529. .240787118953039826354369683426733908346834223779381375433420\ 132097125851999184041021.P200 498 (2,6,166) 3653329.6227157528556681.6381497944213050625875889.P183 499 (1) 1783427.731235661820267173253289476481600895823. C303 500 (4,20,100) 20918327356001.139463359848327184507854001. C241 501 (1,3,167) 101203.144289. .30058838192882078554538354349397380254301027061443049. .91624473675204574882067244970167251090567779850005474747.P114 502 (2) 2448757.268875820632533557.32225721612033377081. .15031681774150472995711082643316600081.P269 503 (1) 2689940050905281.124406973615393503996181711527. .14431277493255383652600216354005959045406674334375840908040203.C246 504 (8,24,56,72,168) 742897.75334332345553.P182 505 (1,5,101) 20201.13500510038221.734251000402501730461. C242 506 (2,22,46) 1013.2453089.9170844677823637140641. .5575108032738819112514182889.P249 507 (1,3,13,39,169) 2029.84163. .298473861998688245073651450854036658780754826996849337412667\ 837029794560543275671163141.P124 508 (4) 678237913.716754837761. C332 509 (1) C355 510 (2,6,10,30,34,102,170) 200809971410739857185121927002619581592745812881.P132 511 (1,7,73) 4808196247.2135538760510804261644688223678697374597789. .303253916633431644653433325612925610925371175782467706721981\ 3898811240065881127.P172 512 2*.19457.23606273.236554494714698753. C329 513 (1,3,9,19,27,57,171) 34104241.36768763. .5187026979075233964349175658921667. .20179266406136366293306914342458938908548361348260029807.P123 514 (2) 116969640517.56399824427293.957628423318361.P319 515 (1,5,103) 306824337181.665319139361.P262 516 (4,12,172) 1033.4129.3084493201.19511773794697.45245904640297. .52396512454609.2159328744538512697.179455927234560583657.P140 517 (1,11,47) 62725213189.66656777947.296550613114009. .669344756701834738010037400949.1185808915589115463187638325977790819503. .88454878749136805475079989662610869569843. .1470647911862063012962128354629862752418809891181735667.P122 518 (2,14,74) 1663105108175775311527481. .250167286245585418284207152745815261470037.P237 519 (1,3,173) 204487.3167773403161.23548601915023.4947361916187143902327. .796566495901153385012824230136787015040409401477243547986541\ 19296217088928225877167.P105 520 (8,40,104) 62401.484675361.1031742401.4353871187948045921. C228 521 (1) 375121.23788861.8817928127.P341 522 (2,6,18,58,174) 2089.31321. .5275190291470265272803388673282122147498250529955921.P176 523 (1) 52398344961841.151306706505561078363159820026981229. .2438031578522051897525216049164414381. .4347998936792990371757427368250896164670794147017084379398863. C219 524 (4) 386713. C358 525 (1,3,5,7,15,21,25,35,75,105,175) 2694301.144472437861892912801. .2704858664735732787120837415201. .51221911570075178880293450950123975334401.P71 526 (2) 24978689.211297357.9573494476958437181129.57370364344047261751973. .34446782443113410904289164131134167536732914603003729.C254 527 (1,17,31) 170749.3529598003287.1820226356716087.789827420043567341. .282472612598651594461367.6157952360951974466688821. .119765322622837683709658359479781009.P202 528 (16,48,176) 2978977.191640769.13124950081.182246536033. .164170280215393.11251766323019640001.149519657468548932688496299873. .65860355276846989197120350157509068780897.P85 529 (1,23) 4903979501749.1066814762345695551773279927. C314 530 (2,10,106) 409876561.131215231241. .319993467214166060693504560600125448696551214669666186201801.P212 531 (1,3,9,59,177) 139123.66482263.82879543.374873477859320023. .267314292857600691481.48266727958752863730427. .6073771594630197479821204227489109. .48715518697383829418413747135221841113089802403.P82 532 (4,28,76) P302 533 (1,13,41) 8150656054856188589.82397877735622769334975701680889. .83421177405664571309417910863828731996178326669. .44870502743212948936745017928623921906901125290918821437538867.P177 534 (2,6,178) 18946920902281597228884176756457436750309820391444610249.P191 535 (1,5,107) 2141.4576884341.P284 536 (8) 17213276593.235365020727694247953723053121.P330 537 (1,3,179) 21481.27818477565727.7787668872919291609673326141. .112273729541498298225591815880543347260070365308763.P154 538 (2) 721997. C369 539 (1,7,11,49,77) 39887.190807.56403728034331220037313127.P258 540 (4,12,20,36,60,108,180) 2161.16090488675463906483649014304881. .25540864554334781154951516915204729464881.P127 541 (1) 2843933563344776556007.19858777672439210774563927.P331 542 (2) 139837.4825969.5339797009.5115632075203472244971533.P332 543 (1,3,181) 6245587.242395255386801469. .3638898397091430205449202125429103.P194 544 (32) 164512129.187312153430977. .6790374245652665093842011652541869834263041.C293 545 (1,5,109) 4626629557771146518427711512403423726361. C263 546 (2,6,14,26,42,78,182) 1093.1636546425044077.9202941751066205689. .199852066328056058281.523690035658364155498009.P121 547 (1) 6831397797068883781.4544685586647174925709. C342 548 (4) 1097.591841.1381891431843295601.840672999104093544374960984524321. .752105340200918972161367196325463440050652553.C276 549 (1,3,9,61,183) 7687.P248 550 (2,10,22,50,110) 58904917399891201.2875381361817657565692601. .9692731426883108488888397645304857869271916556162164071302921601.P175 Table 6- Factorizations of 6^n-1, n odd, n<500 n Prime Factors 1 5 3 (1) 43 5 (1) 5*.311 7 (1) 55987 9 (1,3) 19.2467 11 (1) 23.3154757 13 (1) 3433.760891 15 (1,3,5) 1171.1201 17 (1) 239.409.1123.30839 19 (1) 191.638073026189 21 (1,3,7) 1822428931 23 (1) 47.139.3221.7505944891 25 (1,5) 5*.18198701.40185601 27 (1,3,9) 163.623067280651 29 (1) 7369130657357778596659 31 (1) 5333.49744740983476472807 33 (1,3,11) 67.45686117391553 35 (1,5,7) 71.37863211.1469029031 37 (1) 149.7919.12211.2569799.334286825813 39 (1,3,13) 3143401.1262014275211 41 (1) 8648131.1854850885886497427178961 43 (1) 173.431.7383359.1048953903129961695599 45 (1,3,5,9,15) 2161.112771.19353635731 47 (1) 930911329.45110836129.17821718159716147 49 (1,7) 6527977.122694573317.600827908214213 51 (1,3,17) 307.927037099.23412002806867 53 (1) 13781.357293834576449.7091531088740602980647 55 (1,5,11) 3675127061.3031462959351050977391 57 (1,3,19) 47881.820459.219815829325921729 59 (1) 4866979762781.29050941569087.11522163007228653937 61 (1) 42461491.80057377.17252803354297421346943980322273 63 (1,3,7,9,21) 379.8387947.616332907.5239858051 65 (1,5,13) 11831.1420901.49398961.22533649654910414281 67 (1) 904949028329910415467529.3023706637809542222940030043 69 (1,3,23) 11731.1236385853432057889667843739281 71 (1) 3546245297457217493590449191748546458005595187661976371 73 (1) 44764549877.2436094907761.8439148071138817.138721648424756087 75 (1,3,5,15,25) 601.82051.271041511600591342728451 77 (1,7,11) 484847574510970082567.84002092056248016278479853 79 (1) 1147240288157.26283825237209622143.197531251446059329471533015409 81 (1,3,9,27) 27767002339.37725805717350619429950429139147 83 (1) 167.499.17597.41580677.80781507941.605274844997.P25 85 (1,5,17) 26807981.20891158391.P32 87 (1,3,29) 2694217.1833921547.4706691035521.1357610070580129 89 (1) 8011.2064441331.P56 91 (1,7,13) 48215910563832798697.P37 93 (1,3,31) 186187.290869963.659988451.842660004553.1358539033057 95 (1,5,19) 571.1901.825838991.1298704628041.25425408247171.2995523312517361 97 (1) 389.1747.1586365166597.18969653181299397175271.P35 99 (1,3,9,11,33) 16633.18380539.18414001.226407819331.38167293140100433 101 (1) 1275678077.P69 103 (1) 2473.5563.160681.P68 105 (1,3,5,7,15,21,35) 211.35281.58171.P26 107 (1) 643.5044140393054571.P65 109 (1) 30726149494277.P71 111 (1,3,37) 89728627.187333846633.1487716834806007369.3561693323285489089 113 (1) 107351.54466954894479739.201436862864351419099.P46 115 (1,5,23) 461.1151.44851.257917526307345124973861.P35 117 (1,3,9,13,39) 6553.5958157609.39031258670353.P29 119 (1,7,17) 16661.29032062767.103198889691409.12405291558509977.P30 121 (1,11) 4163261521.1304380464883.P64 123 (1,3,41) 25512169.141304123.P47 125 (1,5,25) 5*.9536585501.117811792772681609501.105875321588567599765751.P25 127 (1) P99 129 (1,3,43) 43*.P64 131 (1) 263.3931.6551.1284827442574221936870974393373403.P59 133 (1,7,19) 11971.188861.1101773.164331230229374083.P52 135 (1,3,5,9,15,27,45) 175509721.P48 137 (1) 6577.25247731.53280671.60042056488501962187.P68 139 (1) 557.21407.128159.P96 141 (1,3,47) 283.13537.753554761.122320721569.989671414201.P33 143 (1,11,13) 859.62545486153056268832471.P68 145 (1,5,29) 132241.150433631394488258261.P62 147 (1,3,7,21,49) 32093041.P58 149 (1) 38538553.1318713554713829548602512956686040272376450743377909.P57 151 (1) 2623968964411.4956504421137000338429923175878885954098593563.P59 153 (1,3,9,17,51) 9757142011.12644443230579801886843521019.P37 155 (1,5,31) 3559267608341.208210289142572055121.P61 157 (1) 6446107.6423436771.81127299702871294523556776543. .8695994904356302134775281276601.P46 159 (1,3,53) 118721004139.67587459957091.P56 161 (1,7,23) 10949.593447.491787574454982121. .3358586137753609961516447641418203949.P39 163 (1) 653.2378523250342970947582043555610171717174452063.P78 165 (1,3,5,11,15,33,55) 331.13724862774476458441.P41 167 (1) 19466857.10301691259.229027359614687.9703107759710968661. .2200446540213260920441013.P55 169 (1,13) 677.3719.1420277.3066042413300025661761581713. .351082413599031251316269147227.P52 171 (1,3,9,19,57) 19*.25896916098621777025320461067950269867.P46 173 (1) 924669087985921.495043698717322221180325946047148316337.P81 175 (1,5,7,25,35) 3822701.114265201.141218351.7292423951.34840572551. .35107498301.2370825139201.P28 177 (1,3,59) 1421059369.P82 179 (1) 359.4297.399887.1126853766403. .171074041901536300021132517497157303.P80 181 (1) 39821.12684206910817829.P120 183 (1,3,61) 22335533202362157841587721.P68 185 (1,5,37) 1063053988637874955869001.P88 187 (1,11,17) 382229.4208612395681.6467774498519851224197542939036067237.P70 189 (1,3,7,9,21,27,63) 10644859.292645031213683.P63 191 (1) 383.120477626957.141173343133408897.172804791061171733536391399.P91 193 (1) 748132849.3759493321.230824001813.344929902064301. .577701497837906594854943.P82 195 (1,3,5,13,15,39,65) 523065274520717779891.795382366687653584971.P34 197 (1) 2235557.10123252906683101.P131 199 (1) 797.191837.3693839.484493690172684383. .2389106853487241752315685035579349880354989277451.P74 201 (1,3,67) 3196645037857.P91 203 (1,7,29) 1458188789.432549126887388039664858367.P95 205 (1,5,41) 66571969781.28852807210022072371.P95 207 (1,3,9,23,69) 399097.P98 209 (1,11,19) 18873119.414230477.84125065520563. .39547815403982363610457333838688241066157.P70 211 (1) 35768449921.127491843407.22502477360820492307768713607212049. .953864267757776424221068538656285528154532046177627.P57 213 (1,3,71) 22301660719710979.P93 215 (1,5,43) 1291.19660072438421.P115 217 (1,7,31) 385227416351.26316013765873042806112463084693. .1265855393578666785134496493194757776649681.P55 219 (1,3,73) 1143619.2820121693645487997956892799666256974847683.P64 221 (1,13,17) 4421.39721657.41183788762160210182927373892714194450477.P98 223 (1) 359734681.19261747635283.P151 225 (1,3,5,9,15,25,45,75) 320851.3388291201. .2056583697041569929017137051051.P49 227 (1) 1393781.141273137445779487073. .1994969355576066549710715311391607571195545033.P105 229 (1) 1505447.P172 231 (1,3,7,11,21,33,77) 174090854323.1526323866435523. .83531679812360869820818648177.P39 233 (1) 568465670186789.3945524703927668484254051089. .630076600824417505174717786052089.P106 235 (1,5,47) 941.88816955621.P130 237 (1,3,79) 15643.393024899619859590739537077043657.P85 239 (1) 479.555643125049.674693399227.2787187926109459.P144 241 (1) 248231.20481747682829.1840889044920084403. .7710038279791808580832936799. .246316726378395449466748758203811907753252397.P78 243 (1,3,9,27,81) 249844450267.47847655472636701140045116262913. .103939380360329666746292370686492281.P48 245 (1,5,7,35,49) 22541.P127 247 (1,13,19) 1483.77071411.329143658741.82569737524705024142782304189.P117 249 (1,3,83) 17929.63871987.30565451980162779163327091617.P87 251 (1) 503.34204273.59351200969.80440705758435499. .3489478020025154776405154855930832218902630153636858925509939.P97 253 (1,11,23) 23*.1013.75168534000121. .259666046866989553234678839986188137176834471947.P106 255 (1,3,5,15,17,51,85) 1199699502336395787186091.P76 257 (1) 9767.17477.3309693452762216327. .9306689489306197083232219997965248298881691751524941849307.P115 259 (1,7,37) 2458852243.128241016566344721609490367365530205308828\ 951059763735701191925429688386832869.P82 261 (1,3,9,29,87) 523.467281506322297.1088767101178107721.P96 263 (1) 131982869.12634882984316388571047983239402938349932097252\ 525834121084935889987017221049.P120 265 (1,5,53) 1061.12721.59499149215409565615862915027061. .1443883079527663603943444340055791696913305571.P78 267 (1,3,89) 18530245891.P127 269 (1) 29083873645382611513.2334775781694290932919. .14914054997566758664316062644331821838847.P128 271 (1) P211 273 (1,3,7,13,21,39,91) 547.2430143818773217. .311093172628257376513996627655635721132089.P53 275 (1,5,11,25,55) 13751.10764601.1080416801397537451.P127 277 (1) 1109.5555507589053.152327217259127. .16183852725411755980358386606565323256380349. .14011053856556766554595009793438946968040153039.P96 279 (1,3,9,31,93) 326892685378628881. .4195369622107561728725528588657828897923.P83 281 (1) 33721.186023.122413379955569789.228566796853368622765083206587. .11762786832623811560644277958387970995125858157407. .28717354535597728468537227064151476862005971007351781.P61 283 (1) 36791.217516631.6650510037106913164557499908650923.1384573613\ 20915478919381975760508114488979126852819238404548238145324558533.P99 285 (1,3,5,15,19,57,95) 47562842881.270596289241. .209547179344816511252551051.P64 287 (1,7,41) 248848212837883.P173 289 (1,17) 671059.606329606788978761264759513146230361569.P168 291 (1,3,97) 111940600727841600317236399112257.P118 293 (1) 946391.193844113.2942031681694832257394740018524925949323820001499. .77296633023286191721507964885438021314817447299007.P115 295 (1,5,59) 1181.19568032756311331.15208118255933834293359009545761871.P127 297 (1,3,9,11,27,33,99) 180794604080179.P126 299 (1,13,23) 599.5981.309379487.2341190333.394098064572643947287218201. .159997585500087414157621168325510579411294626795380708213053.P96 301 (1,7,43) 4941217.210619620359.387153001486618459. .1026218994621353041220001358738943323. .50018859578270750848409089664785836827007246435735770683387.P66 303 (1,3,101) 2529268867.4844162809.36536927761.257934717592273. .31140192590150713382146219858775467.P77 305 (1,5,61) 86011.2112242585382465957468782381. .24506226188880631899928133376464081634967825718604821.P103 307 (1) 1229.4762799.774471014077469888593.205898436168261867044624683.P182 309 (1,3,103) 619.P156 311 (1) 1191554036683.3666342101717.1028123934962242970067317. .7640150264100839651419559. .3364411552706746192178898058705706890749155217602642004211879927027.P102 313 (1) 20032627.1280155603.1145667266428264694407427870250002852\ 640339971370109925272739002529333927038171.P149 315 (1,3,5,7,9,15,21,35,45,63,105) 423123121.1076836800079531. .72725680608108905121706081.P63 317 (1) 15217.494521.P237 319 (1,11,29) 10847.642814987.105726751219.891967447801.22138289428735393. .1409088913314217103.50351395030858047251181629. .4528381576097816452461578808677.P92 321 (1,3,107) 24212302455882717029271553.3989017680658351355297802631081.P109 323 (1,17,19) 647.P222 325 (1,5,13,25,65) 1301.15601.903471092281594039875101. .9458999046244634687622911142066001. .570312905179987052421467082275470442757451.P80 327 (1,3,109) 2617.5233.16823497.161662095193.P143 329 (1,7,47) 13581753427437725779783140643. .5552584966550029192436491703687097023. .9121864969966391515391635599843611190251309549200752213601.P92 331 (1) 314314291.4180768321.23780962384145063253850061. .129666906452652590684803897.217410311169868631779718575225367. .65700141121171476089069828596037497497930556037.P109 333 (1,3,9,37,111) 157475333660422172779.P148 335 (1,5,67) 2011.412051.8595640749841.62977471383821.37844794094580139\ 581697623770911579688837081742561513466850889366516267662341180891.P88 337 (1) 103742130551.256196067835296580684999904063.P222 339 (1,3,113) 18307.13622377.17994204073.196433872316310611137.P133 341 (1,11,31) 17747199053.141625909793194221396635922467362734944\ 0103802386310341690074485254079521022612195192771792469.P130 343 (1,7,49) 1373. .2546288496284990213389598514399701583273729812805688674719861.P166 345 (1,3,5,15,23,69,115) 691.241541401.139954341051841.P112 347 (1) 16657.92013588619490399. .8023776342054310550242315692074754087050026551393750990167. .1129620175217353004491157321491742157218372763619013430072837\ 64634643624748720079471271422964001.P96 349 (1) 8377.16171963.369649633.102551873890900123. .126045115319866344351544439.42718986495841359540531087907270\ 796421704343217605115730109486979483.P141 351 (1,3,9,13,27,39,117) 188270083.1132637392660177. .255071870171283288213182239588434720112842353968893187.P92 353 (1) 13509526133011265183077504963559080738112103111138273231839\ 0846759744072165636542920143351738198057636666351316191686483.P155 355 (1,5,71) 2974779760081. .3606051765934752249146021693030658674181338436335115802421.P148 357 (1,3,7,17,21,51,119) 69259.18052799163122060087025155723065171174003.P105 359 (1) 719.27125323.4712635363. .285280913757251941415180548664485621181937893.P215 361 (1,19) 47848036334820116132986462577147872267.P229 363 (1,3,11,33,121) 2179.309575803153.P157 365 (1,5,73) 6571.138502171.2244077756789983310918695541. .15528751069542868927499643947109862138995169724809336445236\ 00802712902591.P113 367 (1) 2203.634177.161021084117.7840142252089815392041. .2816294841300993066546214031271001.3270112070990954768535379732765321. .41860517287867240460042208225615145479852721.P133 369 (1,3,9,41,123) 739.2575675190386099.47146662106901857. .2335432574534090617.899377009735615553325855097.P107 371 (1,7,53) 743.26801041.56691769.74107993.289848199798750673398\ 0871980599973253064554047756266758938351351888972317093313.P139 373 (1) 1493.5775369006575459687291534776431549197735368225369631\ 30956976981788801.P218 375 (1,3,5,15,25,75,125) 2251.11251.56633527660731428440540758758251. .3331020133962884772706727916696838942815963496129389001.P62 377 (1,13,29) 17703177067967. .4163738647660343644736593693349157640855934319038312150518137743. .102250459166012486477524443575930027004928321838932853206742\ 60124721671052319.P109 379 (1) 46997.1600897.14007805315485347573527029147002036597. .23229132519250730340307782442413365306631261048097.P197 381 (1,3,127) 33581615699197955777738387891299. .89896478576590314583750832427049. .6207497961491001860865708614869208845594249. .63537996418411322893388678898019600654636747.P46 383 (1) 15229370711.26372116867.25278624741941. .248471840056276128633180582390714167359968966984074018920310\ 78680650524090050042476174972667.P172 385 (1,5,7,11,35,55,77) .84830968603508764262084019372469965153618609079506323176640\ 1545260286503867205343001.P103 387 (1,3,9,43,129) 280763808312313.396617565007083620931188002164\ 448757655876754586218585374821747799540417379.P108 389 (1) 18292834838737894009.P283 391 (1,17,23) 40962955644529821015779530249447668761724054284289823431090\ 8958975300252583135110588499332368488448518682064253668907063469.P152 393 (1,3,131) 787.20611007006851.57231871913078689. .54447870968020052083592006408483550889. .1647221037293847764066430890065139050987.P93 395 (1,5,79) 2371.104281.190391.21360811.22525271.4851210671. .1415540984959721223423221.1786772676608961922807433452451202488761. .881461349288847520341747277290496162004544991215461.P91 397 (1) 47019887.11890246390895945222779.P279 399 (1,3,7,19,21,57,133) 109928491.5640242043129165715899642841. .2503258139391324274352072172458469939793.P93 401 (1) 34487.323429759.9322198067780556458918569. .40260621208906991066196904655270499660792620721379455783855\ 8383233661492946837414160194281037405566204720439825351.P160 403 (1,13,31) 195053.594023.806807.6691284581879.P251 405 (1,3,5,9,15,27,45,81,135) 811.51744634164001.53499162725523663\ 97487779386191352470896586975716746667204523845659532441.P79 407 (1,11,37) 217339.253969.34595668539628973486056699133. .698475907912176665118286088415628848552123130910862219690965\ 249686615060315534843429645926024854583566254991.P133 409 (1) 55194551.1594297997364955236049666193876443853. .71803519462949925977654847078016035001. .60296690282523845869537917543950476003959014702641.P186 411 (1,3,137) P212 413 (1,7,59) 4506155564597.P259 415 (1,5,83) 24071.184218422342711.211910698336697951137460118042660571421. .3333605456452402381228509474043950420937637792405993895597753730421.P132 417 (1,3,139) 224530109318798267990497.P192 419 (1) 839.1479620699964596873622221.225066688766683908874389829009469.P266 421 (1) 11789.30313.23864807.133942354061.38368561573169547893. C281 423 (1,3,9,47,141) 2539.239105827.25961228334094267.901282995018904681. .23384328601493048110561.1962056758780675866460803833449.P116 425 (1,5,17,25,85) 28901.220151.243101.P234 427 (1,7,61) 1709.288653.921981817. .1869458624013913791222884220570399145879507347301276919.P209 429 (1,3,11,13,33,39,143) 14064169702441. .54992865055378024329112826586624590857. .79273939682483732394343616776804394264831593590307.P87 431 (1) 863.529445577173. C321 433 (1) 1733.31177.542117.15237429272039731.P307 435 (1,3,5,15,29,87,145) 6961.1489441.3935388233063761. .1678344944256404343567249074912843728758314656626879658903321.P89 437 (1,19,23) 989723472495640900314985156529340457. C273 439 (1) 1835047924377763291446064892740486974344122004429. C293 441 (1,3,7,9,21,49,63,147) 883.3529.5330705689. .423743127971861559828322492034347.P148 443 (1) 887.315367271.6080975059.331317534439063458789618961.P297 445 (1,5,89) 18691.36477836371. C259 447 (1,3,149) 971337783714019.300958963602513102193.29553941320418\ 260314821003628331397840834547738185803704531909190380657241.P122 449 (1) 37320243598177. C336 451 (1,11,41) 2707. .38528614944581911467175570317538005573379413317842652001725792\ 4072336162125777515129814190621826650643462576089520827918649.P186 453 (1,3,151) 907.431257.383699422177.27476281544921467. .59708670274803909173875771.6230030633637320117125625569570897. .7582758873098724784910929092084235688965428403577538167593.P80 455 (1,5,7,13,35,65,91) 911.24571.18558179409052961171723162574551. .5212123433875924124772167212874007211.P149 457 (1) 5442127504257793171.115018225842022485782679531180268674379633. .7504583965646816343215341562816756714447130527.C250 459 (1,3,9,17,27,51,153) 8133481.P218 461 (1) 30427.41491.83903.34605427. C337 463 (1) 11113.24077.5043906204685077747298733.85495385830374364858449506689. .3461776071343228466446640906558613527899.C258 465 (1,3,5,15,31,93,155) 22569241.95541005550158041. .234999227279863137617971.3066470509296976419543571.P115 467 (1) 117258932782039599009463942329116431483203833680513703. C310 469 (1,7,67) 1877.1757326356684525878106283. .399330716020125963037527008475341287949. .26400383521506495598503790243814955990867870174920834881. .386899899473210649626958789084572220222488625727017894505524\ 56484746550889.P113 471 (1,3,157) 15073.15225547.30272113.239635695571.11880978122755430233. .800542271144638085461104957761299178558858869589888434174493\ 960325443463361.P119 473 (1,11,43) 11353.1130471.1566577.2024041474464548089. C293 475 (1,5,19,25,95) 60568682963851.P267 477 (1,3,9,53,159) 3101644705663406427390927198748461508091251939187641.P192 479 (1) 24689062513.5636812407753701.104650088839813432122887993779. C317 481 (1,13,37) 5367961.5170008718105900605611690843220357295579. C290 483 (1,3,7,21,23,69,161) 6763.282164737.4450590563329. .14119361957122353072288949639817831945025845683. .965138057076879648370722366010665290283283413579346222297482763.P72 485 (1,5,97) C299 487 (1) 1949.11475426162619.164214755796153718781.6455463436321554277921.C320 489 (1,3,163) 15649.2628883052394554747498049677948872080409.P209 491 (1) 983.447793.5514913.292396393.2780594730445703.11677264980525481. .20081279129737577144847073.C301 493 (1,17,29) 5774017.445977508157.418255211090238804537287. .22468259187219501202920462874847.C276 495 (1,3,5,9,11,15,33,45,55,99,165) 2971.59941224796217491.P167 497 (1,7,71) 229075173222543094832933533249729047715558877148629. C277 499 (1) 1997.1498997. C379 Table 6+ Factorizations of 6^n+1, n<=500 L,M for n = 12k-6<=990 n Prime Factors 1 7 2 37 3 (1) 31 4 1297 5 (1) 11.101 6 (2) L.M L 13 M 97 7 (1) 7*.29.197 8 17.98801 9 (1,3) 46441 10 (2) 241.6781 11 (1) 51828151 12 (4) 1678321 13 (1) 53.937.37571 14 (2) 421.5030761 15 (1,3,5) 1950271 16 353.1697.4709377 17 (1) 190537.12690943 18 (2,6L,6M) L.M L 73.541 M 55117 19 (1) 1787.48713705333 20 (4) 41.68754507401 21 (1,3,7) 2527867231 22 (2) 58477.70489.863017 23 (1) 113958101.990000731 24 (8) 5953.473896897 25 (1,5) 3655688315536801 26 (2) 313.2341.6291946695217 27 (1,3,9) 114967.883383463 28 (4) 281.337.617.81035189089 29 (1) 59.32713.2727192763388813 30 (2,10) L.M L (6L) 61.74161 M (6M) 181.3541 31 (1) 189491931189200021056951 32 2753.145601.19854979505843329 33 (1,3,11) 463.72073.127236649 34 (2) 934117.8289713345361373993 35 (1,5,7) 631.701.2311.9241.585131 36 (4,12) 577.3313.2478750186961 37 (1) 3923.1096762734443.2054788991719 38 (2) 1030762781149.9736145643041809 39 (1,3,13) 79.9049.868999.8857759 40 (8) 17761.3696985841.121206120881 41 (1) 83.28537.4837453663777044375040181 42 (2,14) L.M L (6M) 804146449 M (6L) 6055984789 43 (1) 412482688627178079807598675848631 44 (4) 89.150080764792922988676714149209 45 (1,3,5,9,15) 4760317816590150361 46 (2) 6073.2259889.9564781.128407494947883673 47 (1) 534577564460822791430647883899825591 48 (16) 193.8641.688490113.6931400449 49 (1,7) 7*.762332681442053.90179616936384011 50 (2,10) 343801.22243201.1748016735462726601 51 (1,3,17) 103.919.980146969.99617785207 52 (4) 192193.14090441.8284434950526240125727017 53 (1) 107.97351567.33685364386033.71080464397105403 54 (2,6L,6M,18L,18M) L.M L 591841.171467713 M 109.932461936453 55 (1,5,11) 11*.1031141.16336066781.84155540944421 56 (8) 113.4817.4048129.10189440239012883075423169 57 (1,3,19) 457.137713.190324492938225748951 58 (2) 349.105134528469779071670501631159328247729809 59 (1) 1163658999540220416412446482708919139658591671 60 (4,12,20) 13441.592575109627400042641 61 (1) 9151.4577830180684945360162613198286645069141001 62 (2) 47552767764994953232854569779888803761183529901 63 (1,3,7,9,21) 127.154260982009.528921402377887 64 4926056449.447183309836853377.28753787197056661026689 65 (1,5,13) 131.199930782298483523040584108028862541 66 (2,22) L.M L (6M) 3037.96493.4629769 M (6L) 622513.16266405013 67 (1) 269.418349.90571543952974835963.191757760647639121941197 68 (4) 137.5849.1536052010629489.51420576374811381403609445473 69 (1,3,23) 24648570768391.816214079084081564521 70 (2,10,14) 13509594555661.1708114263204222806519161 71 (1) 37489.11735704315681.5757417485448059422914748320317168839 72 (8,24) 22452257707354557235348829785471057921 73 (1) 293.439.120855443.1389436303.4221883459378030470824476438562257 74 (2) 37*.4441.3300043400835529.190892407618022993841069346975403017 75 (1,3,5,15,25) 151.168151.573178201.918628247364601 76 (4) 4561.355518408146401.5028187486478069273.13038313680704041577 77 (1,7,11) 57019087134151254061666621717728669167279862151 78 (2,26) L.M L (6M) 8893.197743936282933 M (6L) 13*.157.6429178169720749 79 (1) 317.5531.2832941.99687312908749681.8592319153827988586815914947213 80 (16) 9601.2810800069601.2347110840158563816028186318246561 81 (1,3,9,27) 1783.149862151.3920344350409644507093715799617 82 (2) 4046701.174521133001.246179376206361788466441901958293949537091001 83 (1) 710813.6547890917.21608536062644851877771.54824363564629401758409941 84 (4,12,28) 1176362433121.19100900655540830489319601 85 (1,5,17) 1383638161.72085651321561.740797672014674927371043791 86 (2) 1033.6501601.2914764989376043020733.P35 87 (1,3,29) 68209.92569.1439329.380675809.519258631.24378360481 88 (8) 9307950433.P53 89 (1) 179.P67 90 (2,6L,6M,10,30L,30M) L.M L (18L) 5597780112726834061 M (18M) 9001.211501.2106930961 91 (1,7,13) 2003.2549.36947.52769627.P38 92 (4) 14537.433176829049.P53 93 (1,3,31) 31*.P46 94 (2) 1693.1029538544148223697293.30585762365533687252981.P25 95 (1,5,19) 6271.2666738161.37260330001.61671024221.3229504809106404383981 96 (32) P50 97 (1) 7449708398813963.6571212276076854019883.P37 98 (2,14) 288628033.P57 99 (1,3,9,11,33) 199.110881.P40 100 (4,20) 4801.5801.224401.1006795824867486182291801.P26 101 (1) 607.82013.3866281.P64 102 (2,34) L.M L (6M) 2953728137900959095135649 M (6L) 1785001.12346985995648844989 103 (1) 7211.135025379.P68 104 (8) 36265841.141365953.P59 105 (1,3,5,7,15,21,35) 71191.P33 106 (2) 26713.175436926004647658810244613736479118917.P39 107 (1) P83 108 (4,12,36) 433.115963921.8781208996949976153601.241282001155985351966017 109 (1) 9661979.P77 110 (2,10,22) 423852369601.P51 111 (1,3,37) 223.7993.142969.P45 112 (16) 490972383553.P64 113 (1) 227.8363.586471.5043448999988542328333.P54 114 (2,38) L.M L (6L) 43321.659334264781883756771821 M (6M) 229.25309.2197693.300537265358917 115 (1,5,23) 23126990778420152651.P50 116 (4) 233.250793.4916777.6198809.9008169903032260803977.P44 117 (1,3,9,13,39) 1873.P53 118 (2) 554971222573.P79 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2713.3226831830647224961981839. .1750994408814450803632135259953903.P114 340 (4,20,68) 105401.19294757467336689051203229304905634239161406\ 0796043643547834881402185616614713156561.P111 341 (1,11,31) 683.738801699065626101203. .201829461618484065097678058023863456803. .1931579004923335893545766492796645505817541279. .54244210028135332014784214833039498558612327178902639.P74 342 (2,6L,6M,38,114L,114M) L.M L (18L) 60204997.4765941001.235011794248567117.473164737913969822009.P29 M (18M) 37187713.P77 343 (1,7,49) 7*.2452897437521376917.12929162654221584653.42262681613\ 128083312349381297566288102034789427607264144798179538273291433.P117 344 (8) 186136337.8889718818436619623637354417. .214670565313869275249305269579078241. .44098070546316336069732891124299479167253575131341897248372433.P129 345 (1,3,5,15,23,69,115) 55727811361.10829601768590858922799569083910271.P93 346 (2) 699705783037077375644948197.56164757259658694865317697513568\ 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L.M L (54M) 10794083454463066294342208029552733580361.P45 M (54L) 757.9829.2592266236335984818021237855668549.P44 379 (1) 6215678932110055670241299. .39594233382490829759605818014230525162442624379592766682403039.P208 380 (4,20,76) 761.689321.3939048167443707601. .1991255326339643820867934461881.165124761236284971873587401742681. .430900697980532343944742725010481. .204151655878303598851190023785774256244024641.P58 381 (1,3,127) 136399.7833361.11461131511.740027726500071028321. .1257506539708609283343698143.P127 382 (2) P296 383 (1) 91921.1914729212942473.7001252622923959.23223797215609849. .4880870513072449263361047718936256658889. .47781244631039871123172831093844890197337. .1373828303154919120168021045811475165343965579100056770803785\ 768578210639273287.P87 384 (128) 10753.194651137.2239060935664468407122127993082759905953606443009. .359746302534492382597189148070134087984989179216224257.P85 385 (1,5,7,11,35,55,77) 356816447037821.8130967004568101.P157 386 (2) 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C331 432 (16,48,144) 354938113.P216 433 (1) 6649607265258689507977.1722823570857721499847173811539.P285 434 (2,14,62) 4360499463513733. .739486570934397496079973312923329411370179045088795682121172\ 42234516881.P194 435 (1,3,5,15,29,87,145) 1243596271.P166 436 (4) 225236729.190289675127298323493913. .39261498390673694111920335603137541262097176417.C258 437 (1,19,23) P309 438 (2,146) L.M L (6L) 1753.26245837.51911357917.3329634082406617. .4322128701610242421.6898119095402110707133.P36 M (6M) 8761.283480200282934561.P91 439 (1) 4631572921.1295193187753.106761339748307922218839. .343817007707621462486235847.C270 440 (8,40,88) 881.21121.975773245921.18444967576384646881. .13582822915926141155919400321. .8501907311931118245589440015482543855463013190401.P134 441 (1,3,7,9,21,49,63,147) 2647.49815361.54647204793679. .284341596598806304469490287563303. .52185560309040348461938953629162458695888105633829186827520460060809.P72 442 (2,26,34) 706147626831849631170399995979816911192517429291732\ 198645398298305679014617.44165042417163104514812464129446349\ 017769802839750897303790829748091804739456105441893846874877.P130 443 (1) 6203.539629272555611931390066012467. .102288062363568019086810811979.C282 444 (4,12,148) 1777.P221 445 (1,5,89) 2671.1281517231.1039460507284240092018464682481.P232 446 (2) 2677.74929.45518761.212600173.234813621241.16259409787177. .2875980080674453335965149. .71039051980157813296119317257600375073050644193. .303443655967859052958524113383756061151471131042677.17384643\ 751896005720177573448593897570303084269510284011955791521057.P108 447 (1,3,149) 17334857534194004624977.P209 448 (64) 12092735873. C289 449 (1) 4979411. .461614130871055708167600339498862163996853772078731904511147.C283 450 (2,6L,6M,10,30L,30M,50,150L,150M) L.M L (18L,90L) 26922319201.P83 M (18M,90M) 5771844901.15198535801.2724303865501.312241283985799801.P44 451 (1,11,41) 501014203607547367.P294 452 (4) 6329.1552464219309209. .92141532324445654045497154046509648351199657.P286 453 (1,3,151) 2719.5528983687.33250995548007260911. .250283751499140083714671569546952151263. .86173661253508170752758117519906962881281.P122 454 (2) 9637513.22770904315532655126692701172378701. C311 455 (1,5,7,13,35,65,91) 8191.218401.894690306511. .145164153718800366842958794098286991833164498711.P156 456 (8,24,152) 7297.1327793256599997759318406273. .112628387102449360961226365540483397337314191085572613283033\ 64952769.P127 457 (1) 86208885817. C344 458 (2) 42223021.727943570437. C336 459 (1,3,9,17,27,51,153) 3673.4591. .1169424898575973670675317302665835160738133198152735423165201393. .7079007901327383353519857028218773085389118958989197876797934\ 79170687545929.P79 460 (4,20,92) 36056931870599607020766761. .113323520364075969721280334273348495034777915201. .255521654771918583486040934687782623745002316837542868128245\ 52997398473272011741356856536347066133761.P101 461 (1) 159999951258839117593. .9639890438946401915725325083761191196388310543374492278919.C280 462 (2,14,22,154) L.M L (6L,42M,66M) 7393.55441.449989.2123353.3834601. .447309338300844744160129.P43 M (6M,42L,66L) 938733964477.46094532937993.81154591004568313.P52 463 (1) 399107.2828648497.1151629900827881861. C327 464 (16) 929.5569.18206154484358092218285368892673. C311 465 (1,3,5,15,31,93,155) 464017921.P179 466 (2) 2091409.101228469244111961251354525364400097. C320 467 (1) 144031207.4856963770254755560519991987. .5083268414038654804931085141324887536408068869. .53013565625110686355769459222156409713488946383681. .595390770723466502506688844452406753387754796870286677.P178 468 (4,12,36,52,156) 728209.1375921.23280193.6313945249.30990828961. .18007083727480827025489.324155754750366606785329. .22483131732495740526379651592445382038192673.P96 469 (1,7,67) 252323.353627.1086958153.950588822023. .1950533251824788557053292806955931. .29261136555756683284214962515121720938280765540372272740846\ 522931533550247294931659916891.P155 470 (2,10,94) 155819101.2627211627645600417061252321.P251 471 (1,3,157) 49927.106913409632321417852866717169765414762192137.P195 472 (8) 1743264977.29597532909041695963704964862738395034417. C312 473 (1,11,43) 947.8060712749.7253822473316554499607340242582097. C281 474 (2,158) L.M L (6M) 3793.P118 M (6L) 5689.18709729.317233981.1945096921.P94 475 (1,5,19,25,95) 9241916825905958431301.2294542271996829533994701.P234 476 (4,28,68) 953.74257.P291 477 (1,3,9,53,159) 6679.63069096457.68338963644247. .6721674507103947275348581919268009459726506784859921. .5272469572075351578090914321067037157630487167007628028782454\ 0777127215198557081.P83 478 (2) 5737.318349.2064584293.67008359046637. C338 479 (1) 199613671. .9981682695332156346439828609010017632541179543126883013.C309 480 (32,96,160) 31313147521.24446522594290613929804801. .969468340373808570706508550701726048182646059654014721.P110 481 (1,13,37) C337 482 (2) 89653.2962149551079452709988036273. .7041596191163896388934319023109. .6765065193643877260746826990203508489001101.C268 483 (1,3,7,21,23,69,161) 967.204793. .112198533954077070232717055699596401120985543. .7630960020987589317425826654743575839220472051863.P105 484 (4,44) 68729.2095721.4802007937.1771133748439529. C307 485 (1,5,97) 971.14551.12999941.54917653851524141.P268 486 (2,6L,6M,18L,18M,54L,54M,162L,162M) L.M L 763296049.P118 M 170827321094639893.3409463117689442128783261. .31714835472740596249852635626281791475129.P44 487 (1) 698359.1249255782703.204670538590111543. .128652027960576252352435413580293364102884517541.P296 488 (8) 977.6580100813341193681.747792199856814261442682074177. .27486628313664685882037989112347962512353.C282 489 (1,3,163) 26407.4371985043191.193495649297409957305924407. .1418323875587674609784323012831. .13993349984726575922715094022890800411435841. .943152598545228397431256237234487932385086657213924511326758678343.P70 490 (2,10,14,70,98) 5881.246894812454140761.56505996905771140049492137381. .493846679288044052161895592025852592178594257217032463215897\ 9728755901.P142 491 (1) 716861.11239973.299490361.7668617804268334510901426978778725167.P323 492 (4,12,164) 19681.375524133610657. .258256657651468797641884192161262337620487236582615529120598\ 5818475642367230113.P152 493 (1,17,29) 1973.20340151813381639. C330 494 (2,26,38) 500580499612844480857. .6273967062140441220317771149004798842812596324780689514744641. C255 495 (1,3,5,9,11,15,33,45,55,99,165) 991.19801.468271.12070081. .38402966916271. .40979830599160405824383227766283980904825038226224635277881.P95 496 (16) 323037857.571615463944276122162538417090569976576279894844737.C315 497 (1,7,71) 826662208778360516458256605778051. .3819996742348984567531605814930394353.C258 498 (2,166) L.M L (6M) P128 M (6L) 1993.245351666247788560312408234856037538218169.P84 499 (1) 221048541787323947128840081846119159293. .109948415582118569843821879144351778884841398915942347799. C294 500 (4,20,100) 282001.P306 ------------------------------------------------------------------------------- 510 (2,10,34,170) L.M L (6M,30M,102L) 484601490571886903493518015104501.P68 M (6L,30L,102M) P100 522 (2,6L,6M,58,174L,174M) L.M L (18L) 2089.290924056117.947349493773774517.P99 M (18M) 359137.2797958656485541.P110 534 (2,178) L.M L (6M) 1069.694201.28031381649109.196947355253345341.P97 M (6L) 2137.723739848857641030189.P114 546 (2,14,26,182) L.M L (6L,42M,78M) 15289.P108 M (6M,42L,78L) 16381.1627627815399713377343163471649631733474853.P67 558 (2,6L,6M,62,186L,186M) L.M L (18M) 11161.157462752204253.21124214217163783261. .1520168756245321923557857.P79 M (18L) 1117.P138 570 (2,10,38,190) L.M L (6L,30L,114L) 2281.2358661.3817262181721.6197208621830041. .888066870806284147801.P53 M (6M,30M,114M) 18805516694127001.P97 582 (2,194) L.M L (6L) 1696995935981617.P135 M (6M) 97*. .1083115891949143826648635366282163052400438187303499464609499226261.P81 594 (2,6L,6M,18L,18M,22,66L,66M,198L,198M) L.M L (54M) 28964629.15536649073902661.29426749337349541. .19429747183583833735981.P78 M (54L) 3155329.17698960601683054308649.3512830966112683782744191389.P84 606 (2,202) L.M L (6L) 1213.25453.215737.930985424669173.P129 M (6M) 3637.181339441.73805592037.257309257577257.343320968801689.P104 618 (2,206) L.M L (6M) 33703023049.31712196448668781.P132 M (6L) 1237.33479895313601650365695117603613865333.P119 630 (2,6L,6M,10,14,30L,30M,42L,42M,70,210L,210M) L.M L (18M,90M,126L) 514379712421.9226830539692081. .2531978618650256393162606524681.P55 M (18L,90L,126M) 2521.6797701.34640925953158940597772893101.P74 642 (2,214) L.M L (6M) 5972962561.1426969200507388358761.1740269104463086681404229. .10200602444075618255654001255237011614621.P70 M (6L) 10273.533550328536694908746148449547022477.P126 654 (2,218) L.M L (6M) 132109.878550901.70971053221.7163969211901657. .151876907354130504916630163154066721. .1480112921488586442378283240412840195548801.P50 M (6L) 689492380616435250620242046493112338675621753437796570610\ 6654189483085207293.P93 666 (2,6L,6M,74,222L,222M) L.M L (18M) 17317.242345413.6802442095321.2714523890620249. .7807243011842089.5564977113525793021.P93 M (18L) 343237139281.123715172009307654951839645203821713509. .6172454331546064060948729855755258709149913110601.P70 678 (2,226) L.M L (6M) 39386377.72565033821295009.105290759786101044241. .953764805172418806721069.8968496972740368420580830979099439448387289.P63 M (6L) 14944477.P168 690 (2,10,46,230) L.M L (6L,30L,138L) 2508943501.16919595211074421.236385533406503858612881.P88 M (6M,30M,138M) 1381.4269721.5078401.15550223641.2396217516717195541. .27219154407006602401.2497185445654282204561.P52 702 (2,6L,6M,18L,18M,26,78L,78M,234L,234M) L.M L (54M) 47737.8831161.188486038261.P146 M (54L) 1514917.27140169445190569.16812746447104300364261461. .1822603397490636085779714533101530614797.P81 714 (2,14,34,238) L.M L (6L,42M,102M) 1429.12853.99961.762096489421. .9512924001517525498151238609419754712941009233821.P76 M (6M,42L,102L) 190792782886329146262600258637. .59098535704622825198652652151449.P89 726 (2,22,242) L.M L (6L,66M) 4357.11617.100189.949609.3024276179746273. .111490939699860292494913.147030118753104261600368196682018861.P79 M (6M,66L) 2450040986053.1266392442690013.10476416255479706797. .552044274610152692854436856453869841728449076617.P77 738 (2,6L,6M,82,246L,246M) L.M L (18M) 174169.30089737.6505451552303016203738681444159513490728930149. .3817733856969957712995018866618650405701538477261.P80 M (18L) 2953.10333.1036153.1678974479302069. .4526204177767840748623909655533. .1472102256284019236716925991047155829911467672973.P80 750 (2,10,50,250) L.M L (6L,30L,150L) 327001.514068001.8485607361001.P129 M (6M,30M,150M) 106501.10864275587422501. .40201669583886249313475106001.17652944112619681484515989877740001.P72 762 (2,254) L.M L (6M) 6053329.24312373.247672325565461557. .801635022497602549961802363275046606409.P126 M (6L) 3049.9203437.277440178523437143401157337.79775519839837813\ 6992989897173778551819524893213077735137125857196400787268209.P82 774 (2,6L,6M,86,258L,258M) L.M L (18L) 7741.1976797.632803528420302650173016503452913. .764306314103209605006540297087286189813.P115 M (18M) 1549.5907169.61621539416556138109.475101073392341497734075633901. .5327631746573407308414105279051343357.P100 786 (2,262) L.M L (6M) 17293.5646129480180477793. .10118929876038053687106294473402896087044223570381. .4319857456953911989541977914492633405793099703033623785697.P73 M (6L) 625657.1303189.4304137.5055407781577. .1445119992880549305748401049273. .56960371058218895540378943239158793077204018529205703221409.P83 798 (2,14,38,266) L.M L (6M,42L,114M) 60613424867803248411521814481. .286227504202337752215096844369178117421662207554962805489.P84 M (6L,42M,114L) 10453801.26846778030654037. .1158150966336915157483991531934587159293.P106 810 (2,6L,6M,10,18L,18M,30L,30M,54L,54M,90L,90M,270L,270M) L.M L (162L) 1572593941.326587879716262741.P142 M (162M) 1621.320435243187841.178880165276055876541. .1141474040947210592672032861.310079312179893621392715264037923541.P68 822 (2,274) L.M L (6M) 8221.416023459071517468051297816971923833. .57670113141808252240352311142780968492223118520622897175521034757.P107 M (6L) P213 834 (2,278) L.M L (6L) 1669.11677.241861.51797935791539645260219370581.P174 M (6M) 25746953949025756677019701384808518760023237169837.P165 846 (2,6L,6M,94,282L,282M) L.M L (18L) 1326042098209.52538840002167215571863467874858023754429\ 926220896503430269017224804714278163377001.P120 M (18M) 3300192135812809.P200 858 (2,22,26,286) L.M L (6L,66M,78M) 2214804302687867389438369. .88488175706129575961003838484577355813434553677963527297.P107 M (6M,66L,78L) 13729.26046034873.1712598352609. .1079538754955730279695374033.182190302075325973123362742987797457.P99 870 (2,10,58,290) L.M L (6L,30L,174L) 50461. .30922577412525026949959439423014195086106851618040050861.P114 M (6M,30M,174M) 44140321.1627624442333929108754759271776179141.P131 882 (2,6L,6M,14,42L,42M,98,294L,294M) L.M L (18L,126M) 42337.3814295437.319550543929.14068970619229. .90886564008812535191945719129.P129 M (18M,126L) 49393.896113.2624246630448978781. .101932786755679011662735491411158043922982173186527842352576289557.P103 894 (2,298) L.M L (6L) 1789.25033.4205688901.2127099636560937932152252309.P187 M (6M) 4903826017.124842540601.3643137648806457124070233. .8309168214810018453571876617907495157545012019378171678453833.P124 906 (2,302) L.M L (6M) 6412669.3429659377. .452395874476181695823430208040140704228948649704077127501901\ 565736737557117.P143 M (6L) 54361.13285758196875778746558417115753905731409307565481\ 877931291421319412839205918490512329.P145 918 (2,6L,6M,18L,18M,34,102L,102M,306L,306M) L.M L (54M) 63848737.4066531738947696637.4245688904650848430201. .624009828548490331899474423830567049137608652669197095378675481.P114 M (54L) 599107304340120247908808341277. .2051784009571434185145690963951970150668097. .2537341816473161610935554785356731072836961996177.P104 930 (2,10,62,310) L.M L (6M,30M,186L) 1413158016891781.P173 M (6L,30L,186M) 1861.109741.353939229014074928068464964403700834\ 9534553940341821505760103485676396158549542351230961.P91 942 (2,314) L.M L (6M) 32725081. .134969584754991414081627393376743296461911957004190369617.P179 M (6L) 3769.69709.891133.1265499761653.2516408681833.418432770351526813. .53400059546864999415920637735908227182833949063070369. .348870541113728425895922279252299633124643263225417291039191257069.P69 954 (2,6L,6M,106,318L,318M) L.M L (18L) 211789.4442657952104267997824059061161892367247098732164\ 754980669267975433965157765870423750343469877462005942582653.P129 M (18M) 10736317.597828724993.87999801244777. .2039581908114127792164413715349549.P177 966 (2,14,46,322) L.M L (6M,42L,138M) 11593.22672021.6381701798601250074732661. .1712654377420769448764593657.797218724396299388537010345082160593.P107 M (6L,42M,138L) 11804419292054666838231470773. .2584885432448042042137967020127889871906709706485233.P126 978 (2,326) L.M L (6L) 5869.48553789.39246849464530299188185267429. .349997268606989969304048449480306312772440816323287415817338\ 8723987315871308920212620005059535742589.P113 M (6M) 56269812868359465656989.P229 990 (2,6L,6M,10,22,30L,30M,66L,66M,110,330L,330M) L.M L (18M,90M,198L) 4928221.232689601.6328812601.27199744103982781. .6437239563309137247189276206896321.P112 M (18L,90L,198M) 63361.P182 6^6h+1=(6^2h+1)L.M, L=T^2-T.6^k+6^h, M=T^2+T.6^k+6^h, T=6^h+1, h=2k-1. Table 7- Factorizations of 7^n-1, n odd, n<450 n Prime Factors 1 2.3 3 (1) 3*.19 5 (1) 2801 7 (1) 29.4733 9 (1,3) 3*.37.1063 11 (1) 1123.293459 13 (1) 16148168401 15 (1,3,5) 31.159871 17 (1) 14009.2767631689 19 (1) 419.4534166740403 21 (1,3,7) 11898664849 23 (1) 47.3083.31479823396757 25 (1,5) 2551.31280679788951 27 (1,3,9) 3*.109.811.2377.2583253 29 (1) 59.127540261.71316922984999 31 (1) 311.21143.3999088279399464409 33 (1,3,11) 3631.1532917.12323587 35 (1,5,7) 2127431041.77192844961 37 (1) 223.2887.4805345109492315767981401 39 (1,3,13) 486643.7524739.44975113 41 (1) 83.20515909.4362139336229068656094783 43 (1) 166003607842448777.2192537062271178641 45 (1,3,5,9,15) 1527007411.125096112091 47 (1) 13722816749522711.63681511996418550459487 49 (1,7) 3529.1074473.13473433.6106505825833677713 51 (1,3,17) 103.365773.2316281689.10879733611 53 (1) 8269.319591.38904276017035188056372051839841219 55 (1,5,11) 5457586804596062091175455674392801 57 (1,3,19) 19*.19609.879399649.6957533874046531 59 (1) 459257.134927809.550413361.354639323684545612988577649 61 (1) 367.4759.177237331.1914662449813727660680530326064591907 63 (1,3,7,9,21) 2643999917660728787808396988849 65 (1,5,13) 131.157951.787021.4446437759531.434502978835771 67 (1) 228337.147300841.206244761.10052011757370829033540932021825161 69 (1,3,23) 139.402011881627.235169662395069356312233 71 (1) 990643452963163.169002145064468556765676975247413756542145739 73 (1) 439.3675989.359390389.1958423494433591.7222605228105536202757606969 75 (1,3,5,15,25) 29251.217648180992721729506406538251 77 (1,7,11) 724487149.6809710909.88262612316754526107621113329689 79 (1) 913242407367610843676812931.1056836588644853738704557482552056406147 81 (1,3,9,27) 3*.1621.3727.3368791.70722308812401674174993533367023 83 (1) 167.66733.76066181.7685542369.62911130477521.303567967057423. .18624275418445601 85 (1,5,17) 1531.4931.P48 87 (1,3,29) 2576743207.196915704073465747.358475907408445923469 89 (1) 1805633.18489605314740987765913.P46 91 (1,7,13) 7304123737.231410451435538144122809.P28 93 (1,3,31) 5463751.2211164386353499.P29 95 (1,5,19) 36671.1966385431.P47 97 (1) 389.971.P76 99 (1,3,9,11,33) 199.173647.P44 101 (1) 607.809.6263.P76 103 (1) 17923.P83 105 (1,3,5,7,15,21,35) P41 107 (1) 227109283745807808529.1620221568881364582821.P49 109 (1) 14551288401737861.63505707690048880101785428103.P47 111 (1,3,37) 6217.177379.56713875643149053038693.P29 113 (1) 227.P93 115 (1,5,23) 1151.188831.1446701.723461377501.27229507836853201541.P29 117 (1,3,9,13,39) 1873.322921.2280097.7687225261.P36 119 (1,7,17) 12377.34273.305213588009240737.440779823883628367834893.P32 121 (1,11) 1453.65099.11795261559086963.58792315124013823398811997.P44 123 (1,3,41) 267403.P63 125 (1,5,25) 251.2182816753758823696751.P61 127 (1) 260461507.554351226505275380676162672703.P69 129 (1,3,43) 10837.63350976270733.175446584281395198837259.P30 131 (1) P110 133 (1,7,19) 401563177.2662276961.373740808373213.897558513407803666357.P38 135 (1,3,5,9,15,27,45) 271.185221.175561876921802311.P36 137 (1) 2741.213721.251533.57162922399254002352124124899. .65480203458464902965944539043.P44 139 (1) 19739.673039.P107 141 (1,3,47) 283.5960917.P69 143 (1,11,13) 528808508322667.376215890379315997311416372784691746214777.P46 145 (1,5,29) 4899841.277463632645667965008782910911.P59 147 (1,3,7,21,49) 4060603391041.424770871339903301567509.P35 149 (1) P126 151 (1) 115356256117.36076003832567.206462520503013793561. .2856349001315592319937.P61 153 (1,3,9,17,51) 307.613.4591.44371.44072862804091655188147.P45 155 (1,5,31) 21391.21701.1622982371.9254997611.P74 157 (1) 4397.5653.1039945344901.P113 159 (1,3,53) 32119.1695259.84247682063005850464952755729.P49 161 (1,7,23) 4406588677.4615185796935334098258901.P78 163 (1) 653.9781.1260643.962207945014470392304193. .1648536343690282975764489383562678396141955057.P55 165 (1,3,5,11,15,33,55) 7591.36647640811.1946951063386221338821.P32 167 (1) 2158061509.623932374204290945359. .494816894793945434195756741367539.P78 169 (1,13) 1452979915402500135854417362573926368874134931212567.P81 171 (1,3,9,19,57) 18684829.9674698906207.175336938770236118176950803989.P42 173 (1) 9491935586594867440367391646466925926211879363793.P97 175 (1,5,7,25,35) 701.1237578612719152201.1094471317606762277701.P60 177 (1,3,59) 709.89209.22724865586634953261986967832791.P59 179 (1) 41887.149874987000926513705179.P123 181 (1) 1811.13873726021.618805947190964867.364308807786322943430987769.P95 183 (1,3,61) 5153013553.104199666470736545959920137256413473.P57 185 (1,5,37) 1481.6661.219041.P110 187 (1,11,17) 10099.107969286569. .157663427378398137465490451049503570558624435143.P73 189 (1,3,7,9,21,27,63) 757.5906255349477660375285361.P64 191 (1) 383.35546396841548971517329.P136 193 (1) 14669.85728285355409267895679.756937155910390044916932629. .5994946327304712468705571873826831. .4539546970485536436424707475812653713.P38 195 (1,3,5,13,15,39,65) 567538141.14046059431.P63 197 (1) 3547.6159369299.P153 199 (1) 3583.214661295139431885643832154153997. .86539116653269014086961051020627012232284504261471.P82 201 (1,3,67) 85627.132955527487.775594571863.98527557194917. .428995274049217.P55 203 (1,7,29) 29*.60089.145916619612283783386370190568409. .1158560595990812530792619356788467777477674946730941.P53 205 (1,5,41) 834035491628067397615971778938263976927180494349982302975033997201.P70 207 (1,3,9,23,69) 77569456660417.227556220136287506028942276770826968937.P60 209 (1,11,19) 8048541876545647951.P134 211 (1) 141793.259018281812228908974285857741797668601708632994386\ 95413795254930505191880636307.P93 213 (1,3,71) 968299.582053568181. .1274759667849259732505774376326193816317726317.P56 215 (1,5,43) 31391.822161.11300176322829911971.147795410845880963171. .11916717598664539151308306888803765941891.P53 217 (1,7,31) 604997.1956808820481173.602858801824822604293. .626475940065539137153553.14784849807251837047947491359227676537.P50 219 (1,3,73) 877.16999040225222266951.P100 221 (1,13,17) 22543.760999500977.9761302041992117524910703947100342853.P109 223 (1) 17288166877.132218621369.P167 225 (1,3,5,9,15,25,45,75) 8101.1708445701.121257418374086998051. .20297781182169478546946347835701.P37 227 (1) 62463078483642684523805927784689103088686041429. .985628969754881487322427476013002845424287651017904086946721.P85 229 (1) 50839.8771561006313491618219260558398401.P155 231 (1,3,7,11,21,33,77) 1793870233.125844538662442909. .3752691545947560669458268649.P48 233 (1) 467.79227874003.13514998546886646078035233993. .56785654839475818636487235265635121007558707816641.P105 235 (1,5,47) 2812894619735804087343816418261851587705080375647708714001.P98 237 (1,3,79) 2371.529637338334729405483135077873.P99 239 (1) 479.871986721.643384173113837.4040609273925388685799856703093687.P142 241 (1) 1447.28439.33486078253526557.580351872045743557. .547283138069536869412948975377385222182769003. .2937026550451562627666151150279078330125909163812627.P65 243 (1,3,9,27,81) 3*.1459.169129.1382671.73870787476849933393474604683663.P91 245 (1,5,7,35,49) 4896864001.9152363081.11492120512321. .353207957997402826578121.P86 247 (1,13,19) 6917.22931541257.14975869588530371.P153 249 (1,3,83) 11606389.41491794184631137. .76354359945860977734571491962874304923412180177.P68 251 (1) 503.27611.8895962998159.P192 253 (1,11,23) 1106436299. .35764102873412466090911077602159546824955533626915413469.P122 255 (1,3,5,15,17,51,85) 580381.326568900271.604822302841.P80 257 (1) 1543.1998784090958019204289.25267040262621061993019176762\ 94257618227834546616502466183053066833047277.P120 259 (1,7,37) 3109.65269.35770888872948142944129513041430138973416\ 7320382217282028474835603757.P106 261 (1,3,9,29,87) 523.5743.83226515419.710074092185677. .474062506708242760701771553376690953.P75 263 (1) 111473077.246420328513.125964970427584638596267035086794589086977. .330356473356706630143084182110481076968694111519479821312366757981.P96 265 (1,5,53) 1061.3041671.19069931.187978422699271372501. .212135996587857465774994583472077008056991. .105322961980986497356836647823085697438251004501.P51 267 (1,3,89) 28713855773905923529325586129605726947029936343189321\ 74130446555537271.P80 269 (1) 2153.4462060605403381961780411332028022754534242152003773\ 412732171224503049883657394827.P142 271 (1) 6780421.164514887. .127962646077173632312199483013809163214497588966415507177987\ 147170392729827682423052701976465899731717.P113 273 (1,3,7,13,21,39,91) 1093. .894265285117657047082911243254861366638596090445735393.P65 275 (1,5,11,25,55) 2429297864813474051. .13108478445679585187945846562792720732451. .152254207931524870640907264181257222395351.P70 277 (1) 137947.8954857.607705768105925529871.100854639777998640274485328005\ 2751256841864202057421515367093607755446588358126544676145969493651.P105 279 (1,3,9,31,93) 8248454734032306396350042707176588234070405742014804291507291.P92 281 (1) 563.8431.341614931501.4420135738596254569. .372634096091628229321039358180848549. .41601158252896546668861917466611604127922008421733517.P112 283 (1) 644316289.182739497717749501.P213 285 (1,3,5,15,19,57,95) 523261.93586760776923620671. .80183934664292567561851.P74 287 (1,7,41) 12412177.2405532607493.21747676457911610417. .738710854664932373205737588298090279327121.P123 289 (1,17) 1828793.801172436655296029591646500403317187. .26773640876541335875821092444484138995809.P148 291 (1,3,97) 4657.134002009.951340693.23363930803. .588884936839088389773662393029.11089767531884977816638380462821.P71 293 (1) 587.15823.P240 295 (1,5,59) 123311.204239004182680605398190478754212368873366912\ 490836010105265524712426411236134031.P111 297 (1,3,9,11,27,33,99) 5347.27170749.P141 299 (1,13,23) 1045903.5240570609.64432450872271. .124017815182557414772494313985201. .121219249940833404770079915022116301.P127 301 (1,7,43) 4817.219516040470409575257. .58628254861045912568724329431228508415599499441292512521. .3748787688169844402513004599633138785431253179050314600655297.P73 303 (1,3,101) 1213.3637.9354849642511833165720058628257. .276052467777407518967272068222889.P99 305 (1,5,61) 16199725471.1362349539551924951. .5554678022917560417664065958900541081.P138 307 (1) 8597.54647.173149.507779.P240 309 (1,3,103) 619.220400431.29650439178674631118602918288131887.P127 311 (1) 3733.106363.310379.171251016147061382719721. .300816696076140900609570360532034016686672572500196266141997289033.P160 313 (1) 9450044264774621.1007074189486010153899034973231293881148\ 95443319589120732359180091169312420663896659.P165 315 (1,3,5,7,9,15,21,35,45,63,105) 24391637204467995942644375209216533440485081.P79 317 (1) 240287.1507019.32815841. .22918346757630316344596090121007369869273875683. .399676211948778347375576150888294069325575626336229.P152 319 (1,11,29) 35729.204227297293529257125127118080380016745365752\ 943272818676346275973633953383050572371.P149 321 (1,3,107) 643.859121000285791.23884590227767303. .477280063808143381.1842220342523756359.P110 323 (1,17,19) 647.32384164657733079891391121799890231790807215307\ 992831784347992344927666001261536118647303847.P150 325 (1,5,13,25,65) 416101077937444349085210448786432651. .76703889230394194088755921186703377051.P130 327 (1,3,109) 28962941977.135330649536067.P158 329 (1,7,47) 2633.19384636573.P220 331 (1) 7283.60110252104542020699.1761395429514151665769314691427. .2105702271734308254421459196775092778340834008221.P177 333 (1,3,9,37,111) 37*.33301.129428524896497486302190931106742227\ 6786354955064661561483669329671165989.P105 335 (1,5,67) 56951. .69928721965942485135629295450917485739456015527631493417908\ 99130326926493208020982074306502256720547651.P116 337 (1) 1902213942891704396239. .82636601001479675794891608182882964209535285466591. .820153200285318618923495377706065965006024685305866597899430\ 892937593562646433001877737.P126 339 (1,3,113) 1854331.952667477245436772047525567653711.P150 341 (1,11,31) 1594517.2665939.51216931087169.2538309587015599. .13422653085156210083.P193 343 (1,7,49) 1373.8233.49393.734021.83517610741606021. .1575721793366942921257214180187566081951195327261.P166 345 (1,3,5,15,23,69,115) 691.1381.430907693063791.376720035234076771. .13349802972012134814680881.35136774371091884747048323143601.P54 347 (1) 895387781898751979426080914689. .89823582672830825295829211905814036272016809423171.P213 349 (1) 81667.127037.7291309.29320685133749.91161291484807478873801. .18284716149059665426389383. .2258039418211166054470067466217161065944246913.P171 351 (1,3,9,13,27,39,117) 20359.594937279.2433313988259555128131.P149 353 (1) 166829729227263074982846979557342097. .429467931963862803348463041493298237234810659994743046176740\ 84838125805848164469648543501311376029.P165 355 (1,5,71) 2131.25561.56289276349396871456041. .8626512997499727156919264091.76517845980555473610468712199440815091. .3173000019403116087424802551781937763200511. .641713853752178839895479942132287119308113963511.P50 357 (1,3,7,17,21,51,119) 1429.1175001241.23992463461.136437693760145149.P123 359 (1) 719.2051327.3093863.22452201769. .51473880215775560289559342015479947105948717616853507. .24974251374374973497030283842100592498389535606198279458393\ 10078637316351451019.P146 361 (1,19) 643055501056432548862982717472951454129468794615702292\ 351407486296911123932340995559.P206 363 (1,3,11,33,121) 727.3191497.800245174328620352257663. .241421225374647262615077397.P127 365 (1,5,73) 32605498797939226954141.114889446866709128620469297041682\ 7261082319331812342797384451313174700604983148313611338121323891.P125 367 (1) 5713457.1232836358179.1903011950286996065819486607665149965823. .151407555250986978398908030097699886542514973798863798084641\ 3561226082200895909501.P171 369 (1,3,9,41,123) 4287781.855981109.78025052362534309. .967153401006619950054687111653107.P138 371 (1,7,53) 37500869458383846642957881261029. .4546356086776970486532855270462193.P199 373 (1) 2239.342763782842586373606490121792284462755239269. .874829399507637101640859548906697454121804303327128221023695861. .146963193109402982186685858522202728992449027039726998441483\ 93496691061571694475060801127324516364009.P104 375 (1,3,5,15,25,75,125) 8668167751.7518480999776007258001. .9749495229710098497186543870986809880214868507743932200504888128751.P71 377 (1,13,29) 26006969.920146163.1023200621.4768847677673. .257366523022644644999963.P223 379 (1) C320 381 (1,3,127) 130303.2208277.9809667961.11699360074183.3451948895547127.P163 383 (1) 254655724117.132718300095362903152250689243124998807. C274 385 (1,5,7,11,35,55,77) 4621.2613660216179879661629787646541. .432414771234341663469178268617841682553148346701.P122 387 (1,3,9,43,129) 289414765514841661. .1515492051809463320804633626637111430388057. .4583142681916056752995023804494031799489400087334962946866717\ 203441543.P84 389 (1) 1035744587833.354364364887111871. C299 391 (1,17,23) 2357731.721203469358049113389755819257183928662405067449. .478566296656273815311438559010751123205277732759848440243.P187 393 (1,3,131) 787.49520673229092123847326147892227101575003836232\ 0004497025761514989851251029711561.P137 395 (1,5,79) 141853148269311930125011018018040572551975041. C220 397 (1) 2383.11117.232643.7843916473.P313 399 (1,3,7,19,21,57,133) 39109981. .6931988925147970715443756192320558859369717.P133 401 (1) 148589354219.43922003559070672732197339107. .42082982144192092358730030935244893762710856226163. .88844784271503603122885043757639667529549036692305428355369. .74397337339736687589550031624611059512914961150736213161862986033.P125 403 (1,13,31) 104812241.33629697123498329211502958998299487115621359. .159703539091173717215233350675579780103029299243483.P203 405 (1,3,5,9,15,27,45,81,135) 4356181.121630339096334149604401. .27647079089100876068752908298057505373446650591300028391952835991001.P86 407 (1,11,37) 3257.527907491.736043221.P284 409 (1) 4091.339259613977831999461642401666662666144883.P300 411 (1,3,137) 575401.9712753.109781389.329437051.27500724319. .8350989090751.21597040515507988471.P158 413 (1,7,59) 2094737.1856688483235393866448784969. .112973432365763374259029418243917224029093. .11838186665371524135112487663262769193087880357344613650265\ 205952745591351133580113.P138 415 (1,5,83) 11621.58704241.3332338781.239838191551978888291. .472147873240510126308071.P212 417 (1,3,139) 6673.1522051.2788198850651341.371266463450323577863263631. .4517590853092752320324288547287650695871.P142 419 (1) 839.15593245728932434133563441. .204474379397946598737178171975016296366280689.C281 421 (1) 120298224779693.1169407471026387018305554817094515359. C305 423 (1,3,9,47,141) 4904535443967721.74344711992811394446323372079. .123073308832989689693844493084849.156035321945212360260109221423643393. .5719374442762619138354952842044488751. .236797435223187931175815185235335037279.P47 425 (1,5,17,25,85) 6269759010776190508301.6175607140671472910167602851.C221 427 (1,7,61) 165649067659909.P290 429 (1,3,11,13,33,39,143) 859.41992891745212707322119446859153217\ 85461696099889610109560039448020763861.P128 431 (1) 3602407438103418087310110702859943140744217508967. C315 433 (1) 1733.885919.341532829437623. C342 435 (1,3,5,15,29,87,145) 76561.84391.59796922604452021.87163539657316351. .144975423216697187157750841. .3018134674629431661103715628858892719721420190476720595671.P63 437 (1,19,23) 2095853.2108089.9887086977363287. .871625877266359638463636983740325357448571165302789.P256 439 (1) 572749682520506652634407616247. C341 441 (1,3,7,9,21,49,63,147) 3186701281.7973534017.216238581721. .479133961673103577.148604037346679149806473694800108374797541959361.P118 443 (1) 887.111637.409333.235997978920007672111426348459. .17814837704717959838644280277218893615422175774849. .246485575893980371628538160283793076128413053123407170715757721.P219 445 (1,5,89) 10924751.3612821501.16850251787024593038901. .384276490074557683474810649698324621931592661.P215 447 (1,3,149) 39945205405751238799.3683855663494683375748297353964\ 8824615080119512438133496027443673310157100341377857495377637.P139 449 (1) 48086529969893. .2169045785839981131097669344768376286338016422298393. .1965281595471152337355304576224552008572362093777262877223.P257 Table 7+ Factorizations of 7^n+1, n<=450 L,M for n = 14k-7<=889 n Prime Factors 1 2.2.2 2 2*.5.5 3 (1) 43 4 2*.1201 5 (1) 11.191 6 (2) 13.181 7 (1) L.M L 113 M 911 8 2*.17.169553 9 (1,3) 117307 10 (2) 5*.281.4021 11 (1) 23.10746341 12 (4) 73.193.409 13 (1) 53.228511817 14 (2) 13564461457 15 (1,3,5) 6568801 16 2*.353.47072139617 17 (1) 29078814248401 18 (2,6) 13841169553 19 (1) 351121.4058036683 20 (4) 41.810221830361 21 (1,3) L.M L (7L) 309079 M (7M) 51031 22 (2) 661.1409.83960385389 23 (1) 3421093417510114543 24 (8) 33232924804801 25 (1,5) 79787519018560501 26 (2) 157.1195857367853217109 27 (1,3,9) 1628413557556843 28 (4) 337.2129.517553.515717329 29 (1) 402488219476647465854701 30 (2,6,10) 61.555915824341 31 (1) 373.9754399.5420506947192709 32 2*.7699649.134818753.531968664833 33 (1,3,11) 67.1357105535093947 34 (2) 137.59361349.133088039373662309 35 (1,5) L.M L (7M) 421.12128131 M (7L) 71.603926681 36 (4,12) 42409.137089.32952799801 37 (1) 149.15572244900182528777225808449 38 (2) 2598696228942460402343442913969 39 (1,3,13) 79.23850061.115868130379 40 (8) 881.542081.2312581841562813841 41 (1) 4849399.8999993.1636258751.78009515593 42 (2,6,14) 195489390796456327201 43 (1) 947.19867.20899.163573.235211.3799051.4749781 44 (4) 89.8713.8206973609150536446402438593 45 (1,3,5,9,15) 541.154351.295831.7777981 46 (2) 26681.649981.15513961.55681942361860463813 47 (1) 655417289594537954307682339857743931943 48 (16) 97.104837857.108604397663266369 49 (1,7L,7M) L.M L 197.883.161309.19847549 M 3823.1445599.101361401 50 (2,10) 5*.101.13001.25301.38327966300231909291101 51 (1,3,17) 1135261.12192877.90920746649833 52 (4) 313.85094881.1377454635342537460935008154217 53 (1) 107.345449549.35416476134069.58902316970027001503 54 (2,6,18) 26893.167039577217.590297313273013 55 (1,5,11) 11*.331.2311.38501.2864401.7840815905526451 56 (8) 449.673.39648001.21535258550401.142256806230113 57 (1,3,19) 457.24006520939.275430251632699963 58 (2) 233.136853089.55716067510309.116714640028973541741413 59 (1) 122131.4261190159.1187164242679.14683403662888806475673 60 (4,12,20) 12913561.85560261859655897641 61 (1) 444519128147170444656914672945689439050880209231501 62 (2) 33947629297.74502648768583254173.196846325409292090901 63 (1,3,9) L.M L (7L,21L) 127.9829.1506625093 M (7M,21M) 20801593.67979647 64 2*.35969.1110623386241.15266848196793556098085000332888634369 65 (1,5,13) 1175071.35695043869049049222174543845808031 66 (2,6,22) 29569.2784937.678240817.116320403133001 67 (1) 20771.6557750853567755279.383942665465635068312581125821527 68 (4) 20129.94793.638991748543082113037456009420293477766438233 69 (1,3,23) 277.7396787205469.8501948915136155490673 70 (2,10,14) 102314938321.18690488255321.19584845505919961 71 (1) 1351405472411521.92914860840816888117372433724419584467881183 72 (8,24) 129169.25726609.51385969.635311009.338325042961 73 (1) 3067.279883.7167647480643504302058174754486698790538818746798241 74 (2) 6891042949305882214394659726647344864958515967158596120016737 75 (1,3,5,15,25) 151.6005492312551.7021370289199888801 76 (4) 44118001.700197881.1295161807633.1299254811081649.135214434686939513 77 (1,11) L.M L (7M) 258576319.32817262777539703 M (7L) 463.333103.443632323630099913 78 (2,6,26) 13*.365302616611175569.7886422107556319674933 79 (1) 317.2874811.7573763065938754357.P39 80 (16) 38470561.102118777045028801.P30 81 (1,3,9,27) 163.487.15877.P37 82 (2) 33842057.5449628176194898649.P42 83 (1) 6963362191.P60 84 (4,12,28) 3361.4894546210513.2232059760329037670187857 85 (1,5,17) 1590988506392861.P39 86 (2) 173.1033.P66 87 (1,3,29) 5406066031.1284564941030772067.34720058992462423813 88 (8) 2085729338353.P56 89 (1) 179.3917.18691.1179536907057197599849.P44 90 (2,6,10,18,30) 9901.1795168434777002101.2065025164427492401 91 (1,13) L.M L (7M) 732700162559.1362621396812563889 M (7L) 467280997.17225454456724489912483 92 (4) 1657.197202518881.1812487089636161.P45 93 (1,3,31) 149731.P46 94 (2) 95881.4574857237.P64 95 (1,5,19) 571.1765151799417091.2440590160473742205021.P22 96 (32) 2113.9917569.596878081.16356157057.5962150442139230211450049 97 (1) 599599487.146533138940077.P59 98 (2,14) 16073.1933665951863017.10148051647066664017.P33 99 (1,3,9,11,33) 8095532743.244188888967.P30 100 (4,20) 401.P66 101 (1) 230281.3843253.P73 102 (2,6,34) 2857.85647973.P43 103 (1) 1031.490201721.1058638292629.461785968654529. .41875773535891952971477.P26 104 (8) 17712988461899423081645348353.P53 105 (1,3,5,15) L.M L (7M,21M,35L) 450798894542150330401 M (7L,21L,35M) 211.338640865331157691 106 (2) 15053.7627549.P77 107 (1) 1499.82413922847.P76 108 (4,12,36) 40177.60922880584567163834041.P34 109 (1) 5233.10059414761347582747.P69 110 (2,10,22) 2861.32561.543841.47045037529563701.P38 111 (1,3,37) 15015834247.25443079695091.12558090335903767.P22 112 (16) P82 113 (1) 1583.8654522423.120249742857138175784797627. .4842723074886320121848080733.P28 114 (2,6,38) 229.P59 115 (1,5,23) 1207501.100429501.P61 116 (4) 14153.769756513.33510280238484636857761.5192033853710499967501529.P35 117 (1,3,9,13,39) 1171.1174681.5075833207537.882351727670323.P25 118 (2) 149153.165437.1024477.6551912456787047841933817.P57 119 (1,17) L.M L (7M) 953.377231.20123377.1910207075448557917128553 M (7L) 239.2381.973897.P30 120 (8,24,40) 241.5789644155060072001.P33 121 (1,11) 26863.2174310226212366107469266007290639.P56 122 (2) 4497653.133440673.369232401898464835382701047039367301441.P49 123 (1,3,41) 395617447.P60 124 (4) 4217.2541312025433.23235518871793.P73 125 (1,5,25) 751.1173001.4833574921448501.31818863467130251.P44 126 (2,6,14,18,42) 1009.250993.2304793.31864919689.P36 127 (1) 35852863.P99 128 2*.257.769.197231873.6856531741041792239054980342217258517995521.P52 129 (1,3,43) 43*.1857499496101.499711620081214598029911373.P31 130 (2,10,26) 134358901.P74 131 (1) 263.86461.1686923681.P94 132 (4,12,44) 1321.532489.98138029441.P48 133 (1,19) L.M L (7L) 254997629797.265043186297.193935377097018854700131 M (7M) 8513.P42 134 (2) 269.3217.4591913.39144122221793.27982218262152281.P69 135 (1,3,5,9,15,27,45) 40724371.17796529171.P43 136 (8) 17*.5388077170097.49853897949169.P81 137 (1) 28771.893081081.7448353120289.P89 138 (2,6,46) 829.21529.26497.5755716973.153943464633957793.P36 139 (1) 557.5312442648966139012589.190705279598948669274660288301207361.P57 140 (4,20,28) P82 141 (1,3,47) 7333.P74 142 (2) 569.853.29537.810253.40109647514545875958117.P80 143 (1,11,13) 108109.145861.2547984152429.36383445305923.P66 144 (16,48) P82 145 (1,5,29) 227327521.P87 146 (2) 293.20149.36793.729810133110395035429089427259624129.P75 147 (1,3,7L,7M,21L,21M) L.M L (49L) 10157701.10738939.2868318061062142721089 M (49M) P36 148 (4) P122 149 (1) 10133.47338433355189929279110650931837806119829008573928501623.P66 150 (2,6,10,30,50) 5666701.169293601.1149016121562093219301.P32 151 (1) 1014952541.P118 152 (8) 12161.34961.72353.P109 153 (1,3,9,17,51) 56611.734707.469022340889.9035330762005111.P43 154 (2,14,22) 617.5302529.4181043906823655873. .152111801516025381573834946322977.P42 155 (1,5,31) 5581.60761.6689491.136823162401.92105555489371. .18127525360389024220391.P39 156 (4,12,52) 8737.45553.P73 157 (1) 57149.538511.3065983647843013.6053210945000213. .1296120348255709333595477995627.P60 158 (2) 13059374383501.24911171121703051981.40157473329867190572836333.P74 159 (1,3,53) 305033517629290547304139.3475913288653967871883271299609.P34 160 (32) 641.163344191041.4821999754197347683089799168482241.P61 161 (1,23) L.M L (7M) 49613117.8884810040009.P35 M (7L) 1289.P54 162 (2,6,18,54) 33049.52813.6115477804490161.P67 163 (1) 99640870978732398443. .5073984584534267042701366192312558139347152929.P72 164 (4) 141375169696201183349885463641977.P104 165 (1,3,5,11,15,33,55) 951113761291.83723745489451.539555593782065191.P24 166 (2) P139 167 (1) 84609883.18840106986299.819417374559877.P105 168 (8,24,56) 121633.334224081623006401.8636794070026393288992369697.P31 169 (1,13) 46307.39899177220516741740469143831233.P96 170 (2,10,34) 1021.15425560249042501.26072363006406325854739861.P64 171 (1,3,9,19,57) 2053.6841.538309.74560887186814269973. .3805658347924925639235001.P34 172 (4) 9127292833.1240400287144237937. .384756252551799653157355170166535055814550369.P70 173 (1) 347.2423.50344039.471539527. .153070037700933331054524248476494792173.P85 174 (2,6,58) 349.77216590050964983143652251131561.P61 175 (1,5,25) L.M L (7L,35M) 3851.8230203760252601.P32 M (7M,35L) P51 176 (16) P136 177 (1,3,59) 82483.30308419.1463159201029.P74 178 (2) 2137. .6670001035767378656954255161929184701347978922160475516532776621.P82 179 (1) 359.5227541273369.191499930339009469.484537357606024275557. .97776360820654218154951.19818717012982215688309021529.P46 180 (4,12,20,36,60) 93273670767719119849201.P59 181 (1) 1087.3259.869887.41293569401198114715784283. .222115594362913033859606616935084264949119264129.P67 182 (2,14,26) 4208753465884607397726922333124602824618429719033.P74 183 (1,3,61) 22308770410847159047.P83 184 (8) 184369.6291093953.293615126959601.4961889461604693798857328257.P92 185 (1,5,37) 325852711.637267603891620815515472232790301. .1803380635085187494461189037326621.P48 186 (2,6,62) 1861.405148344889.60515949735938678857.P67 187 (1,11,17) 1871.7119993477462624445303.P111 188 (4) 326369.650909936062481571307414656986709933264881.P109 189 (1,3,9,27) L.M L (7L,21L,63L) 379.75736555536290042899.150497847036363835206199 M (7M,21M,63M) 198829.415801.30584009107.1707078974907610627202377 190 (2,10,38) 2617061.110943661.2250656021.3050589519086201. .45065286561682421139793282921.P54 191 (1) 1896349613. .31965885239172324178492996736290000958581033942895383913544482645687.P84 192 (64) 1153.55681.12644353.2474441815297.3020677481177462138881.P60 193 (1) 7542501761.64335170279671. .5023922419530075554880849680462185748909.P99 194 (2) 79153.11695740049349.101761712426028087493813409017. .5682612984161495984352311495269241.P82 195 (1,3,5,13,15,39,65) 1232401.118177021.P67 196 (4,28) 68993.500977.P132 197 (1) 7246911739.P156 198 (2,6,18,22,66) 397.257401.246830400797725347589009.P71 199 (1) 4588543.34266607.P154 200 (8,40) 210127601.14462056001.283231036001.P106 201 (1,3,67) 1475302430815774454593471971258812767057737919471.P64 202 (2) 11717.32844797.P158 203 (1,29) L.M L (7L) P72 M (7M) 699539.10931551.252777631.640915395596561.P35 204 (4,12,68) 2852622546217.14736450261056323705201.P74 205 (1,5,41) 821.982435845672451.P118 206 (2) 3709.51913.115361.38774969.122087137.28702255943293301. .24643851880680753997.85260663016194334109048149.P82 207 (1,3,9,23,69) 1200187.5394493693.43363095901832281006261. .46987948541428377962695535792142217.P39 208 (16) 41237249.905547932264861071666229565143230129859275489.P110 209 (1,11,19) 2927.326589253.2953667228251580029339756726838729574091.P101 210 (2,6,10,14,30,42,70) 5981641.147388921.P67 211 (1) 255571219.986018415638331144897705149152887163110839. .1782698571759822944425464521670215514283481531471069.P76 212 (4) 29930161.P169 213 (1,3,71) 2358779222910769.5163412518685933. .1886450423022355815248392428881107832527.P49 214 (2) 5606801.13864445393.4170493266061.148187590480662837474891\ 196151696943458464698104641724559095143058921833.P79 215 (1,5,43) 431.41281.4674932375366381.13470457618790060895951151. .40183448134459496127723158417549037223081.P54 216 (8,24,72) 433.2161.19009.455761. .193509085665339680074571429441497198565924689.P62 217 (1,31) L.M L (7L) 25638551.10471226501.3880053969769335736807493.P35 M (7M) 1048084151605026323873056941440759.P43 218 (2) 133417.1689506462393.1183634452833113.15902619513553141. .198558877793513066390969.1854413147145016784219270865881. .3316547850397693557131427838097992150273.P41 219 (1,3,73) 329021320690441177.P105 220 (4,20,44) 3153774361.7018271947721.66582594292663681. .34347664112526074866442921.P71 221 (1,13,17) 443.1327.65312573.588631616197.P137 222 (2,6,74) 28063132333.110960237137.129405102503301790657.P81 223 (1) 20071.210020081728371166287199953172049233. .14552020391616867751861787376003405019.P111 224 (32) 45697.2425413779895399260276908118509697. .344893183164325811790731098404717953.P89 225 (1,3,5,9,15,25,45,75) 1801.142845016408087602151. .1083803739493312667701.P57 226 (2) 1702570097.2678163373711493257558608239592337.P147 227 (1) 229035283.154282766133562846357.709711268528327341336958053319.P133 228 (4,12,76) P122 229 (1) 13301829773559449929333573.1786097907260768050299030591589751. .5560213957904401146976358164020003882623.P95 230 (2,10,46) 461.48203401.1853224081.9118947413041. .996024428653721875791186905187314201.P81 231 (1,3,11,33) L.M L (7M,21M,77L) 8317.207734163253.9508049868703.71301115589607904751983 M (7L,21L,77M) 6007.13399.4612609.P36 232 (8) 2101854113.2138683649.130274081659436626244163195262181879\ 47853507444338426479716946025178422538544097.P92 233 (1) 179411.9017101.54708069359245754606781357934918261. .1192706415763298890845976083472521853266125069053369107042854117723.P83 234 (2,6,18,26,78) 445069217792093194807364989.P96 235 (1,5,47) 77081.10943951.2963635864903802720551341744191. .3526044283547082417510281214088597814021244392943907181.P59 236 (4) 143400661121.17543686562323601.187381402716244523401. .72365309203156796180466302654219233. 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(7M,21M,63M,91L,273L) 32153941.1855216819. .750901310847020216911896822227864994984538990147663.P115 M (7L,21L,63L,91M,273M) 8191.3326360311. .112969481006265581832550676735801786622675472031076187.P116 833 (1,7L,7M,17,119L,119M) L.M L (49M) 4286904553.1044315454077887670730334324367061. .77527321680425768687177358942000903460123955419415148661765\ 11136730419608888410542001.P157 M (49L) 1667.104959.228618517.121210088231.446421836477.138646856861549. .9532354560627331217.28899785961568906898754636615374801178088\ 8688118745319796415584832475868378576054839819741911006933777533.P108 847 (1,11,121) L.M L (7L,77M) 242243.12967571.147942785940553287297921372606275925908411. .55587253587696854278028744890186371874421484069597260913894\ 165172311346305563413.P146 M (7M,77L) 3159704810685347.4782096685998787. .106738675233569048375019161.P222 861 (1,3,41,123) L.M L (7M,21M,287L) 10333.36773499417008677534452697. .167903422849439694359557500098662356581226001. .19344710971010459148138213408427678876357496377655918457430081567.P66 M (7L,21L,287M) 5167.609599991041962774143403.917444523840511470\ 77934097442692368546615714847318048492091454895567497437670631.P95 875 (1,5,25,125) L.M L (7M,35L,175M) 494592001.28023084251.476856731468823464501.P214 M (7L,35M,175L) 59812698235246414817686986669613526719545252592\ 01218819973152037967341455930044377106256056753751.P157 889 (1,127) L.M L (7M) 51563.602743.1869374977. C300 M (7L) 3557.5572253. C310 7^7h+1=(7^h+1)L.M, L=T^3-B, M=T^3+B, T=7^h+1, B=7^k(T^2-7^h), h=2k-1. Table 10- Factorizations of 10^n-1, n odd, n<400 n Prime Factors 1 3.3 3 (1) 3*.37 5 (1) 41.271 7 (1) 239.4649 9 (1,3) 3*.333667 11 (1) 21649.513239 13 (1) 53.79.265371653 15 (1,3,5) 31.2906161 17 (1) 2071723.5363222357 19 (1) 1111111111111111111 21 (1,3,7) 43.1933.10838689 23 (1) 11111111111111111111111 25 (1,5) 21401.25601.182521213001 27 (1,3,9) 3*.757.440334654777631 29 (1) 3191.16763.43037.62003.77843839397 31 (1) 2791.6943319.57336415063790604359 33 (1,3,11) 67.1344628210313298373 35 (1,5,7) 71.123551.102598800232111471 37 (1) 2028119.247629013.2212394296770203368013 39 (1,3,13) 900900900900990990990991 41 (1) 83.1231.538987.201763709900322803748657942361 43 (1) 173.1527791.1963506722254397.2140992015395526641 45 (1,3,5,9,15) 238681.4185502830133110721 47 (1) 35121409.316362908763458525001406154038726382279 49 (1,7) 505885997.1976730144598190963568023014679333 51 (1,3,17) 613.210631.52986961.13168164561429877 53 (1) 107.1659431.1325815267337711173.47198858799491425660200071 55 (1,5,11) 1321.62921.83251631.1300635692678058358830121 57 (1,3,19) 21319.10749631.3931123022305129377976519 59 (1) 2559647034361.4340876285657460212144534289928559826755746751 61 (1) 733.4637.329401.974293.1360682471.106007173861643.7061709990156159479 63 (1,3,7,9,21) 10837.23311.45613.45121231.1921436048294281 65 (1,5,13) 162503518711.5538396997364024056286510640780600481 67 (1) 493121.79863595778924342083.28213380943176667001263153660999177245677 69 (1,3,23) 277.203864078068831.1595352086329224644348978893 71 (1) 241573142393627673576957439049.P41 73 (1) 12171337159.1855193842151350117.P44 75 (1,3,5,15,25) 151.4201.P35 77 (1,7,11) 5237.42043.29920507.P45 79 (1) 317.6163.10271.307627.49172195536083790769.P43 81 (1,3,9,27) 3*.163.9397.2462401.676421558270641.P27 83 (1) 3367147378267.9512538508624154373682136329.P42 85 (1,5,17) 262533041.8119594779271.P43 87 (1,3,29) 4003.72559.P48 89 (1) 497867.103733951.104984505733.5078554966026315671444089.P39 91 (1,7,13) 547.14197.17837.4262077.43442141653.316877365766624209.P27 93 (1,3,31) P60 95 (1,5,19) 191.59281.63841.1289981231950849543985493631.P33 97 (1) 12004721.846035731396919233767211537899097169.P54 99 (1,3,9,11,33) 199.397.34849.P51 101 (1) 4531530181816613234555190841.129063282232848961951985354966759.P41 103 (1) 1031.7034077.P93 105 (1,3,5,7,15,21,35) 30703738801.625437743071.P26 107 (1) 643.999809.9885089.215257037.2386760191.511399538427507881. .646826950155548399.P38 109 (1) 1192679.712767480971213008079.5295275348767234696493.P60 111 (1,3,37) 37*.30557051518647307.8845981170865629119271997.P29 113 (1) 227.908191467191.P98 115 (1,5,23) 31511.19707665921.20414137203567631. .5799951513941382144830754391.P30 117 (1,3,9,13,39) 240396841140769.537947698126879.3352825314499987.P28 119 (1,7,17) 923441.3924966376871.768736559421401249042753476963.P48 121 (1,11) 15973.38237.274187.P96 123 (1,3,41) 1811791.626920594693.9425856976319889649.P43 125 (1,5,25) 751.1797655751.176144543406001.P74 127 (1) 18797.90679.P117 129 (1,3,43) 210769832431.407429732767505248479163.P50 131 (1) 80173.109517.141811693.446790173.7370364319027.15594845538029429933. .7317723970031057677693.131758351065116151205213.P27 133 (1,7,19) 1597.2021015460335957.P90 135 (1,3,5,9,15,27,45) 1577071.16357951.310362841.258360989311.P39 137 (1) 2467.2535528323.1029879756928762117455431. .140175894162990609843314797.P74 139 (1) 119124859925363.P124 141 (1,3,47) 283.721030498171501831.P72 143 (1,11,13) 2823679.180523201.47428676444591705727929369346443.P74 145 (1,5,29) 9605671.15589280974996818911. .80684370001269698853996151670133742711.P48 147 (1,3,7,21,49) 63799.4715467.267652966241599.2603941883787374089.P40 149 (1) 12517.535596779200919.P130 151 (1) 907.429360649.29877981480806017715604631. .28656552837574546515657117360191971140211910788651135283.P58 153 (1,3,9,17,51) 307.18973.11910133.25332185271529.41331541464123787.P53 155 (1,5,31) 311.9294566806081.P105 157 (1) 301670477.5180282664612031.11427999892821876397004936937893.P101 159 (1,3,53) 351391.3852774594841.185328247384490197483.P66 161 (1,7,23) 6763.472341157.11273170771131750391. .1626777403161656797092007877.P74 163 (1) 5764066668537270911379761. .403925722833778378107304989280994102850314855068615959021587563.P75 165 (1,3,5,11,15,33,55) 471241.138267770127916457629034873443951.P43 167 (1) 18843947.106811083848465643. .37576897811119167463436962410483708090653.P102 169 (1,13) 11831.2709246550432452192307438140153898730002165574677.P104 171 (1,3,9,19,57) 229162071140015324614111. .1104249349362995181144668003642191.P52 173 (1) 347.21528169344472027. .46194618816084982100679234312974236345786346173.P107 175 (1,5,7,25,35) 18525843918490695886751.991474271662986957800680951.P71 177 (1,3,59) 3187.232199557797964905143390121842739619033812919.P69 179 (1) 359.36558961.4201521652717.352543640588653.P141 181 (1) 12671.28865519.995130761.16814655289.414479952329.P138 183 (1,3,61) 2520277. .26384856922809741239246281240888980994567902544116187.P62 185 (1,5,37) 6511230041186560022095681.1936570114827069923550119591. .63441573295906607253783211246544893041361.P52 187 (1,11,17) 143899867.19886424182370875870239184131623563.P118 189 (1,3,7,9,21,27,63) 878075126908698927928483. .33030636037992147205820927521.P56 191 (1) 4473297929.112103021940812743353521.P158 193 (1) 773.39373.561470969.639701219449517.4274417556076113498947. .26409540111952717487908689681403. .447798287131284928051408304965265782892174953181087929.P55 195 (1,3,5,13,15,39,65) 1951.35081393881.360924572424391.P68 197 (1) 52009.79040479805615687465683. .3599474961483053310878605135585111374469138078226023233589649293.P105 199 (1) 797.29453.2253079.P185 201 (1,3,67) 1609.2046166739518832881. .184976479633092931103313037835504355363361.P70 203 (1,7,29) 18620680471.68616805173400502243.223072327648229020879.P118 205 (1,5,41) 41*.275521.21158848681.P143 207 (1,3,9,23,69) 109908191603107. .823799348530495507269035013254489287846904557.P74 209 (1,11,19) 257489.1246477.9269802917. .42545662673095831743789692955596677.P124 211 (1) 692624557324389620662782322677336711138108482588281739734\ 375570506492391931849524636731866879.P118 213 (1,3,71) 853.1594093.1182534679.17469229933.P112 215 (1,5,43) 431. .41398275939670867448911914339156680381343777006826487831.P110 217 (1,7,31) 3662093. .51508652116008872412773338336289708669037765081397085489.P118 219 (1,3,73) 439.2212293763. .39316310783659104892252157287077969239619734325044334592964583271.P68 221 (1,13,17) 443.1661422610776235605151630089.P163 223 (1) 2677.130975483.18245827708616526161162207345793404732623912772\ 2446775785510707991660410777011553955711177150186323623147.P107 225 (1,3,5,9,15,25,45,75) 2002877551.2636899200194401. .97671987485517534751.125899659866627764313267482289910001.P41 227 (1) 113136621886721.61743174809323855441087480850698944226478\ 3116181403206744221352101186333.P141 229 (1) 9161.43544351.9006996017757809392117.P195 231 (1,3,7,11,21,33,77) 2311.22187551.535212994471849. .234904066377148960506871003.156813120797253579231191970121.P40 233 (1) 467.47533.115081654907.89412401116867.42983757528467293. .10857980200444401822643. .20131492120828919814484857298874674155298711142397769181347.P103 235 (1,5,47) 518203357921.190893195970004711.1589908647339072250321. .605431706028029946531059199512572282414786250085768871.P80 237 (1,3,79) 90758677.1603873536486496162414778277997333003.P112 239 (1) 479.142847911.383155477843726029783939406113226468701730728790004161. .128780300340244872385688233345188210841783983757299260103530\ 718169486826135819357.P94 241 (1) 125997820213. .6864117620760368762783548070444378476387203247067308861991.P172 243 (1,3,9,27,81) 3*.411361786890737698932559.P138 245 (1,5,7,35,49) 336737801.23609565631.8274923251622825388807721. .74689140199104459031993110210054016743223513365511.P75 247 (1,13,19) 1483.1024516164479902988921.1299823520026173021751. .153360717056181938148119886537684707068363643930609.P121 249 (1,3,83) 4483.1413141919363039. .79631228080621938573499710253940180960724841. .3524445389714777887659796421466286321350017806951.P53 251 (1) 52371653.P243 253 (1,11,23) 1013.3037.72932311.2615313691182114927177553117.P179 255 (1,3,5,15,17,51,85) 77967508765681.17452955481423492661946457391. .34194473116159546979818689031.P58 257 (1) 1017721.4271961427. .668337078771358175173561511352921717498789809202021239. .206817820350950125703487701930279675704645733385400100293482\ 10640101028474215350858563.P102 259 (1,7,37) 2591.64638631.3663802449983927390483. .68941184253610253169908132923.P155 261 (1,3,9,29,87) 523.670249.44974999.9113995243.7299238406959. .9136734149894295938064503769037. .131108694538423601496731528051392288744803439.P54 263 (1) 40199712048008930571428131875902950777477607917.4409834792457\ 0538726555032711112035074551402751062500493727027459523924634267.P139 265 (1,5,53) 116721153193946736160194298023751.P176 267 (1,3,89) 9613.540913940517169.P158 269 (1) 5418307589425009.44052813154697065841.2211459886311754779116554\ 026679494335670326227547524190235297713426923019604371977151573671.P143 271 (1) 1627.56369.4790817014835738008638872886922952208975172696533. .10481543497847518793826699836636416832123886468989308584252\ 49862927198203812672579936297773867.P121 273 (1,3,7,13,21,39,91) 1093.32786209.139708570703521. .5331924088485663758835996822909123141656859869805374791.P65 275 (1,5,11,25,55) 7151.15401.59951.2495283264895779020253203931608951.P154 277 (1) 1016157022810759.102092644289739525085919338335107091799. .327650532696035587659287570766072667236893650986365027. .1791947410655996336975059053251127469487134368847917252099082548089.P104 279 (1,3,9,31,93) 18989357081041. .1986554577939642346080445591065987383029299397551517.P116 281 (1) 563.2597610354323.380431988961690791. .133355295524380732608674846305692470329. .609446372423851439353648647681174123227270385268469142812394\ 2057856885180480111114373298517228174199.P110 283 (1) 16809360945688609. .42608585710315399434791772854102387791567329009634088723. .145812343191030660287756724896936765853561086802175576458946\ 67901188624395417379659379946959868199.P114 285 (1,3,5,15,19,57,95) 18449288550044654139241919401. .844267447094321323435601792968017601. .219414044208440803345204019137889332111.P42 287 (1,7,41) 1723.13365428707.1941851180301719.386736023165016911\ 595773048286586040278275120007787504683197800313250373.P140 289 (1,17) 42773.93195753455238027770502373.P242 291 (1,3,97) 1747.18043.1625625533641.1953725183587.1012047221926483.P145 293 (1) 587.9476124263231731100867. .72753092406224481018194292737207864791672573037959. .1221988126336010683636167127168551453717779986523154333004279. .1636304654662619858552944817897722943031367354529440721228203.P98 295 (1,5,59) 366111286951.215168431547401.6898649252938113791.P188 297 (1,3,9,11,27,33,99) 55243.198397.1981560241.31600574312077. .165426670443186506567467. .7907009307594694001053552000588658391100974093457603716419437.P64 299 (1,13,23) 599.646777215499244129.P244 301 (1,7,43) 821856609631.13403893556831. .1141240390081433457327371568501745249133720840602413587.P173 303 (1,3,101) 2096761.272295362253883.P180 305 (1,5,61) 1831.2441.38981441.23886931441.2589575105599981821056130911. .119724826129796860249638217747306760831. .15036424216810835394267218232384724378143658798913881034271601.P89 307 (1) 526199.100066684713521521.11357792009472146190882003383320587841.P247 309 (1,3,103) 167798066344417387.3462948230491376473027. .5294796903161592416528456780680376286484870226446771978908657527791.P99 311 (1) 4344673058714954477761314793437392900672885445361103905548950933.P247 313 (1) 1879.2099818661161079.P294 315 (1,3,5,7,9,15,21,35,45,63,105) 631.142809770881.P131 317 (1) P317 319 (1,11,29) 723493.798763879.25815444138362212501215782602427193330961.P225 321 (1,3,107) 167805961.P204 323 (1,17,19) 851908127328669427. C271 325 (1,5,13,25,65) 77351.200201.4347195468174001.280672874149406424401. .3733209604853765522511798189559871765401.P155 327 (1,3,109) 1147117.13675561831.46553630477420371690681.P178 329 (1,7,47) 1964089881669809395643. .37633698993045258670863410188544865190871951.P212 331 (1) 1987.507849415889107.P313 333 (1,3,9,37,111) 96455449.2503678796850536532770633167883644999. .2391225903192434229494639627847286709185128947978708401. .378910432397861194405369041242690342635541471617136043289.P61 335 (1,5,67) 161471.50473006151.8480807579201.164168826950706906612751.P212 337 (1) 427991.282549563.288525099368866187. .16917315519781128734365649437223631827. .906533749251005245151122204670351312590267105760052002862150546121. .100404996104580113327338384209837460516989223104605474660002\ 55532841658478393221611341226016666610043.P102 339 (1,3,113) 406123. .777734075184513369134763199249605543798943174359980119. .18291566303691914139457741657555501180932574564840850694321009277.P101 341 (1,11,31) 683.1309536986943791.1214990613179601809. .246254302494824359942225692028596828479. .77617683268614779848612867615549232510150162228416842360054700961.P161 343 (1,7,49) 1977439591.62612348451548943616787.7754637448036836493958053. .108164182562832081427746076140676111780117904145681235787387\ 789905399551977213797293596351.P148 345 (1,3,5,15,23,69,115) 5521.74521.487831.19277911. .35645906496364306434849378023333297827811383782580351.P102 347 (1) 27067.P342 349 (1) 127037.28974679.6558190177933.P323 351 (1,3,9,13,27,39,117) 35803.355087294364791. .1786946360382838276990549597027.P167 353 (1) 1781225293.1044667255801249. C328 355 (1,5,71) 12071.48630031.14541138145721801.637608923699011111. .2816176140325775182481.12291800548749837777601. .30124399372383431732349878765015295744155071.P148 357 (1,3,7,17,21,51,119) 4999.143556841.3329808692827. .43451713720907517733.1118941080585995263069320373. .15958610536514031269673402704345512354924969.P78 359 (1) 719.73237.799853.33569502677.18200054748466867994849. .8745075387933004096394385246656921347. .10483559820031479418770210067382566319984375940690615649203032945707. .294766099902304487217227321881960481383427771094619317067283\ 63904658577135165687400308933318612320601.P108 361 (1,19) 81671197.88231338953639484307.103143975536225777711. .2747268108721464854672161.11614395396735967816534625117. .220706363362058009698248377980921202870796191. .338672903965083087378920536692185596496049493492739500693.P141 363 (1,3,11,33,121) 622001227.1830142890743707. .51608689304855151108853779386362027836720295184509344267160\ 29249879502627.P124 365 (1,5,73) C288 367 (1) 3671.129919.1628747.20211847881829188997. .2455930880606076809434613843.P305 369 (1,3,9,41,123) 1900016393894413508477719. .3151445759294008336434146467746716852125711. .4624740815741021164555032450406356165555243059597323.P122 371 (1,7,53) 2969.51199.26628696860763170757415075888614691991511099147227. .84432782131426436838808509529295022641378322928899102974874455\ 26484776400899484558952278931894560501953983650020256591767199.P131 373 (1) 1493.125329.P364 375 (1,3,5,15,25,75,125) 21751.47001751.4471031976001.13754361071\ 64906400113195032668541009729549504205143102033627145732751.P107 377 (1,13,29) 11311.30161.75401.428991023449. C311 379 (1) 3581077009.123816570976184709280372723.P343 381 (1,3,127) 9783462102370544239.45830377642600710169. .591082109095345424416413908752729. .82548590511975869997227448819484483748713764399174373.P128 383 (1) 852559.1628675880394909638591813700831880313095925587. .23181229247696012268805890210990826546682789683. .4444575092571167489534267707374644429886101712373400879.C230 385 (1,5,7,11,35,55,77) P241 387 (1,3,9,43,129) 23667927744614744947915146673639. .17166471209447081476714474614222447364318892065797214003761\ 10588630763194268685679597826668704163.P125 389 (1) 1991681.9673567199.30613946219676519851696681. .534106762532886493971950663223965323. .295666607855148525951669299929669849601357.C270 391 (1,17,23) 7039.15641.140346818465014013770407271092917. C312 393 (1,3,131) 787.11983466231266295686798098306470812807267. .1100517845115354201024243897527295703743726722437.P169 395 (1,5,79) 870801991.25439781075319591.4706625334158237778391951. .388603184868446209952357338208961774763421470820867551.P209 397 (1) 15941835894241.414655644406744473813179034437272581119641. .306705064286388936780828266137942480452220517447677. .1026361165663372453250598274116269654182086724746239639.P237 399 (1,3,7,19,21,57,133) 6316969.34282879.1473464802559. .7459654752238258604700923083.P162 Table 10+ Factorizations of 10^n+1, n<=400 L,M for n=20k-10<=790 n Prime Factors 1 11 2 101 3 (1) 7.13 4 73.137 5 (1) 9091 6 (2) 9901 7 (1) 909091 8 17.5882353 9 (1,3) 19.52579 10 (2) L.M L 3541 M 27961 11 (1) 11*.23.4093.8779 12 (4) 99990001 13 (1) 859.1058313049 14 (2) 29.281.121499449 15 (1,3,5) 211.241.2161 16 353.449.641.1409.69857 17 (1) 103.4013.21993833369 18 (2,6) 999999000001 19 (1) 909090909090909091 20 (4) 1676321.5964848081 21 (1,3,7) 7*.127.2689.459691 22 (2) 89.1052788969.1056689261 23 (1) 47.139.2531.549797184491917 24 (8) 9999999900000001 25 (1,5) 251.5051.78875943472201 26 (2) 521.1900381976777332243781 27 (1,3,9) 70541929.14175966169 28 (4) 7841.127522001020150503761 29 (1) 59.154083204930662557781201849 30 (2,6) L.M L (10L) 61.4188901 M (10M) 39526741 31 (1) 909090909090909090909090909091 32 19841.976193.6187457.834427406578561 33 (1,3,11) 599144041.183411838171 34 (2) 28559389.1491383821.2324557465671829 35 (1,5,7) 4147571.265212793249617641 36 (4,12) 3169.98641.3199044596370769 37 (1) 7253.422650073734453.296557347313446299 38 (2) 722817036322379041.1369778187490592461 39 (1,3,13) 13*.157.6397.216451.388847808493 40 (8) 5070721.19721061166646717498359681 41 (1) 2670502781396266997.3404193829806058997303 42 (2,6,14) 226549.4458192223320340849 43 (1) 57009401.2182600451.7306116556571817748755241 44 (4) 617.16205834846012967584927082656402106953 45 (1,3,5,9,15) 29611.3762091.8985695684401 46 (2) 1289.18371524594609.4181003300071669867932658901 47 (1) 6299.4855067598095567.297262705009139006771611927 48 (16) 97.206209.66554101249.75118313082913 49 (1,7) 197.5076141624365532994918781726395939035533 50 (2,10L,10M) L.M L 7019801.14103673319201 M 60101.1680588011350901 51 (1,3,17) 291078844423.377526955309799110357 52 (4) 1580801.632527440202150745090622412245443923049201 53 (1) 9090909090909090909090909090909090909090909090909091 54 (2,6,18) 109.153469.59779577156334533866654838281 55 (1,5,11) 331.5171.20163494891.318727841165674579776721 56 (8) 113.73765755896403138401.119968369144846370226083377 57 (1,3,19) 1458973.753201806271328462547977919407 58 (2) 349.38861.618049.11811806375201836408679635736258669583187541 59 (1) 1889.1090805842068098677837.4411922770996074109644535362851087 60 (4,12,20) 100009999999899989999000000010001 61 (1) 81131.11205222530116836855321528257890437575145023592596037161 62 (2) 2049349.483128549554512237305554588359039822397307149685578249 63 (1,3,7,9,21) 5274739.189772422673235585874485732659 64 1265011073.15343168188889137818369.515217525265213267447869906815873 65 (1,5,13) 131.8396862596258693901610602298557167100076327481 66 (2,6,22) 5419170769.789390798020221.2361000305507449 67 (1) 909090909090909090909090909090909090909090909090909090909090909091 68 (4) 152533657.65552746171882583264230070868884366877803237222654400793 69 (1,3,23) 31051.143574021480139.24649445347649059192745899 70 (2,14) L.M L (10M) 421.848654483879497562821 M (10L) 3471301.13489841.60368344121 71 (1) 290249.P65 72 (8,24) 8929.P45 73 (1) 293.10826684964539959837294043117.P42 74 (2) 149.3109.111149.708840373781.669031686661427842829.P29 75 (1,3,5,15,25) P41 76 (4) 457.1403417.5240808656722481737.P45 77 (1,7,11) 463.24179.590437.7444361.4539402627853030477.P22 78 (2,6,26) 3121.53397071018461.P31 79 (1) 1423.9615060929.P65 80 (16) 1634881.18453761.947147262401.P39 81 (1,3,9,27) 1459.2458921051.456502382570032651.610600386089858349939139 82 (2) 68389.P76 83 (1) 167.997.3565183.2097307081.7742098247001476863.P42 84 (4,12,28) 11189053009.603812429055411913.148029423400750506553 85 (1,5,17) 87211.787223761.P51 86 (2) 338669.P79 87 (1,3,29) 638453709757.135080726389891.P31 88 (8) 10100113.P73 89 (1) 179.12147237304901893.P70 90 (2,6,18) L.M L (10L,30L) 1105097795002994798105101 M (10M,30M) 181.4999437541453012143121 91 (1,7,13) 21705503.P65 92 (4) 2393.P85 93 (1,3,31) 373.44641.3590254957.P44 94 (2) 45121.2144906157509411684424913774078958939881.P49 95 (1,5,19) 1812604116731.121450506296081.P46 96 (32) 193.769.1253224535459902849.P41 97 (1) 102527361354613106010527.323338434891034089173475790125293.P41 98 (2,14) P84 99 (1,3,9,11,33) 7093127053.P51 100 (4,20) 401.1201.1601.P72 101 (1) 607.809.1213.1327067281.P83 102 (2,6,34) 409.3061.5969449.134703241.225974065503889.P29 103 (1) 1237.44092859.102860539.984385009.612053256358933. .182725114866521155647161.P37 104 (8) 1249.49297.300977.648961.249227787818677482257.P57 105 (1,3,5,7,15,21,35) 29970369241.1661378260814161.18276168846821336356291 106 (2) 1061.5051749.245391150214875249502685807421982149521.P56 107 (1) 1499.28463.74687.392263.795653.P82 108 (4,12,36) 1726290008991504500177463302688697.P39 109 (1) 3338786746233023.14060959683864286267405933000927102019.P56 110 (2,22) L.M L (10M) 661.148721.P32 M (10L) 18041.1121407321.P28 111 (1,3,37) 223.4663.21606064498691505246200058094681.P35 112 (16) 673.43735845217.217860610452031121598489279950204653537.P45 113 (1) 4973.4426889.P102 114 (2,6,38) 229.2281.4789.304077901.52875286008709.739653893349540289.P23 115 (1,5,23) 691.P86 116 (4) 233.355193.21591416633.17468739848498438039329935679794457.P60 117 (1,3,9,13,39) 461917.60034573.P59 118 (2) 430148941.P108 119 (1,7,17) 1868879293.5673320472670315859129.P66 120 (8,24,40) 1132716961.281259985248437790051014401.P29 121 (1,11) 11*.4357.25169.1485397.102502981431359171598893.P72 122 (2) 1587221.81183810541.101444162656037151745878558385892753596849.P62 123 (1,3,41) 739.148339.16419517.P65 124 (4) 1489.640543322297.27908132670449.384705444182230291105649.P68 125 (1,5,25) 21001.162251.10893295001.P81 126 (2,6,14,18,42) 1009.43266855241.P59 127 (1) 3557.857772733.1094479651.1125629957.616896149073719728613. .10860110813777339731289.P53 128 257.15361.453377.P116 129 (1,3,43) 304768036847074491064894608014695867632997.P43 130 (2,26) L.M L (10L) 1031498834064949381.P31 M (10M) 2311921.12763852652999774041.12119730504567977254081 131 (1) 263.1397382241.306662501757259.525786373041914526306757. .112506283680098168752627601991569.P49 132 (4,12,44) 2377.16369.432961.6796152793.24387741577. .126197002179733470481.P27 133 (1,7,19) 247025236977306025681323889. .61828645758322140842666144519962696417487.P41 134 (2) 269.4021.260587121.94927228208573594069. .2302527353565357450759725122262880394277261.P56 135 (1,3,5,9,15,27,45) 6481.577603663291.31023833790241.P43 136 (8) 17*.13355595217.P117 137 (1) 364393423.117651465889.441651480271681.676321006412903. .218801242136856556680173235529.P58 138 (2,6,46) 829.1569889.536430531035337769.757108543129939106221.P41 139 (1) 557.2503.P132 140 (4,20,28) 851761.P91 141 (1,3,47) 344887.9127213.1160803383934463712259.P59 142 (2) 569.7669.380623849488714809.7716926518833508778689508504941. .93611382287513950329431625811490669.P50 143 (1,11,13) 51767.22144088539.264752347289.104730101107272149081.P74 144 (16,48) 13249.1067329.P86 145 (1,5,29) 1451.30104611.58765601.2433146345771.17996132431060961.P65 146 (2) 5911541.16692085818029.5774294197526381. .182202742802607835615596881.P82 147 (1,3,7,21,49) 7*.P84 148 (4) 61544617.16444765848115921.P120 149 (1) 2087.9615683031450065714899. .165459609176797865866134365329792270635207840943.P76 150 (2,6,10L,10M,30L,30M) L.M L (50L) 261301.P35 M (50M) 601.3903901.168290119201.25074091038628125301 151 (1) 181288487.153653579173.12331942624071394811. .2646756758131654397378192081701748003041997.P69 152 (8) 134369.31735795756961.P126 153 (1,3,9,17,51) 2142001.5364487.832339891.276402747619.2405782797823.P51 154 (2,14,22) 39511854229.P110 155 (1,5,31) 11161.3925963357681.5167617497664851.P88 156 (4,12,52) 313.1101673.1358074433371719716641.291593563046646669491593.P43 157 (1) 4397.3641773.P146 158 (2) 5689.507998564486483655774880939989709. .646301962916453492325383567253991760083617720844121.P69 159 (1,3,53) 3499.2784091.54137839415767.917813298871770308465539. .26526333976234009593263527.P31 160 (32) P128 161 (1,7,23) 967.1569936761.1203881882727712699967. .23391028206417273637358380573.7775058388319250595762800404689.P40 162 (2,6,18,54) 2925721.P102 163 (1) 653.13693.14286890032106357. .66953479943839030979655991920753816099754871899.P93 164 (4) 121553521.36637591407529194237097.P130 165 (1,3,5,11,15,33,55) 4124507971.19835636682880495867311241.P46 166 (2) 23023967955265160767768376873521136169786061.P121 167 (1) 63716179.116011189311149998139.272828068791212993437. .301525294918950432087520298129941558711551656822567015411.P62 168 (8,24,56) 337.2070270028985341766616009080161.P64 169 (1,13) 677.987001237. .1592730232155679902273246343099578009020762979379345291.P90 170 (2,34) L.M L (10M) 7568346838961.237612993541791006121.P31 M (10L) 26861.P61 171 (1,3,9,19,57) 19*.2053.4410785971.2911579215499. .307010852070382484317401373.P55 172 (4) 277641151780258438310079109077611969. .2645778409917434965592366282025495569. .38993135849791157061060738352944105076217.P56 173 (1) 9689.16864733.P161 174 (2,6,58) 997369.15565833747318241.157002934023127338801841. .4477350074169470752905544969081.P36 175 (1,5,7,25,35) 3612546001.299547376801.P99 176 (16) 11969.4913921.470909313601.P138 177 (1,3,59) 60247408327.968385024074451409.2676157881043509853. .3203031926532314264104769060847481.P36 178 (2) 38449.138841.P167 179 (1) 523661705392754764972834211810001059.P143 180 (4,12,20,36,60) 265183201.95853807664312827399794371014650641.P53 181 (1) 13757.1467439874822650361.5781376922797866530410940379929\ 1636496876923883191635824278127299864929561.P84 182 (2,14,26) 654721485601. .3571618567996393297210217238290456648947344377957590363519828421.P69 183 (1,3,61) 367.51745081.40498340376691. .42936744040512685057308971520417028077990465463.P50 184 (8) 120553054891405588545727822543281066162803459003848166118314367809.P111 185 (1,5,37) 49173925574833481.P128 186 (2,6,62) 5209.139716865184144864008269344660199946429.P79 187 (1,11,17) 192611.1284680342573.6315203673292075607. .125797399492676917721.P104 188 (4) 70313.79337.485041.118710721.6578404633. .169905327561162104198557246291921.P119 189 (1,3,7,9,21,27,63) 379.8642670625016390971. .63060936944326674212591995662102125143.P49 190 (2,38) L.M L (10M) 780548018657747948342675331841.P42 M (10L) 761.1901.3041.74861.417332341.P50 191 (1) 383.679961.4041943.955059211.78087485383. .3370796736173938091727422330529475982098304687381174810841794\ 785884893349397.P80 192 (64) 3457.12289.418725889.338579887181973006729167651681190977281.P74 193 (1) 1931.10037.1430131.166376423.P171 194 (2) 389.78412655334235167606162810513004420610966509546603404\ 268745999503561001.P119 195 (1,3,5,13,15,39,65) 15601.925081.P86 196 (4,28) 52781463673. .5010620991340707523594168804430658367520003649793780623118456073.P94 197 (1) 15761.7187743.300567477887394052365757. .29811355463297742645615812791522446524687.P121 198 (2,6,18,22,66) 79082656489.1538607523068637497164701.P85 199 (1) 3545105703277.10765760180213.12277415800813. .180724074168604579796294647309331. .314293140427626491056008875724151058487007.P86 200 (8,40) 24592788001.3475700719926956233659563848134955052440801.P108 201 (1,3,67) 7237.17830074841.851109498533797. .45360300267343173645804799921.P75 202 (2) 101*.3679329001.19384130081.12793360409007449. .4908990488743183603681.5383539446793990416488818114381662511041. .147987024898557331825270928295100820916509.P60 203 (1,7,29) 19489.243720583.2563963356465898129. .13569612563320403017443683179.P109 204 (4,12,68) 2857.13266937.1119527384827710553. .53043011765949537815976769.P74 205 (1,5,41) 436026711667335044426416921.P134 206 (2) 801341.29286597879221.33670587927455442579575167786879669. .95000575486937988681435170477136054984821.P110 207 (1,3,9,23,69) 37916801893.143409436964525899. .831759677425747570837717.117680633072620952134930832292859.P49 208 (16) 19725473.40336502753.754651871841089.49190086416352961.P143 209 (1,11,19) 419.85691.258743.P168 210 (2,6,14,42) L.M L (10M,30M,70L) 42681134161.424451728681.P27 M (10L,30L,70M) 1384194841.P39 211 (1) 2764617069785703725933625413.P183 212 (4) 18233.67406298457.1488067111584049.899319337247551841. .23641392997940421257. .54469179239047116300845682623717697162577784999950014081337618457.P76 213 (1,3,71) 2107849.21977699107816352490639478201.P106 214 (2) 40882343106721.P199 215 (1,5,43) 1721.18920435284033918144809657490533251.P131 216 (8,24,72) 433.491413179769291800875985377355914924161. 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C300 347 (1) 368720813.805697219.89700105169. C318 348 (4,12,116) 13921.11090099157944399977. .246900403017958787131873605843061988161.P163 349 (1) 3491.3361543170437980531667161105832265329. .35927713091621749764338565947172319082597.P268 350 (2,10L,10M,14,70L,70M) L.M L (50M) 701.422100001.1125310645201.P97 M (50L) 213567756617511209506778605497489645838025587933288349770601.P61 351 (1,3,9,13,27,39,117) 592489.30742515591607. .6862390300547244074038319769783944997739006024946890580945655121.P133 352 (32) 23447080358593.26670033927811409112897180097. .222688353792418778799593928777532880641. .3162086824598326714007856976523611232833. .196492106862714324563103086902334481596741493532094589569.P145 353 (1) 1006029527.56540001776360839594874218856939642617050503. C300 354 (2,6,118) 709.P230 355 (1,5,71) 2131.8521.1026684688942915478900251.P249 356 (4) 158777.118638175449391414217. .205634535002357125750465106981645977.C292 357 (1,3,7,17,21,51,119) 17851.P188 358 (2) 530819489.7788750761855821. C332 359 (1) 25849.19210610797963667218565939. C329 360 (8,24,40,72,120) 25827855590409981859166961366395445866961549\ 22477921.P141 361 (1,19) 43321.5140192330491733331414521378576126342075768810496980939. .3223374037812410694155224757327965568352798312019085047331.P226 362 (2) 928417781.469968172441.2136569912461.15470952779187481. .3467369151629862044701.314547891171506427278717744569. .22780106292572351730658730234738216404394547689.P214 363 (1,3,11,33,121) 727.1453.3481311540961. .23001119290738574648920681856831153293580786040140280069899\ 8509497721478420289331088499239362108691.P104 364 (4,28,52) 574393.10727809.286569193. .146922836547557380904624883811070801579636649582426027039761. .12363864432864160008452059822963107626029967969207066306934\ 50425385353425494707969.P127 365 (1,5,73) C289 366 (2,6,122) 76129.190321.390889.4801921.2834820061.3812801341. .2418666002101476599410229029. .13057041824482269098458887905989751147403593970934212233550\ 30629345156521.P100 367 (1) 6337012003051224701798337646203298967.P330 368 (16) 153089.107896522139513920752730643638401909724513.P306 369 (1,3,9,41,123) P241 370 (2,74) L.M L (10L) 1481.6336499381. .271880675850180367872653023164942909880799363524216099671322919521.P67 M (10M) 15541.68821.74615611921.4098464044501.107771345624719321. .16206170837408945509907221.P69 371 (1,7,53) 743.1057997274797.2584863032795023. .157098960626439851618648929549692694031560694047. .254817118213049235446411359583382178158806414098687434807545\ 9263402328971040215243200625902015381883224397137647.P124 372 (4,12,124) 700849.11110153.5419392721.1220725699657.42367299139993. .16584440161215846282167330487128069170776821649169. .23140616853203983900922551785166946660605063239337678349130406077337.P76 373 (1) 90060564940204590241091.31789742592325236493677867077. .216526856157522033346992833381986034131.C283 374 (2,22,34) 7481.155623169021. C305 375 (1,3,5,15,25,75,125) 25005172023963824973001. .59244397795882902986928930001.4709825349852110182615878875374\ 419529306990314325041101342026868334001.P80 376 (8) 84977.3056129.801310897.71306567377.17432639655812883290745409. .24675897452175673572108819041. .497739854873037449538282211022770570513.P245 377 (1,13,29) 484688693362852875650185421098728254915802251. C292 378 (2,6,14,18,42,54,126) 165358820733883770736233015527320175869593121. .344410449392555791991391842565560527204857067026484035552706\ 583597118812185729.P95 379 (1) 10613.30817249.4918445244727502358176820280164673127. .33584520860278767011970207517032237108309731086439023.C278 380 (4,20,76) 12231385993824607429587973444912801.P254 381 (1,3,127) 2287.451897625287.1053449334720579590200819. .4444349792156709907895752551798631908946180608768737946280238078881.P147 382 (2) 77929.106961.13968004259021399202183274452648726337203224861. C324 383 (1) 11491.262739.4685623. C366 384 (128) 434689.859393.33649448872371457.145778507161340929. .14201814954885944779899043084237189743158239327057547504266\ 7940048026473157944321.P131 385 (1,5,7,11,35,55,77) 3851.170873011. .1051543809110704722613632495009411089889481. .3815465557445576556927066195758955772398238343771.P138 386 (2) 1439921227944130405196041866693950149. C348 387 (1,3,9,43,129) 1708219.10455967.41130156794062447. .35037423610997086622096063353212253926195272207441939622830\ 330161546317292588303.P143 388 (4) 89889606269073901082901578436277965983883967076039535258233.P326 389 (1) 110477.147351852638675482771921. .20869977631748901447120178621975588066249.P320 390 (2,6,26,78) L.M L (10L,30L,130L) 201721695849323521.2685647186330706081032050321.P51 M (10M,30M,130M) 19501.9160020509281917601.P74 391 (1,17,23) 2955961.2140571729.37633218241.9101279023169. .473608692432035450677211738101499095303.P275 392 (8,56) 54881.403539336813078648113. .5649333362757164788488040397332687608183771313.C265 393 (1,3,131) 78447517.2247064574420005776288509534269789472160532543060948\ 7291715500041029950763944163993319007373686738769124162721892380653.P134 394 (2) 27581.39183683903547299202471125940449908897423309. .95857172574244109092139928579854506165297073472804809.P291 395 (1,5,79) 6295632499623851.4539787279569136988691351491. .24966203549341539495819194854679625225811. .36135553580039597739744803188558136917651907171.P182 396 (4,12,36,44,132) 761113.99677548081.440718109921. .4987445373502665124237014313. .7408727338313716781446937691661250885891761.24628894360746\ 3575049631057704872789315648893038409344335438892115177.P73 397 (1) 15149521.16790376230301757.P373 398 (2) 581140178513809.25318162873760593102299508147845874260505144789.C335 399 (1,3,7,19,21,57,133) 425991366045253. .17499101101496101893247811440257935152097401. .9284668536078237580134472469990637899155265743957.P110 400 (16,80) 4801.43201.980801. C306 ------------------------------------------------------------------------------- 410 (2,82) L.M L (10L) 59090021.1266925593264677597290950641.P126 M (10M) 821.639601.11036695406441.1073380218518144441. .1350059351915828990550200161. .139074671904011778473984366758527524121792121.P49 430 (2,86) L.M L (10L) 7741.2198478623863901. .7549370642855106064318428883982856249713821.P107 M (10M) 1044817620601.P156 450 (2,6,10L,10M,18,30L,30M,90L,90M) L.M L (50L,150L) 1801.33301.139501.560701.5030101. .152372720018473862927761564984708391701.P57 M (50M,150M) P120 470 (2,94) L.M L (10M) 941.29096340761.474181059033108701.P153 M (10L) 18465110677523332168571918701. .36278027867431861993452659830529311893020335861.P110 490 (2,14,98) L.M L (10L,70M) 268330861.32422034720694602873554553373241.P129 M (10M,70L) 366395073564101.354434210886621881. .28706164502711390875680641913825481.P102 510 (2,6,34,102) L.M L (10M,30M,170L) 8161.2586721.5071197096181. .677827125083342723075551469213357648491441.P64 M (10L,30L,170M) 1021.855781. .114797635898427958794033542315180663747542680841.P72 530 (2,106) L.M L (10L) 10601.5087682140647502286078523305727177388588041.186658485605\ 0670751142049533200645741569755944852998334484263922627299824538001.P84 M (10M) 4241.1103461.22534789481525070481066146802824209631029\ 690388674663333618185041786620876200193924826168812981.P104 550 (2,10L,10M,22,110L,110M) L.M L (50M) 2471701.486904001.133157371602664723858501. .212890462662706052906860201.49094895915282817628267672401. .3668996113223183559833250396711179251902642533701.P59 M (50L) 126239370797267198368490274128272780260464262689211651471701.P141 570 (2,6,38,114) L.M L (10M,30M,190L) 211592942161.481612717573381. .117008737749609201563737321.P93 M (10L,30L,190M) 20521.7594681.70532941.3685902392604541. .9025836525591423620461.14634428294824755331225520581.P59 590 (2,118) L.M L (10M) 193274561.347811486461.12013233555242641. .8505896978256278656680007081.P168 M (10L) 1181.35764621.3064985101.750373580343320570787901546930969804\ 95187922731710294362515981973078279750268757439593899891657607361.P112 610 (2,122) L.M L (10M) 21961.51241.9818561.28474644365651641.17716886277230798340041. .39069669288697789469488625615834711944836425801981.P136 M (10L) 6101.217345835281.555818110301.8950221294967070861. .17751033585336286181.30177150878514090521547663054628235944221777770161. .27186363592392725942593454290345801336551729326489701011779461.P65 630 (2,6,14,18,42,126) L.M L (10M,30M,70L,90M,210L) 158201922061.56541586842121464411050521. .229209947541611916250468549073491977346097487987121.P57 M (10L,30L,70M,90L,210M) 1351855459456741.33822732328831925621101. .19825744781339712457003608841.938366482703941691072746568832156530761.P40 650 (2,10L,10M,26,130L,130M) L.M L (50L) 1301.P237 M (50M) 431684501.23098714167966114959599501.P206 670 (2,134) L.M L (10L) C265 M (10M) 99908656408081.28120888763986481.P234 690 (2,6,46,138) L.M L (10M,30M,230L) 1381.63691382029918881694921. .316699822269639096888937801.114061789660900413328637822705950861. .73137716939443396538710479664316724061.P52 M (10L,30L,230M) 9661.6193371433274461.59483540558994759763795801. .53836677179343252802536411876638569921.P93 710 (2,142) L.M L (10L) 3988107351414007354990781.9986944549901581065584141. C231 M (10M) 2006461. .101956533794009284800765131459172391943780858147641273764890861.C212 730 (2,146) L.M L (10M) 1574095173557315161.665787365080314723361. .430290068517717503314541569581514324311872414409341453561896330801.P183 M (10L) 405007685327621.8383648187691944581.14947162642878875393981. .4941698957237831273165154533595725287181.P194 750 (2,6,10L,10M,30L,30M,50L,50M,150L,150M) L.M L (250L) 473217092140501. .36605832263463437733314604426708004731796978480010361966001.P127 M (250M) 3001.89285503565971501.3405964732740856789870552501.P153 770 (2,14,22,154) L.M L (10L,70M,110M) 177663162067596466801.557377949694929416901. .198618138138638637771823241.P173 M (10M,70L,110L) 20021.1607415137021384783510881. .647799461893729229242068652342456021003805852058736425973158\ 141325454469108253161834095467738437014341.P111 790 (2,158) L.M L (10L) 14671834360812557354682189761.P285 M (10M) 102701.99834305852659737721.9881484126026806397682037921.P259 10^10h+1=(10^2h+1)L.M, L=A-B, M=A+B, h=2k-1, A=10^4h+5.10^3h+7.10^2h+5.10^h+1, B=10^k(10^3h+2.10^2h+2.10^h+1). Table 11- Factorizations of 11^n-1, n odd, n<350 n Prime Factors 1 2.5 3 (1) 7.19 5 (1) 5*.3221 7 (1) 43.45319 9 (1,3) 1772893 11 (1) 15797.1806113 13 (1) 1093.3158528101 15 (1,3,5) 195019441 17 (1) 50544702849929377 19 (1) 6115909044841454629 21 (1,3,7) 7*.1723.8527.27763 23 (1) 829.28878847.3740221981231 25 (1,5) 5*.3001.24151.1856458657451 27 (1,3,9) 5559917315850179173 29 (1) 523.303309617049998388989376043 31 (1) 50159.2428541.157571957584602258799 33 (1,3,11) 661.1453.637265428480297 35 (1,5,7) 211.42437717969530394595211 37 (1) 2591.36855109.136151713.2615418118891695851 39 (1,3,13) 79.157.547.84631.480091.32508061 41 (1) 83.1231.27061.509221.14092193.29866451.840139875599 43 (1) 1416258521793067.42534656091583268045915654719 45 (1,3,5,9,15) 9842332430037465033595921 47 (1) 2069.22666879066355177.18806327041824690595747113889 49 (1,7) 510810301.1065264019.100641220283951395639601683 51 (1,3,17) 10711.457315063.15085812853.25994736109 53 (1) 107.351497.6005113.6918082374901313855125397665325977135579 55 (1,5,11) 25301.39161.643170158708221.645654335737185721 57 (1,3,19) 19*.1047623475541.1412900479108654932024439 59 (1) 1181.70845409351.33083146850190391025301565142735000331370209599 61 (1) 440177.520518327319589.1461808298382111034194027645506019619578037 63 (1,3,7,9,21) 127.8317.867259.106431697.316825425410373433 65 (1,5,13) 131.673267426712748387612994804392183645147042355211 67 (1) 15277.2160349.76394148218203559.P42 69 (1,3,23) 139.8209475377.P34 71 (1) 1847.64327.159248456569.1273880539247.P42 73 (1) P76 75 (1,3,5,15,25) 151.59302051.1826934301.27665283091695977275201 77 (1,7,11) 593554036769.P51 79 (1) 317.185277551100523662054683911.P53 81 (1,3,9,27) 139026457.14010692617072784593.P29 83 (1) 167.12119.178057577.52447614013.P61 85 (1,5,17) 584916791.553393500180551.P44 87 (1,3,29) 398113.54415717.P45 89 (1) 73111721.2103114787086589.4180235017418376525776333.P44 91 (1,7,13) P75 93 (1,3,31) 2791.3163.P56 95 (1,5,19) 67989221.180124441029509240214675551.P41 97 (1) 389.4247091263.P88 99 (1,3,9,11,33) 397.2377.1240500097.P48 101 (1) 341459085477993311443.86408339296208914807632672776254957729.P46 103 (1) 24103.37723802531.995301206162659155091.P71 105 (1,3,5,7,15,21,35) 421.540751.599551.2598121.126713791.P22 107 (1) 1276033068038437.304971297664201988898688683700564748747693245597.P48 109 (1) 35970728459102446279558069.P87 111 (1,3,37) 651950416864148392635280596760630561.P40 113 (1) 227.45902861.20884152591287817709. .22455907106840364577416382241618449.P53 115 (1,5,23) 95911.333041.9964291.17184010031686356151.P55 117 (1,3,9,13,39) 9127.1810693.P65 119 (1,7,17) 239.20580793913.5787647502138040836760695667.P60 121 (1,11) 30977.1595696213.12407691244609.P88 123 (1,3,41) 174907.28385941.142971820992006871646588679396397417.P36 125 (1,5,25) 5*.1632185486501.27678437808551251.P75 127 (1) 2985212831443.6073732108394141.108345618426999904901.P83 129 (1,3,43) 1549.1389891409.2338110553.44012945778511. .3440126314390780951.P34 131 (1) 263.7791763956749016154215607697892626144401.P94 133 (1,7,19) 292601.1889399.4085166784889.P89 135 (1,3,5,9,15,27,45) 271.P73 137 (1) 8221.339761.3677081.136238281.394711476243912154244261783.P91 139 (1) P144 141 (1,3,47) 283.64192789.44682948968412414039336007.P60 143 (1,11,13) 3433.3111663528084541.191144869353686249. .39087214421959708068637.P67 145 (1,5,29) 38861.144801130358116982559692328954495371.P77 147 (1,3,7,21,49) 7*.6469.712319250521341.1965320765521339221407672989.P41 149 (1) 95648167.12386903337067381971073.P125 151 (1) 16944919.13665285883.18462023135737378116249335576687.P108 153 (1,3,9,17,51) 307.1531.35236819.25167354031.2926326645433. .290204982599509251565261308001.P35 155 (1,5,31) 112582632731.21008012759943211.12981042678412809421.P79 157 (1) 88388104773677.40715753678177846062481. .20186536221332782615476135581.5898938014844761247631748773851299.P64 159 (1,3,53) 1399201.2622229.23393486084531921650287976389757830429777373.P53 161 (1,7,23) 967.48359249.P127 163 (1) 391313358915050362321.1568405349185888385874441.P124 165 (1,3,5,11,15,33,55) 1321.121679581.1454598708730201.P57 167 (1) 2339.1353068069.312708742481.2371759568436871497727. .3523115712994289296116782558201078504837006181920850717652507.P67 169 (1,13) 2029.362685493. .5276574100195101793609935574565521674231026096229661942697690104397.P84 171 (1,3,9,19,57) 32491.406981.368030647.27361000362650239.P78 173 (1) 347.593979931.19313697101202731.P152 175 (1,5,7,25,35) 1849051.P119 177 (1,3,59) 31153.128857.77162089. .7005596150545816426029108678026870967790150254367.P55 179 (1) 359.260690365910973937.133424628147697995732126527. .30262061969946294833518392497.680728835990076713808763658029. .459009579117136530987907464707351.P49 181 (1) 42811641487.8439877927139263645774810523.P149 183 (1,3,61) 1640962831.470011312403953.252792952756496725399. .120213931658422906698644629.P55 185 (1,5,37) 3701.2341771441.8942042341.586894211641. .9469266456252868041356465741.111979611651060119297676530503786924451.P50 187 (1,11,17) 625293470077.1187896992833. .759915556656723468789897776052021738313604080983777078304038497.P80 189 (1,3,7,9,21,27,63) 757.2150969311.452555562844477. .5578141711502710729.36959230870280730074750882077.P39 191 (1) 195967.232767887540024567510779793146810415249588466971308867.P140 193 (1) 1931.P197 195 (1,3,5,13,15,39,65) 50311.3762447001.P86 197 (1) 3012710549939.1060717191208815311.5407146368827614877351. .616346818465450400938401858863608277357.P114 199 (1) 797.140893.18242336369.4645373755026923.74228785249216074\ 982007362154907801499582555623361265045414501593697.P105 201 (1,3,67) 1609.66046284412625914877623090150129. .14160915264340305525070590511634038738687.P63 203 (1,7,29) 5279.60901.490738600321966404709119573187611258997827\ 809661439583138969212062707.P98 205 (1,5,41) P167 207 (1,3,9,23,69) 2631980958036751.P123 209 (1,11,19) 6689.3107455009693.3215499310277.1056394526657537. .342732573655364605155483163584083618987113.P103 211 (1) 88672307809797915061.P199 213 (1,3,71) 4813252624072182882141229.44043095909867219792359537381.P93 215 (1,5,43) 431.133680121.6371112819065042612731.P143 217 (1,7,31) 29605139295060799.34514330538357089631548744956304208\ 8092193070582663064824478011700982631848113970347.P88 219 (1,3,73) 439.4072194187. .514949924967851751873479083936952760941875001182553509.P84 221 (1,13,17) 27847.312937.3473237.1126168894058957269. .13720057759140780365187158337101. .63175972422516768191112129923662644433466537589571.P85 223 (1) 453137.47060137.7672126756781.326495629795175719. .1368635346986648651098441242784461410529545236877.P140 225 (1,3,5,9,15,25,45,75) 5851.2438939252251.P109 227 (1) 14106056111465766059.1792798399719936463007.3512874088041514\ 415629259979371189298837569093924708389342263553138925983161371.P117 229 (1) 84743741.15587642569099. .66157780611522342577190626116891913815998182079204936302870501.P155 231 (1,3,7,11,21,33,77) 312313.6103043101.355797740761.662072596417. .10965056258773.P74 233 (1) 1399.2797.57401881.308184993449104253. .175138501604778346236805296173.31513927454012854176230052426\ 40794734378391578098410519327139047230646694631.P106 235 (1,5,47) 2351.14749541. .1795306125519308524148513029485573280444347858061.P133 237 (1,3,79) 34273461979846373350261832761.P134 239 (1) 479.8285191862304684343964056513492287490082820226741820275\ 4896053781339383815475865139010283031120138773381203773546959.P130 241 (1) 2916583.96275249243.17283881969371.13481032538182091601592197159\ 764283428446996889522592995122633187551394091030343864894913804279.P126 243 (1,3,9,27,81) 340201.27927019.772481047563804024037. .103669238531679886100470429.87544425099333860745692064391. .94217522053663555122045893874149431.P45 245 (1,5,7,35,49) 491.10781. .35298179827301484394489355118456864978337754561.P122 247 (1,13,19) 6917.24476655191.735397416472535503838087. .149892886761153843524520239.P161 249 (1,3,83) 24350945041.7888937372474051689.1827801163850144120227. .599211790772708425085047.1390253425907256501848065153.P70 251 (1) 503.219716501365259540843452614863811940554249320274071. .60634613440713747674833428094591922473642332299712911.P155 253 (1,11,23) 266458589.P221 255 (1,3,5,15,17,51,85) 1021.1249304905334053222308181756477664071.P95 257 (1) 1194023.293147639462911.292888771585604069921. .6543799984554591443839328899263899259342186404598168438689777. .805032746003109074737699697391412905296725633709745035528902\ 24363591969.P94 259 (1,7,37) 15541.205129.2377363597313183110008925690954044490406493\ 8914911124864715041052439059710396217007689153081724632638290089.P110 261 (1,3,9,29,87) 252951559910787169.19864252986467602941327475561\ 536514877625112981282421400939628042342057.P88 263 (1) 1579.273046601. .49391898816054766538923603477001696252091125305146551. .448866386956193192214273839601521010068755980565222687036249. .380549523864966453861633605277889962330998118668910286697829\ 1285109261.P80 265 (1,5,53) 6361.11131.27949021.42205548180360044106789555435605\ 671828340296762566168044074969751821.P134 267 (1,3,89) 1087344877207993177554437630922355039.P148 269 (1) 11299.3333683107.5828875024969181.255350778829531783. .379749916955459023190063113899187518168377382942698639225633\ 43401762892759385052449.P150 271 (1) 1627.4337.265948315388080203780860845505259306067883090581971551. .311006777771915742193035968199784938786286501731510874194069\ 83803271763409673711419893743796156087899.P121 273 (1,3,7,13,21,39,91) 9283.2794301073442243.P131 275 (1,5,11,25,55) 9051647644285437885101.223893595825973074419211201. .931084679774419841402323884878358835892768665158019684562289483001.P95 277 (1) 15811956653.30664514555051823767929.862162491495911858677651. .156184546393536577782392890775878891. .160675559417607736722985168684203817. .142462975852899743955336966823561898597398549051.P114 279 (1,3,9,31,93) 5023.3149911.684249865168469384243216119737381211.P142 281 (1) 563.34283.133593583.158691941.33336224302061537657. .1302985948504262874372500460540357486269. .42056897140345980513090610629221667708001747337163664155114169.P148 283 (1) 157349.2911476233737954178339. .216393554631205759139663397369547242957385092556243733932808\ 9208815965709802705713361030484808230504878101465442961303.P150 285 (1,3,5,15,19,57,95) 571.19919700302204669731. .173516799777015420048132343577477787151.P90 287 (1,7,41) 2297.1350623.2880001951. .2966421405449263029972348335713817510596628749. .51971621500986223244212523671250525729469527072643035829454\ 271071301.P118 289 (1,17) 228311.54761697917.8310166294858615047708541. .525222955395094276264268486999488266551. .55046695546239509301375603158875976783741983320572166350721391.P142 291 (1,3,97) 532266937.2344437427.28829500653651421. .234778562725637665057.P145 293 (1) 56843.813601310175627094507455297079027530878234404737855\ 5585561585387889119801.1577884048353256430733367605081794830\ 440438335762837550393722450391999126174604418117077204056081\ 19721245631817121.P114 295 (1,5,59) 106185841.P234 297 (1,3,9,11,27,33,99) 90289.699733.1247401.20085349681. .3249930677185678753950409. .24893014912495257280062069983035338781764623985517535857.P81 299 (1,13,23) 1779649.1824499.2642814404626969. .720460482163043076385421612673778487. .106825672875471270997848867095123851403297226546235240262851\ 3652176733564811994170858466697.P122 301 (1,7,43) 43*.397603948349938967643011683296280624263031554230\ 5918376132402951153973900378536972807171245752233930860633.P156 303 (1,3,101) 607.549643.72993247727041.14805045516568764516541. .224121152998661467362601857061.P135 305 (1,5,61) 99431.23907106086511.P232 307 (1) 5325223.1173589163.187636088080013. .100752119638328441415480711405595944160236367357438231134888\ 036154494113606382325483272491194615675025255629.P182 309 (1,3,103) 11743.12979.21013.28996906699. .68828989885361322595519970117407210788931.P149 311 (1) 30459009939602861494971472687053052580318606397842276141402519\ 82523294187.C251 313 (1) 26293.635650227956785861513.3880320581063035678040086253. C273 315 (1,3,5,7,9,15,21,35,45,63,105) 864361. .15831500924590739433785234537507170517388765931.P98 317 (1) 16233990343. C319 319 (1,11,29) 1277.1439329.26081392219869643454900559026263626987737. .14978807366465469901781211522134256689606367241271212809544\ 470554171309.P172 321 (1,3,107) 998311.111525083440182079.565907075298149659147. .297571581361738410622071889.2829934760722845283610290789677553. .8094394036023237528697722819032319787.P81 323 (1,17,19) 2381158034448093931. .56578296812880347324235203127838981571573.C241 325 (1,5,13,25,65) 3706404001.15844660651.1964913713101. .64316761908335051901852539103433300202032901.P175 327 (1,3,109) 12955087.243080029.513121293388817431.214295338877551\ 19730119595614924016204166409187192755551700121403671529935823.P116 329 (1,7,47) 659.35533.28626519766363.291586837522633380328138353103. .2652677386708393681880310461059.P207 331 (1) C344 333 (1,3,9,37,111) 2657295303701652382339.11781861706172482362289. .14919583772234049458190757699987.P151 335 (1,5,67) 673756021.48300757513284632351. .87900046570413580603596754467808180534206365954745642251.P191 337 (1) 6067.46559921.21229887259027.14453046629815457. .5673955595662669101970583839. .52292944999629776824795513871467860743. .179598085147837571508313392515514877119723272316896459.P191 339 (1,3,113) 643810446382567117188524103323463470990370010759293\ 381799712563863244254073580461427551183.P144 341 (1,11,31) 2729.89311448226532458653. C289 343 (1,7,49) 18523.28813.1142191. .10223108605732304366853815645687388223619921. .494906580307068767240152526214497538068427810449. .88526798069252442100248525192584061516005502709083449143.P145 345 (1,3,5,15,23,69,115) 4831.138213632971.116563335563581. .279365907858391.355201733241601.868298599610923233331.P105 347 (1) 2777.6247.116593.142271.6714513049207. .4446514959758693859922315046963615663.C294 349 (1) 182179.12873866489397440487918401. .733519460202487621006385622952661108933.C294 Table 11+ Factorizations of 11^n+1, n<=350 L,M for n=22k-11<=693 n Prime Factors 1 2.2.3 2 2*.61 3 (1) 3*.37 4 2*.7321 5 (1) 13421 6 (2) 13.1117 7 (1) 1623931 8 2*.17.6304673 9 (1,3) 3*.590077 10 (2) 212601841 11 (1) L.M L 58367 M 23.89.199 12 (4) 10657.20113 13 (1) 53.911.59583967 14 (2) 29.1933.55527473 15 (1,3,5) 31.7537711 16 2*.51329.447600088289 17 (1) 71707.264793.2218331 18 (2,6) 3138426605161 19 (1) 191.229.83791.1390636259 20 (4) 41.1120648576818041 21 (1,3,7) 3421169496361 22 (2) 251857.2649263870814793 23 (1) 47.1013.241363.6493405343627 24 (8) 97.241.1777.1106131489 25 (1,5) 46601.14436295738510501 26 (2) 9768997162071483134919121 27 (1,3,9) 3*.379.4889988840047743 28 (4) 113.449.2521.77001139434480073 29 (1) 59.10979607179423.204064664440913 30 (2,6,10) 46329453543600481 31 (1) 311.1303.10789.3658524738455131951223 32 2*.193.257.21283620033217629539178799361 33 (1,3) L.M L (11M) 9439.991651 M (11L) 67.1169382127 34 (2) 137.2481791513.9598959833.641625222857 35 (1,5,7) 71.71.7561.17011.1649341.10047871 36 (4,12) 73.40177.3358335487319458201 37 (1) 2691614274040036601.10527743181888260981 38 (2) 1990415149.15403468930064931175264655869 39 (1,3,13) 313.63649.538953023961943033 40 (8) 5281.399806412551699044818733915681 41 (1) 711628063.1216150172449.479378523680060338823 42 (2,6,14) 19069.520799717831587692709 43 (1) 5333.9413099125139413690486707432096974989067 44 (4) 353.72689.13585441.1298256794387169996154165633 45 (1,3,5,9,15) 181.631.86306335830799838011 46 (2) 201757.2004414397.24737721275161.656943272596448809 47 (1) 844309.549524471.26097456317.60699948346804199382437 48 (16) 577.3659233404740477018363752843393 49 (1,7) 11467.800171.176784259.33761096386802842263303497 50 (2,10) 101.2248313994601.1993099906542710819727884501 51 (1,3,17) 103.1348033.16576413357576409067287639 52 (4) 97010607829826070873559937268360584022789501553441 53 (1) 1697.5353637.17148893.8357265774463208206521728596439861293 54 (2,6,18) 109.541.388174681.1350472353550875103121929 55 (1,5) L.M L (11L) 21537414911.85480219991 M (11M) 4951.411841.131525983711 56 (8) 337.394129.236352238647181441.3090443962383595123379137 57 (1,3,19) 6043.75013.74337838382167137728921322559 58 (2) 349.16585333.32637413.109181877624126996017801852385627698243261 59 (1) 22067.32833036072593109.59845177539010249.53199025841281128499153 60 (4,12,20) 52020741601.40589999671017742452961 61 (1) 53320740257.137218978667473446671.38147158686655703132426388314683 62 (2) 4311672901046383796549.70039146133823870629334170297294343364149 63 (1,3,7,9,21) 3304981.468843103.71596275661.278853374647 64 2*.316955440822738177.7032401262704707649518767703756385761576062060673 65 (1,5,13) 1301.25741.3160327139569513638485230516120919120957201 66 (2,6,22) 9863099401.46266666682081629547022793157801 67 (1) 269.181303.2354458793.2778466094669.76388592846687031.P23 68 (4) 409.11969.739755736441.14387579997041.P35 69 (1,3,23) 691.394648951.18013255921.932225927887.1577386579003 70 (2,10,14) 2970941.P44 71 (1) 149852362577.5604196051154865381517.P40 72 (8,24) 110161.331921.P40 73 (1) 668243.147031637.51866303408957.9863258277206753.P32 74 (2) 149.243595717.254246981.3275634569.5555901630889277.P31 75 (1,3,5,15,25) 751.299401.P34 76 (4) 457.35613601.52215193.P58 77 (1,7) L.M L (11L) 23577401.2040583524866430994330651 M (11M) 43037232701.160418704149053207551 78 (2,6,26) 13*.7177.26833.225889.21493057.11771471409361.683665316878909 79 (1) 7901.681676939.3238766178025207268898109882481893.P35 80 (16) 641.2081.4001.232961.295090738600481.1037593750081121.P23 81 (1,3,9,27) 3*.163.5705803.P47 82 (2) 2789.57073.P76 83 (1) 325440677.47433880332031195178437273.P52 84 (4,12,28) 201407641.70107576001.P31 85 (1,5,17) 34511.P63 86 (2) 173.11862832433.P76 87 (1,3,29) 13399.7596493.1727522113.P39 88 (8) 3169.269281.2224106369.1409524185566665684709841121.P38 89 (1) 179.188606309.5089163291.75893828851.23510589261592841. .371848407757843241773.353082502532286628861787 90 (2,6,10,18,30) 9001.16921.22501.P38 91 (1,7,13) 12343942084000822751.P56 92 (4) 34961.324599369.P79 93 (1,3,31) 237843323473654847623.P43 94 (2) 1693.6678701.181894150853.1823151514157.P63 95 (1,5,19) 125391374277955216479795494641.P46 96 (32) 2689.850177.7746049.13928006777524033.P35 97 (1) 3881.200924352971689432250644561.P71 98 (2,14) 197.33976720793233.P72 99 (1,3,9) L.M L (11L,33M) 95885659.166222146279939538766671 M (11M,33L) P32 100 (4,20) 401.2254601.5931105001.69084589801.P54 101 (1) 20201.228104057.1732951869588220873.P74 102 (2,6,34) 382645993638157.563620766036953.P38 103 (1) 1237.51396929137.3842537250772226605747.128288938117946418355541.P48 104 (8) 86759222313428390812218077095850708048977.P60 105 (1,3,5,7,15,21,35) 275310421.137031343051.P31 106 (2) 410982353.23746234974173.22250800656016001.72744498860303958101.P51 107 (1) 841021.P105 108 (4,12,36) 433.8209.P69 109 (1) 11119.14389.P105 110 (2,10,22) 1327481.36318547582241.110374378040081. .136371262802069831801.P30 111 (1,3,37) 37*.223.P72 112 (16) 10529.15233.132833.7782479531201887486913.P65 113 (1) 909877.P111 114 (2,6,38) 37820720459377.308673703543834165513.P41 115 (1,5,23) 2531.558956737278445325461.P68 116 (4) 233.287681.60604269272032563100609.1502477990708696255525449.P62 117 (1,3,9,13,39) P75 118 (2) 1291321673.1013563312793953470363741024001073. .64838817747578095323592827914385846481.P41 119 (1,7,17) 110917283.124214819.69796946717.256644509902201. .63063653308203311.2091456376138057349.315440418833726113081631 120 (8,24,40) 3121.114001.1698371041.12658046117876244394801.P27 121 (1,11L,11M) L.M L 727.1663628038071022183838437.P31 M 122453.2095721.103569468207767.P32 122 (2) 61*.733.15373.19042493.615339081285269009. .166945076296840267580084657135863728824204737.P47 123 (1,3,41) P84 124 (4) 1489.6449.11161.5721113.92247817.P100 125 (1,5,25) 251.559001.30877424283969568616368678353563069501.P59 126 (2,6,14,18,42) 2017.21673.1540217047797575204407748160801193.P35 127 (1) 509.2140352083. .4402640625848258016840688846660358437130425243742595514279.P62 128 2*.15361.111489577217.574341646346402207998363393. .4018529583345312964042058778793458689.P55 129 (1,3,43) 1291.P85 130 (2,10,26) 521.P98 131 (1) 9858799.119235724375228558113076040277225949839796708740043.P79 132 (4,12,44) 57563039928769.504278350263601.P55 133 (1,7,19) 23204027016899114504903.P91 134 (2) 47271776033.555596265747977.5653530366032833.P97 135 (1,3,5,9,15,27,45) 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24354718003686851166976918099216697074964832543020808326586271.P79 280 (8,40,56) 4481.120499161543956061953521.P174 281 (1) 2165143447416427.73717873044643423196357. .47677949460728118782533826487424424473. .46402408546690245400968842648859676155371.84283989953808426619846\ 6820541942750943860088703946121840940131686719691460399191375953.P89 282 (2,6,94) 4513.74449.743221153.9367589929.882790848027637. .50386240544439469245337. .541280232778157933269788549025666464572420599006025732317.P70 283 (1) 956895449.21535519113007.72176379693191. .261049615363540599071810933613219383163605706772662958674771\ 01728152593793222171516484343013.P167 284 (4) 569.12497.P285 285 (1,3,5,15,19,57,95) 2281.2917899073047729238516802295331. .6420530775230480256516185608218811668539531217931.P68 286 (2,22,26) 76649.279137.25789193.26212089408649. .65835490021476935761.5390779113965945529821604718249.P169 287 (1,7,41) 10104697.7754478257. .1288007568447966007443299836505937120229847933950331902054131977. .15161614250757079812344364260297902244477764299924276760549\ 254462414383.P100 288 (32,96) 1153.2984614810561.785602694273121056085121.P161 289 (1,17) 3469.6359.405179.6719845184674354000239729883051. .13809514198555273556233360064629771908877014988964567.P188 290 (2,10,58) 551581.22703521.161983561.4383624035501. .130831137879822169771306398161521396945129959491397886755855\ 8809234749152012568198058619381.P110 291 (1,3,97) 1747.69543313187791.718354750537744483. .1434216758035156452062274787.12624322881812991993463959241.P110 292 (4) 4673.127440856783318855066075619237628626201. .5192103684222119306235254426448808742282351155573082880593\ 2993591274124218572848834736881111953534155623053411657147273.P140 293 (1) 587.2605170569440429.30140580360800090029058026244148121. .3682985778017638025031089403228751074233. .21947273783791761093614489838837482754970749053587421897582\ 3680425792291622681699094271447792709.P117 294 (2,6,14,42,98) 21757.P171 295 (1,5,59) 6491.P238 296 (8) 593.4317448897.1788997688657006918650513. .58666781720610399244227419994433. .9060949789407186960278515603568493413961904897.P186 297 (1,3,9,27) L.M L (11M,33L,99M) 60212927509792800235219.5343727611107427419946338417467.P41 M (11L,33M,99L) 115564483.P86 298 (2) 1789.3606385337827009. .254442181550180651601277598631486236645518614349. .154806132285319551777239359361799894570309555020910519600398\ 2729407280999332562311132966982788080931334204935403494788957.P122 299 (1,13,23) 599.1956094976608247701896596369. .458746773771966112757553818419340476760124151825458575445089\ 446060903472233019295524244427122690367884661.P141 300 (4,12,20,60,100) 601.27903093601.302956332083401.780571892394001. .504562013892511955344201.P101 301 (1,7,43) 3674609.40295958308091656541502564223570748179655566501. .170920844325612905840916943523743951423190963646926798465595\ 61815616279952787216109466069268882257785721.P107 302 (2) 611699189.1159555032903063749. .4610070317541269927674709759388451137929126988817497350602369. .27593004643558013039920530863071021572553078389312164689843\ 7534846315631347429953603627190737133773612841197.P118 303 (1,3,101) 1213.35759258032327.P192 304 (16) 241941740353.1172114946038362181282076457121. .183697098171726302313332156255969. .2423519964979291113481330286900083663687819393.33684202681448\ 6816413712532665671525518487238461533945786937785048474675329.P107 305 (1,5,61) 4271.35381.208622441.23942823301.18663710568453911. .26048593137734883614562822525600177808035009491. .29700155154641488560407811062047160510629521685109587812775049761.P96 306 (2,6,18,34,102) 613.1998793.230287218850527957657353501592644\ 1913945044975483579529517513795897664211127797.P113 307 (1) 4039814843.8132665777.180234430917083008608707. .392523427524746439982851120144101968447119848114924683060835\ 653057570663845857957667510384212410153445603417.P169 308 (4,28,44) 18481.50513.977741949096529. .100720934145206647003865921718551257916212922968493793099470\ 5968483657794085307777435167137.P136 309 (1,3,103) 619.39973623597165369654516508417454816513380531516\ 14862757301308438592709.P141 310 (2,10,62) 10860541.165639769507777505367372967986878035634521.P202 311 (1) 3733.173539.344353507.642552529706732121511. .70161787000947490363193407535005064309.C247 312 (8,24,104) 35317371853661533351902318980131104007135296358425\ 93430789873.P140 313 (1) 704251.295689223.29417935526887963481568899726343335080199716901.P265 314 (2) 15073.60917.663797.4699118016361729.1295353999762740721. .12086948104233344813736680582120770728887603613010317521.P222 315 (1,3,5,7,9,15,21,35,45,63,105) 390943731740941. .652173369161401023151532831652601.P103 316 (4) 117567026551063291227924640993. .7155465604647337902319962697367340026929. .247424313899676299698981126627309131310099266504913.P206 317 (1) 244091.554117.79998300691.108164292127.840369370319943851919409. .15880128149464154373940101584719888617347484244645733. .2024284524747675543312054053591400075389609177870838179. .43910797820198256764873074087063104960203535430489100755798567.P104 318 (2,6,106) 8269.P213 319 (1,29) L.M L (11M) 126069439.54453236653277002250524018661761985258743661.P94 M (11L) 96937721.22395964041133.1674399383651611.24440702406360967. .4250822076554186563.1362428565267452997267408860021.P45 320 (64) 424961.507600819435356754028272641.1848907969970330213870279041. .3550556591025613568771382218881.7423640128382244670648175746561. .6800123162600764857457510501187194988801.P106 321 (1,3,107) 643.13193101.1702625731. .15299929510306445350107845675613264798349. .29194560952259073891892014090720729640848284768524401572983309.P101 322 (2,14,46) 17161957.77119626524711597.P251 323 (1,17,19) 647.2435186453628716329. .12107858863529284616503651547395268004876547571229106371961. .482632031053134403896770035981249734273506307638396123269389\ 497006923.P152 324 (4,12,36,108) 2888049935070066815962684201. .679188425000626416088279404318811562690493819422929687708282\ 989379246971684433.P120 325 (1,5,13,25,65) 138462632232622338863674068371678951. .374404623024118768993406523648306986081965533238881708312021418151.P150 326 (2) 16301. C334 327 (1,3,109) 5406619.1432803475655673783716616777940836814160352\ 556650668256433626238662987613578329196657326773067537083.P120 328 (8) 12477816017.469683445458881.56965518203817494469609266641969. .56566162512665889895778196622003489.C242 329 (1,7,47) 2633.108571.22631911.53277752683.2397451434733699. .1556543494988180754973.27703433830946030718449519. .2009870631152891310641538539362700614849620316329839.P148 330 (2,6,10,22,30,66,110) 169786321.P159 331 (1) 2855869.11512843.11226209905343101. .888734765538195469027258728828783694276578611227121075599.C258 332 (4) 1993.518577734497.777866807677827503314309139574028744758793489.C282 333 (1,3,9,37,111) 354979.P220 334 (2) 46633083150289.11192226607559931809570895958007330033033863477. .14235995907758631892531697715944750931872259404844380963512850552189.C219 335 (1,5,67) 160362548659171.56073052565336146651. .1556839871447009376471730140581.P211 336 (16,48,112) 673. .1536731903606645487928038023494931232265538470741424658529.P140 337 (1) 8089.17813821.105537617. .135646594049296771170445778216904705662436127982301622601547440209.P266 338 (2,26) 677.15139245109.78668530751625723046280741209417. C281 339 (1,3,113) 553249.68894480469960903562541911.P202 340 (4,20,68) 6180521.160820474504707575972997668648361. .5225808238016771052341582635280201. .225523082265910924158412282931185806144850915752922636170546361.P132 341 (1,31) L.M L (11M) 683.13751401821439225165451143629880111. .1012000371041933382912608396702713889156167.P77 M (11L) 88661.10766053.492922321.644552386633. .3454061988006506245928197.11635610293174280651716530998551.P69 342 (2,6,18,38,114) 2053.47881.59373696615049.1797862738052870017281253.P179 343 (1,7,49) 1373.80764846592083051952741744555923.P272 344 (8) 3674036273. C341 345 (1,3,5,15,23,69,115) 10493015204281.82093337481199195111. .4653540256149079393531. .268329760256288474139750611836167259046916142267161253213874311.P67 346 (2) 3461.21953872309. C345 347 (1) 67230557.1690623559.92506992924969525587726138341853500373. .17166943551662789534484656176718732909706992577882601. .332882478461707787889800188958133518677224778474934846426497.P194 348 (4,12,116) 5569.41761.394461481. .508013567572801156672056299462377737806650679005620374628466\ 587445783275204131411087667280100956328698633.P112 349 (1) 249953801.849321927973498816829218867. C328 350 (2,10,14,50,70) 701.322001.458501.56956081489652801. .14903525246049041675501.P197 ------------------------------------------------------------------------------- 363 (1,3,11L,11M,33L,33M) L.M L (121M) 2179.1213873.17156544164914857424669597171794606247.P68 M (121L) 4357.29698483.32054828257.22132988093371.P80 385 (1,5,7,35) L.M L (11L,55L,77L) 8939701.371071471.518583951271. .1048947375246657003170213161.P71 M (11M,55M,77M) 5487540521.3474031899426599281.P98 407 (1,37) L.M L (11L) 82262238908095416625629847487.P159 M (11M) 24421.368743.101730015473692321.1583171273015273165687503920221. .21787690102053357819275404496594050478419978850603026773289483.P69 429 (1,3,13,39) L.M L (11L,33M,143M) 349207.361219.P114 M (11M,33L,143L) 105121516501.80026964062240068874678393. .136781281056972929796341020181077888593676549.P45 451 (1,41) L.M L (11M) 2707.336017551.8911290961.1072881923818635144449927674819. .1815484843668506267988330171633365999003. .547152724762445363229755616341664505869098913767.P69 M (11L) 776075370379457963.8287290957329109961678200239527.P160 473 (1,43) L.M L (11L) 947.354751.744503.69716417. .909075700936753324607060003389347319598236051. .11984437123431823969432655822865428382472038412325377.P100 M (11M) 8000323.368900269.38042842158630893.1285274840618548862537291. .57335965989876943599721563601. .637251616253169487561721883573539113866676363414067411.P80 495 (1,3,5,9,15,45) L.M L (11L,33M,55L,99L,165M) 991.11958211.190193081816052776283014786485321.P83 M (11M,33L,55M,99M,165L) 5367781.16810373035171.21073064227519555351.P86 517 (1,47) L.M L (11M) 1124993.3667016900282341.983961080031284058011551. .6853595694861280196431693023336020912080543.P151 M (11L) 613010003.1886657235101.6745592152089407. .55451364604890843829478778327403507.P169 539 (1,7,49) L.M L (11L,77L) 54861577.P211 M (11M,77M) 407338502687715596115358127487470490418246750544163\ 971491334277829082933253343295496772186775301667418404051.P112 561 (1,3,17,51) L.M L (11L,33M,187M) 4084081.P160 M (11M,33L,187L) 16751666614463105957923251458276278361045881767\ 53727418215155806318287571.P95 583 (1,53) L.M L (11L) 2333.32695611782383722933302653. .938509815257270359930858171287230975557095541946255923121216\ 72071626246224288553401691848823731637291887972261614092287.P124 M (11M) .1119751655173869310149858084768567822077427368780883808066750027. .739513587752679216766472383450546391761653148298184510309145\ 76395216197015466262106956947.P119 605 (1,5,11L,11M,55L,55M) L.M L (121L) 311910094981. .268434542073679460995491979817594908480865172257695421947063\ 279147725982570364102083222974457430047378482011.P111 M (121M) 1572282138461. .2004663729659289641484462859257997795349557607442069835421.P160 627 (1,3,19,57) L.M L (11M,33L,209M) 1533643.869428920847610609334746364721.1958880449\ 11392396983137104777620556536510978940692324331073219455541483.P81 M (11L,33M,209L) 620851639.3274892479.269910166889244750311463373. .155068814653531517509568600031495715567600294606655230695719262343.P78 649 (1,59) L.M L (11M) 7789.9369512164935472598423. .27545943179609998311195551404610332522564397045837053621. .10083502299526288359565972617590684810076598006581030595310837. .213731942445981456893464989931879569305342526815846636580387\ 05565906033593.P86 M (11L) 18885112648777.10221328485170194723. .5410357883109774891519720099304751879228446735472027.P219 671 (1,61) L.M L (11M) 169093.10117339.12159863.475754845613473205967241693. .3080111781389487605391515831.671819683799848074426292995963337. .24992475535762872560382976434484500422126199403.P160 M (11L) 8053.9100103.15628882622798803818989.35577970082819640959026237. .50805127037488203754081521327814341614957309300864017. .166201308227103938714572581688535924327465244182929867396122\ 5758595437789216081.P124 693 (1,3,7,9,21,63) L.M L (11L,33M,77L,99L,231M) 429661.4008313.19880779444219.13676327952909931. .1924577528309700089593064924830974752077142124451790072191537.P86 M (11M,33L,77M,99M,231L) 714386046101113. .62374753101477731854227222815497.9612514200467663770065345284\ 443055909719868124964766522328421150545733.P71 11^11h+1=(11^h+1)L.M, L=A-B, M=A+B, h=2k-1, A=11^5h+5.11^4h-11^3h-11^2h+5.11^h+1, B=11^k(11^4h+11^3h-11^2h+11^h+1). Table 12- Factorizations of 12^n-1, n odd, n<350 n Prime Factors 1 11 3 (1) 157 5 (1) 22621 7 (1) 659.4943 9 (1,3) 37.80749 11 (1) 11*.23.266981089 13 (1) 477517.20369233 15 (1,3,5) 61.661.9781 17 (1) 2693651.74876782031 19 (1) 29043636306420266077 21 (1,3,7) 8177824843189 23 (1) 47.39891250417.321218438243 25 (1,5) 303551.12629757106815551 27 (1,3,9) 306829.86769286104133 29 (1) 59.24767.368939.3335672988472972523 31 (1) 373.126883621.23364027983.234187563803 33 (1,3,11) 886381.5999137.661269577 35 (1,5,7) 71.491.806821.6089651.425455031 37 (1) 3933841.196560666553286126588980353347341 39 (1,3,13) 36973.17654521.111704871987697 41 (1) 83.1977898057.97668924760419986491370101198871 43 (1) 431.12313309.13444466603.32359758358562524963364461 45 (1,3,5,9,15) 30781.5234401.21456901.22981681 47 (1) 10617249990997021.4509348865973648037702008076799297 49 (1,7) 77617.27268138641564464649627762762033543154129 51 (1,3,17) 20757613.1510376787258214230993801577 53 (1) 107.743.1694941.29504677.3089222210773.11639817348279944053139101 55 (1,5,11) 5281.442434513819541.5766308324790114380136001 57 (1,3,19) 114001.129733.20526705689989.2141456811167917 59 (1) 22067.33565608845417661253.576319092656266231937955277485160608227 61 (1) 1706293.1000831393.35995548461449237368649937465097120608531155491049 63 (1,3,7,9,21) 708391688852136898302887193094373767489 65 (1,5,13) 131.1932288541.596827590710414051.38346067178495390031121 67 (1) 45464593.16180787699.17577834702049211.P38 69 (1,3,23) 6279903241741823809.P29 71 (1) 5113.19597.P68 73 (1) 50654608967364071.P62 75 (1,3,5,15,25) 601.80342401.P33 77 (1,7,11) 4621.379101493.191199728567.50565974802015289.P25 79 (1) 162109.130479719.P71 81 (1,3,9,27) 5937949.660198074631409.P37 83 (1) 167.997.1993.22079.557889481.35238620437.2731547200091. .10052468384786123.P28 85 (1,5,17) 1021.22271.4832761.204560684821.5383015065849288291601.P22 87 (1,3,29) 349.1741.74233562929.936727604123432773.P26 89 (1) 179.2137.120863.3163346581.16649789224075621. .35035317869663569.255053775727906405559.4656868283889935515079 91 (1,7,13) 152705150363039.1091317880778743355464526983.P37 93 (1,3,31) 8929.1261081.16185865453.P45 95 (1,5,19) 191.P76 97 (1) P104 99 (1,3,9,11,33) 397.3169.9143902271574719666671109149.P31 101 (1) 20359133179252403.P92 103 (1) 3709.7417.1309643353.13951770188639477959439. .226319692803146344014357964333823.P40 105 (1,3,5,7,15,21,35) 2521.126001.9562853581.P34 107 (1) 126047.8368183883.P100 109 (1) P117 111 (1,3,37) P78 113 (1) 227.7450459827983.316093109705519.753692779085581623227.P71 115 (1,5,23) 2531.P92 117 (1,3,9,13,39) 6553.774101091754693.5363939350752581033772013.P35 119 (1,7,17) 239.1429.137089.23082431.P86 121 (1,11) 11*.7019.9971358563.13448069471. .36801041190212623908408703917306494049155113.P51 123 (1,3,41) P87 125 (1,5,25) 251.13751.118751.P97 127 (1) 88750555799.2597995311343175210111334225450311.P92 129 (1,3,43) 3784861.P85 131 (1) 263.P138 133 (1,7,19) 67033.365876351.153373238287849222871747653.P77 135 (1,3,5,9,15,27,45) 11719914497486992163161.45726761961907655567941.P33 137 (1) 7894763.99485649955791433. .4270306101158898662140485488376974936909627.P81 139 (1) 32830711631.149723271154501574581. .13976446202665769757077661403698383112061728500003.P70 141 (1,3,47) 3504133.5136890928835357.P77 143 (1,11,13) 1068975337.28151299084766629509889009.P95 145 (1,5,29) 8458141.152107892171.2833016858862791.P88 147 (1,3,7,21,49) 7622826121.3053140047080689861. .29014061524726574502110353.P37 149 (1) 11027.1919442572897362836803025134228929025089.P117 151 (1) 16537237851564688924261407041648853990657743.P119 153 (1,3,9,17,51) 613.3673.6128894197.1644982406845777. .216486853727393579797.53294740218449478902707453.P27 155 (1,5,31) 311.17379312247321.32179535439223966162981. .504159451473002560362013386812584959284471.P50 157 (1) 3769.896587135133828036528709133.P138 159 (1,3,53) 30529.526468081.564397849.P91 161 (1,7,23) 1933.36709.8820656418738378259508980670038453.P101 163 (1) 3123955328977664272236491.3085088915212385601857770168909. .55276244920832349213682617306044898442152509401.P74 165 (1,3,5,11,15,33,55) 475350812105401.P72 167 (1) 553194672940916339.P162 169 (1,13) 273854127119.42085870270393.171074557867837392887. .2236719302927635268499980471.P96 171 (1,3,9,19,57) 2053.25309.P109 173 (1) 347.6229.178537.16520618724247316579377. .133631610959030020559251207363442895201402950558413165227170111.P90 175 (1,5,7,25,35) 2453984000813135412614651.P106 177 (1,3,59) 6373.472683457.29664964237.48253224577.215006774581. .2245657505577169.247679421927970902164473.P42 179 (1) 359.23242390265122325064379304298589468949738258002565951\ 689210803734501431778880443.P111 181 (1) 56473.188954578048573195547226930925499.P158 183 (1,3,61) 7321.7756968162619561.P110 185 (1,5,37) 6441085856120368040593352248224844221696350548901425367127551.P95 187 (1,11,17) 7824829.6367170107.5272292087965614119.P138 189 (1,3,7,9,21,27,63) P117 191 (1) 383.2293.5576463887.492394777262152830140779120613620261.P154 193 (1) 6563.143593.876772490946684644304688840806507849770157877.4521744280\ 9188335376258573027831301630813739280371078165650059881162723213257.P77 195 (1,3,5,13,15,39,65) 24263325716698381.457644272256236018195571421.P61 197 (1) 115947686976447121232614605064425479503790185147312659732\ 8861230702273.P143 199 (1) 11941.50445745393.534989935052173.452633703528239603. .2408107039243923308111. .2312692670375121170444589429146936204459886179063617714050658717.P82 201 (1,3,67) 492853.337362557588033581. .2340033136012362062475950746729856638028655463932144793.P65 203 (1,7,29) 2437.2032540343.168010120865329. .4038644506148119439397242761.P127 205 (1,5,41) 50860501.61708179551.109423722071.594458960231.1272168094511. .59114755745455413432518951.802612658538701099788630604070125125897621.P52 207 (1,3,9,23,69) 123373.46359329929201.80965151313250177.P107 209 (1,11,19) 419.167246399.19043506626213169.2877972269567413524001. .131258359076578876173923.4714073727036453202094931887.P95 211 (1) 98327.599663.8960574127139.1374686882866127. .11442157099782185036780447859311. .389491106120076990268950453219202572305807.P116 213 (1,3,71) 853.668821.5938441.14726274721.593597578469053.P111 215 (1,5,43) 14565360661585652954030814514011338526900517564549128\ 68460861932571472151310875724311.P98 217 (1,7,31) 5077606871.30847829203283.3621684771405978346406298479029.P141 219 (1,3,73) 877.384229369.13036824921402558973.P125 221 (1,13,17) 443.9640021.52016377765223.141523296304179193. .27267433046893619404631197.2767487366128813243478189568387004020073.P102 223 (1) 1423187.23385119.14130288853.43954882455277. .1006249991892868346686216789.P176 225 (1,3,5,9,15,25,45,75) 2363726892633483756321124302681778344117301.P88 227 (1) 147551.256057.152574419.1267583437.110565744056955405733. .65427844998422797036464287486758625198640908952234347.P144 229 (1) 76487. .5614625825187525959903363633922994959000986456830889529904105379.P178 231 (1,3,7,11,21,33,77) 793717.1053467722693.237808105253287801. .1285249260419549776349461.P71 233 (1) 467.31223.78863682072342587129533815443.34300372461915991\ 31735595170257684385396651267213817380250534229.P151 235 (1,5,47) 4982941.11664037157021516682204241. .17622268090118561496454088499627774029883062124055059841.P112 237 (1,3,79) 6637.114598432057.1286930998217149714369. .27567862476721705741499814127507129428735247904137980751231873.P71 239 (1) 479.17585764699549862561020053258920461069906105666613231. .179256757895304380363489872564436535109638603576525313377489\ 79546505319537448070430985057717492820449.P102 241 (1) 146879693270660089750065267283010036196682888164682484908\ 678010533.P194 243 (1,3,9,27,81) 19880317.P168 245 (1,5,7,35,49) 34167708909181.1100673907592638009772080006291497491.P132 247 (1,13,19) 263303.320113.45198395571733. .181384271025146414891081795590642472433633074203346511651451\ 593014726951273853234819568382677073912063.P108 249 (1,3,83) 1417303413610237.825176156498150775878180145483505039849.P123 251 (1) 503.195781.289444667.1155793163468786851614675409281577. .548481679382194709448031861812868591262551381.P176 253 (1,11,23) 23*.3037.1696862399.P224 255 (1,3,5,15,17,51,85) 79561.31144681.419335261.50540765443957214580241.P95 257 (1) 27262561.3210333482150938236735353240875928231167166319686291. .188450740719909159336830902905523390447337618754289401133431\ 724604081138003712971.P138 259 (1,7,37) 8807.13683163257201265013663. .27061148352191633314197974751800952154655200940479609.P155 261 (1,3,9,29,87) 44956729.17638236042841.P161 263 (1) 1933972763996644233329899026760057.P250 265 (1,5,53) 44512772676958707670636861.13540628227343143513585152841.P171 267 (1,3,89) 1069.28837.138151576813. .46992000437847692882153515791466203156562909. .38377631790110438168929289924771541551278936312860162633912589.P67 269 (1) 139343.210448392071.435969870238402935098824427. .867262062344332574857370903987335252122781. .976463786759488319539298814999860605449808297945114865996750\ 0169916281299.P132 271 (1) 128684351.82563258586244744645506795146107567270927259291623. .185812320789950486715465961599572669990642837828516663953293\ 0145263805746638767329880410679791959.P138 273 (1,3,7,13,21,39,91) 1513979377.55088522581.127471845172490875057. .4058519934585456806481289.P91 275 (1,5,11,25,55) 3301.9965388674060051.23481556650628451. .2238729366218120051.342057173738154343151. .1253637273890699938095461437151. .20730228394927104240276793781652047312213543451167483401.P56 277 (1) 14607061984967. .493013607157379867180138441305247145669676896361683316973054\ 74662185137510226810191600615067.P194 279 (1,3,9,31,93) 7357522785371991109.P176 281 (1) 563.397897. .154221955662163766350969445193101557505348095881398705668451. .70024352386637746350335151254965242728559092465367557675865257632933. .211921506481163021174310073307986398243690686825095355801892\ 82981257889633.P94 283 (1) 9039254891.574415003477912224164865138245789464170840631670479. .26785545731954172012083541498222514926995420384520155335872\ 125976832022624491270145042619171968998041828057751013519.P129 285 (1,3,5,15,19,57,95) 110621041.3070127161. .1060198543142555940529623642541.154501946388922582618190838253261. .670944760331657801031002660478241.P43 287 (1,7,41) 1754535469.154051237757089.P236 289 (1,17) 7401450291499674166985824937646679091649406429. .12152882260630918179835904742399811900295875129959937626501\ 72001245585787957.P173 291 (1,3,97) 31915708783183821611425247734471919077. .2720790319906484616848247043137589307514425929.P125 293 (1) 587.70321.1266949011911677. .9771922873124382005094167427793101275584860962883802333. .130234326810885639876279764199952736997166570238639431908314\ 307881978171073494590151413084090685311967677.P134 295 (1,5,59) 6491.18432781.552959784071. .125138885231034988809967351229996025110100954283062840217801.P169 297 (1,3,9,11,27,33,99) 84349. .283060719736432770539523360816216456291213229.P145 299 (1,13,23) 599.150697.320800091.3733087268543387. .1500398624174864772818715119622474419. .10257808708998033162862892522269646365380529. .6979910079264567598677637979206973805557999725393713501833999\ 03406406626529359323.P93 301 (1,7,43) 5807370698691870215013649394858844267065452599990947\ 6945029022220501436983707684999473013263439.P178 303 (1,3,101) 10909.2214418537.24125673647216919378135313.P178 305 (1,5,61) 1178521.P253 307 (1) 7369.94096729.11783758873224547937048029. .17423936241502551794842921669334366618339345461.P248 309 (1,3,103) 2001736609.309374768985359817697.263635209887150875\ 569050631759020888724964357478349281766142758325445593.P119 311 (1) C335 313 (1) 251653.6291301.46831805567.59873266690305132380666276323091. C283 315 (1,3,5,7,9,15,21,35,45,63,105) 47881.171983701. .218091611031474291036310925141825298495406141.P99 317 (1) P342 319 (1,11,29) 611369881.15406509463646344244268006401549341. C260 321 (1,3,107) 16693.167286787894754920547692043638956253256902045\ 5774895092945762169614919462630040441992901410932528575509.P123 323 (1,17,19) 647.3275970874871. .558895751949928786907792675124137800780786393. .179134544380790814260416617296669096266685485399301527791299405233. .576900328665130580370845137079171833421482176785895848512893\ 7537875714996001.P110 325 (1,5,13,25,65) 341814926104786345514126466594657551. .382344335747896460311759063643358251.P188 327 (1,3,109) 143738197371411694773160046593. .16492617608862490237522578465424837490149. .17339193980846828558826459587442268412622933423234917276494873.P103 329 (1,7,47) 20399.682212592131841.3671373518199997. .158589522718743213642152038007140433117329869003553.P213 331 (1) 329677.23036939.25107013.3974393645579167915081. .3980083576443946028213641.C290 333 (1,3,9,37,111) 37*.760423621162033.12245270545202412137509. .14808645751988810312789743801.1331602837917505840054805334769. .1196408840938561086029281556942464469657460995400533142379321.P77 335 (1,5,67) 2061421409850805735582323552961. .1687363633055095804826223129926492457496350011.P210 337 (1) 150246814646321946446767942785606503. .339309255680410415657068111365964544508075829804149997978999513.C265 339 (1,3,113) 389173.2847204379448437. .854270814106127054303133380351118620893. .22584037486802473012423638657465661578829.P142 341 (1,11,31) 683.34105461457.14417227486664700326423174953. .1458732274149215313019517022707. .1210825726041172608205606863638504578784630870741567056159350851.P189 343 (1,7,49) 115249.176989.182894461. .1382001534481119476973565388948661828220648658937391650671. .825188006975164155085687886322767467255535129121895065570177\ 2822592880012309.P166 345 (1,3,5,15,23,69,115) 5521.680341.3565921. .628504350611880407413191347426400523621. .1330866830549480068481583775754970102386701.P93 347 (1) 220663649769943822513977215399. C345 349 (1) 3491.2637743.7169159.16556418110480683764860099. .1300659329285336079983846947175493896921651.P292 Table 12+ Factorizations of 12^n+1, n<=350 L,M for n=6k-3<=699 n Prime Factors 1 13 2 5.29 3 (1) L.M L 7 M 19 4 89.233 5 (1) 19141 6 (2) 20593 7 (1) 211.13063 8 17.97.260753 9 (1,3L,3M) L.M L 1657 M 1801 10 (2) 5*.85403261 11 (1) 57154490053 12 (4) 193.2227777 13 (1) 13*.79.36037.222379 14 (2) 673.13156924369 15 (1,5) L.M L (3M) 31.421 M (3L) 35671 16 153953.1200913648289 17 (1) 2551.66900193189411 18 (2,6) 73.122138321401 19 (1) 3307.8209.905265296671 20 (4) 41.521.127921.67657441 21 (1,7) L.M L (3M) 1885339 M (3L) 7*.43.17011 22 (2) 2377.3697.6337.68368660537 23 (1) 829.12421.49489630860836437 24 (8) 7681.40609.592734049 25 (1,5) 1951.60601.73951.438472201 26 (2) 53.677.2200289654266792155913 27 (1,3L,3M,9L,9M) L.M L 109.47336293 M 271.487.39097 28 (4) 79493013628273739882868481 29 (1) 1402596253.1084876017544880450377 30 (2,6,10) 186168115009253521 31 (1) 1263499.173420475484059478781201647 32 769.44450180997616192602560262634753 33 (1,11) L.M L (3L) 67.199.1453.5479 M (3M) 39105782299 34 (2) 79471453801.427152748915310957418697 35 (1,5,7) 86121235964912696227980301 36 (4,12) 2231857.3684845809.9666387937 37 (1) 5250079.4150805645839.30023720899326796981 38 (2) 1977673.176477034940417.2016864235215616489 39 (1,13) L.M L (3L) 859.17793645013 M (3M) 313.17991125491 40 (8) 34182189107670005092862256297738241 41 (1) 12301.1684652527.13657436942593.47936660465075191 42 (2,6,14) 80048881834094656438235281 43 (1) 71209.372060253.10273420681.7177727914895266742809 44 (4) 67651673.217245283970973197278039678825711337 45 (1,3L,3M,5,15L,15M) L.M L (9M) 181.47263556341 M (9L) 9298142299081 46 (2) 302669957628317561107372328495588758678132736113 47 (1) 18049.12349627.21622395121.8405516927437711741762092271 48 (16) 7489.3122881.1461573322938242802306049 49 (1,7) 8356734198817312279063.253265324522131745115559 50 (2,10) 5*.101.1201.700936801.2334798291701.14807687049800501 51 (1,17) L.M L (3M) 307.380355066717049 M (3L) 103.3077130526103089 52 (4) 288913.25265657.865727447657645665290857439836665912121 53 (1) 3181.33073.77366539.14861828970617714166257633556559606415803 54 (2,6,18) 433.3889.42729553.165042892009.59686188135337 55 (1,5,11) 331.6271.164018234982236911.46768482029635739671 56 (8) 113.2129.244721.527633.22232950788588289.9150512297530943809 57 (1,19) L.M L (3M) 19*.884986147755302617 M (3L) 229.62701.3178598581687 58 (2) 29*.1277.378509.9533379150437.507127415651053993.39821279284774257217 59 (1) 709.1063.25232402089.21271304642628211.892931082048097905588129990661 60 (4,12,20) 241.141841649932724596178535977341201 61 (1) 111997.7361466337.5188602220069.P38 62 (2) 617521.26825115448057.87873272984241400393.P26 63 (1,3L,3M,7,21L,21M) L.M L (9M) 127.79277059.2537121133 M (9L) 27764103747580691401 64 36097.81281.69619841.73389730593973249.P35 65 (1,5,13) 37831.52960051.P40 66 (2,6,22) 109297.219649.1717321.P27 67 (1) 44623.2291803.P61 68 (4) 137.17019338113.P57 69 (1,23) L.M L (3L) 139.277.8419.22542577.129512587 M (3M) 348670382471247108491803 70 (2,10,14) 71874601.10365509281.1612092376073761.5298455664688950121 71 (1) 48058613330617.P62 72 (8,24) 577.2752993.15670947324691873.P27 73 (1) 439.346059859.6325722879776491.P51 74 (2) 149.48989.417509.21617621.13721476576343266613693.P36 75 (1,5,25) L.M L (3L,15M) 151.2251.1696501.6625387201 M (3M,15L) 395251.9733315100252251 76 (4) 7889080897.143529155542303647618953713.P42 77 (1,7,11) 463.P63 78 (2,6,26) 3247609.23709901801.P35 79 (1) 5434599708664429598203.270354982362100782692527.P39 80 (16) 2081.2478806527025281.214538593513800809975201.P28 81 (1,3L,3M,9L,9M,27L,27M) L.M L 163.811.1621.641065152502677063709 M P30 82 (2) P87 83 (1) 499.8305623819547.5277826961453441457872455753.P46 84 (4,12,28) 337.10753.284065793761.P34 85 (1,5,17) 235111.32182021.182593435609480192119451.P33 86 (2) 173.195049.1260760517.247819688992536197.881572852017880141483757.P33 87 (1,29) L.M L (3M) P31 M (3L) 2032959451.1390046661396154093141 88 (8) 2481601.6188868577.49514757601.8200539405448794297995729.P35 89 (1) 7477.572511347126394968679427.P68 90 (2,6,10,18,30) 1653489395093881.33276147172349761.114859125525232035721 91 (1,7,13) 1093.44773.2322926580703.2620222710234691381.P40 92 (4) 23369.36433.44805941084686008411833430562841.P55 93 (1,31) L.M L (3M) 5209.24221034391.1188277798029874021 M (3L) P33 94 (2) 941.1129.6581.56078144420933.1645156433564398201. .19141017664453895628642529.P33 95 (1,5,19) 251831088886489381.P61 96 (32) 1153.2689.4993.22273.3124609.3531754753.P39 97 (1) 322429.P99 98 (2,14) 197.81667460066590930293917.P66 99 (1,3L,3M,11,33L,33M) L.M L (9L) 5690162377645219.43504476926662819 M (9M) 2971.P29 100 (4,20) 15601.55201.9880627023929801.P62 101 (1) 1213.21211.P101 102 (2,6,34) 409.615782161.P58 103 (1) 1237.289765369.1003041977479.13561251678157.987452638049443. 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L (3M,15L,75M) 862768857355002751.26061802206090827529591526287333751.P56 M (3L,15M,75L) 751.1861999501.P96 381 (1,127) L.M L (3M) 1524763.12721529803.206375981018136378198643. .22179455009646313890461937208319215171.P59 M (3L) 2287.970789.409795207580354851.1480444859343993091644952608883. .1140932738223148258864544522278327.P47 387 (1,3L,3M,43,129L,129M) L.M L (9M) 6967.4388268096716033913973672130408161496791. .202923202077686203277513231859003158873473.P52 M (9L) 5419.34057.51859.607848517.11281513627.169315811495745796632187.P81 393 (1,131) L.M L (3L) 787.288931243.7853352071229031. .3540037548679408652606516870379751.P80 M (3M) 47161.540200509.173461409377.P116 399 (1,7,19,133) L.M L (3L,21M,57M) 7928131.1262555546640315313.P92 M (3M,21L,57L) 332767.17706929602633139191.1062177777127068280484149.P68 405 (1,3L,3M,5,9L,9M,15L,15M,27L,27M,45L,45M,135L,135M) L.M L (81M) 171947421803819953791091.500131074548916716314179353131.P64 M (81L) 9230674951.P107 411 (1,137) L.M L (3M) 32059.88630068743448247758082010402431935794978004066530299.P90 M (3L) 139729711658022289818417409915604887567.P109 417 (1,139) L.M L (3M) 1669.15013.110923.208501. .5638888896763019486450225237314251285030538064074261.P80 M (3L) 3964837.P143 423 (1,3L,3M,47,141L,141M) L.M L (9L) 103169155868277226048549.10455277041391964392381265548669243. .381846165419473573914787041977491293397073551.P48 M (9M) 554977. .49428368266998575771508427851382501624434884685008412777493.P85 429 (1,11,13,143) L.M L (3L,33L,39L) 3729230661964237.P114 M (3M,33M,39M) 274233961.593967524131726603.159504077463298584589. .43450210975084947437977.P61 435 (1,5,29,145) L.M L (3L,15M,87M) 69872836351.887257418543475083551.P89 M (3M,15L,87L) 3628562344662781538711332722241635752511217245360661.P70 441 (1,3L,3M,7,21L,21M,49,147L,147M) L.M L (9L,63M) 3529.11467.69710998267.162145535833.1208862422525899.P92 M (9M,63L) 47629.312229.3819943.147915811.400268955783439. .80563595863991546010661115881806884967004027.P53 447 (1,149) L.M L (3M) 242685942045674495792268869293516616521379017039547818607\ 03146532721181.P90 M (3L) 13411.3740497.27760489. .2085436050830101868627222971448078347771532442559785477511.P85 453 (1,151) L.M L (3M) 7345054738129351972681432555641148061413364808769116545344488307.P98 M (3L) 1348129.2092861.112341266088109835884435114483. .3206046355269404360980173532840459.7154409726952489428326850247389343.P54 459 (1,3L,3M,9L,9M,17,51L,51M,153L,153M) L.M L (27M) 6427.8263.3290873941. .4772949043296938327540555652344566627901623072447285275681332599.P75 M (27L) 2583416323.1848577259045898983521.P125 465 (1,5,31,155) L.M L (3L,15M,93M) 33661195621.7608436297012031616889789008167761321.P82 M (3M,15L,93L) 31*.4853358451.P119 471 (1,157) L.M L (3L) 44704452965167992989021059. .3373910943552318560566312255270898933180978334214232817297798982057.P77 M (3M) 7537.15073.12453241.35010373.74479461399093993433. .31289406059597855950513457417424955206259.P86 477 (1,3L,3M,53,159L,159M) L.M L (9M) P169 M (9L) 6679.126563242535798869117.121272451003595655053743013354\ 36857963786417904384880169071412408713919.P75 483 (1,7,23,161) L.M L (3M,21L,69M) 967.P140 M (3L,21M,69L) 607006142583726902226615046763509882376974181278444022803.P86 489 (1,163) L.M L (3M) 13693.53791.73351. .1589450798887141029369915280596841501323098573956641339782791.P101 M (3L) 1929515761.636076523128573.617979037622870188705978539097\ 764755562007183462574733638849717988229201.P80 495 (1,3L,3M,5,11,15L,15M,33L,33M,55,165L,165M) L.M L (9M,45L,99M) 53639866668586533056821906301274295479310292221.P83 M (9L,45M,99L) 991.4241102915611.19211052014551.931826707797528452251.P80 501 (1,167) L.M L (3L) P180 M (3M) 97174963.P171 507 (1,13,169) L.M L (3L,39L) 2029.24337.75037.38915923723.P146 M (3M,39M) 70981.19818208177.142020168733. .44962084852792428976301085987770964908163039004483.P93 513 (1,3L,3M,9L,9M,19,57L,57M,171L,171M) L.M L (27M) 76041217116941473.P158 M (27L) 105856254362071.20424500075336986891104565020294665487061027. .48621554404118655538174883189588506054052233.P74 519 (1,173) L.M L (3M) 2163193.1392394853916259.77800409639814848538397771424169\ 207356806135954509605930376319347717201490361707.P85 M (3L) 108298213841149.P172 525 (1,5,7,25,35,175) L.M L (3M,15L,21L,75M,105M) 720301.113023051.P116 M (3L,15M,21M,75L,105L) 1051.6301.17851.6442801. .137674063225843198051259632503102522001.P74 531 (1,3L,3M,59,177L,177M) L.M L (9L) 70631031907.1641292827443365429.P159 M (9M) 273997.P183 537 (1,179) L.M L (3L) 16111.61676889995993664538489477189609. .395990847983499230629473507336067593585583. .6553202059289007592766882635476749822940266122999.P66 M (3M) 17619052443834679.P176 543 (1,181) L.M L (3L) 2278429.194599456260344351580850323437144589278651832091\ 1083354368578944419107392783511986751617.P101 M (3M) 1087.2472823.7842135398918588368969.872467473285058707693422089. .13080055006360860550237644443085429757. .210113748844700144917711383538967015427673.P58 549 (1,3L,3M,61,183L,183M) L.M L (9L) 7687.358789069.P182 M (9M) 354960413514937.26896003358908279221661679473939478241981255703. .322410908070969630339041359359164154612901586904078700184707.P74 555 (1,5,37,185) L.M L (3M,15L,111M) 7771881751691625037690129926078250918116885996408721.P104 M (3L,15M,111L) 3109111.38689265837367032644023417953163545911.P112 561 (1,11,17,187) L.M L (3M,33M,51L) 1123.32562842234539.78324649527879819109. .301185864380214605485651.1058569077572449333936789312141.P83 M (3L,33L,51M) 10099.4496981131825488660800158938461828526815530233607.P120 567 (1,3L,3M,7,9L,9M,21L,21M,27L,27M,63L,63M,189L,189M) L.M L (81M) 28390394386299961.809314740206179298645509353511. .5230055597704998513749511222169. .563331271783469665535306255634948806914286843491.P50 M (81L) 40278547.1954561267.32835102679.16351687657198086505701607.P123 573 (1,191) L.M L (3L) 60344482942982897615998724470855285226949321551984117995\ 141479519932977.P135 M (3M) 2213558629224791673406902242107. .4073110572177402880358023433665428834389887.P132 579 (1,193) L.M L (3L) 208441.6439316280967.35135274085230907447. .212633762985937736199663727. .114016331193920092225584659338086215629841839071424207154308069.P82 M (3M) 1140068969221082768792175765231766327060329518346066867530983.P147 585 (1,3L,3M,5,13,15L,15M,39L,39M,65,195L,195M) L.M L (9M,45L,117M) 1171.44022421.8778178115705076853830510781. .30191929647961734821233855062192311705657444483644561.P65 M (9L,45M,117L) 11950124941.16644914911.866757827669435037422729371. .91264931872794338368056566736419162905070295091.P62 591 (1,197) L.M L (3M) 1638089365033813.394269001208982069133.674591191048755553063.P155 M (3L) 89833.389945631679504093322073487.1139807681135944776240219\ 053639595390947513666853190760367107498802022946752383776898613.P94 597 (1,199) L.M L (3M) 3583.65817972421.110693643337.406687074361. .94502328581673515370642457513.P148 M (3L) 3127087.762655517470452162449734755292117546105489225453\ 443649619017774346819409553725976907519534883432257137.P106 603 (1,3L,3M,67,201L,201M) L.M L (9M) 148339.201403.6184033301861061495534163. .15178718159191862986321182462902328570118849.P136 M (9L) 37948886981947.165005354024346709.20954239462618482188564604919. .210469877070599169710131278720871. .110012113226229710240682655743829157534683.P82 609 (1,7,29,203) L.M L (3L,21M,87M) 223392163.1160863969736521.P158 M (3M,21L,87L) 354439.230170764572701.15490835686571781132456091. .15727168385623148492541628907161124166451. .1240697482177556343186105031360712849993338609.P52 615 (1,5,41,205) L.M L (3L,15M,123M) 6151.78721.8249098321.2884308215671. .281244358113238895941.P121 M (3M,15L,123L) 3691.55351.356701.1591621.171466377571.25050543163651. .20180587175658253004616750165991.P97 621 (1,3L,3M,9L,9M,23,69L,69M,207L,207M) L.M L (27L) 26083.1274293.89529571.P196 M (27M) 4969.33231611842309.162867909058707122777800081. .70119412232223755484393713461.P142 627 (1,11,19,209) L.M L (3M,33M,57L) 440058305413851717971272530016562468807621216808\ 084576772657852505721114879019027.P114 M (3L,33L,57M) 1628947. .8787995406315951919107350324404077876341098916495079079.P133 633 (1,211) L.M L (3M) 677311.52705058891327197.2154119276174593827225346815506\ 072804273310178999017719073090487659900376339736455327.P120 M (3L) 80829037.48905430935845333.49891472380880789396701818619.P174 639 (1,3L,3M,71,213L,213M) L.M L (9L) 34640191.664420699.40458622045663.2257301371994760106268101. .24752404177714641379678295389502621948664385737636721. .11641511676221153929913639540391472331642774085802484299.P65 M (9M) 219543900759599833.8846249843523180709. .408216148851735217586472186250508977. .45479081371595503912835755156173312700350635081277400243.P100 645 (1,5,43,215) L.M L (3L,15M,129M) 939454111.40910714281.11150342377317712395921365514091. .1407216440781659667913939499482114354965287087363025295681.P74 M (3M,15L,129L) 1291.6451.P175 651 (1,7,31,217) L.M L (3L,21M,93M) 1303.112802546902065665107. .71169445303802234735786658317266702403783513781659317.P118 M (3M,21L,93L) 24990802831.36028936189.561132068323. .360479288619067687307617.411875176065360161587300408902901.P106 657 (1,3L,3M,73,219L,219M) L.M L (9L) 28909. .245142646001600156707457150801791469142756055291541614368482\ 476593307151944951.P152 M (9M) 1646867935776737809275643.3877144229695685240495907541.P182 663 (1,13,17,221) L.M L (3M,39M,51L) 162137977.1503347617784689.157592515616244619. .700708021151315893. .498879037352635364498613339989309354418616397863.P102 M (3L,39L,51M) 1327.1233181.1319371.357677893.148274130187.748666777787839. .2890957359269611534651704429016643751304132238522607369799.P100 669 (1,223) L.M L (3M) 2677.41479. .680497789048791885103910081993768343472049600417986310203. .1972448504999621521439068495860239627663890074133786628781254\ 273114065461688207219.P94 M (3L) 189579237297301919317987811692524940058881.P199 675 (1,3L,3M,5,9L,9M,15L,15M,25,45L,45M,75L,75M,225L,225M) L.M L (27L,135M) 32401.56701.453601.192777182040889797948901. .1680728931864805116751815208682974380430435651.P111 M (27M,135L) 11137501.165703590060751.53392538491036948052546133\ 075482081118585630931545744788577193471501515381419251.P94 681 (1,227) L.M L (3L) 22629619615938888254201870077907110666230401369223889176\ 675792844220262524953877289424152613.P153 M (3M) 2235293971.54093457591.5109248384137701763. .3707420036070776039316539892257906160506899. .12669120436520044485987795458014401852146921908441.P114 687 (1,229) L.M L (3L) 678757.18792199.7390147732544628690937350679946659. .46075889381383659882439600165031402233297. .1366223774428423819329153408095022201995011254144291368203.P102 M (3M) 17863.496117051.507278904810174576049.P213 693 (1,3L,3M,7,11,21L,21M,33L,33M,77,231L,231M) L.M L (9M,63L,99M) 117811.5907133.853926587452519813. .210079688110361883223974683653843.P133 M (9L,63M,99L) 5082463.2969760894507793.18892616365226143. .7458885348605265661401547.4659689620661748959806904052023307877.P95 699 (1,233) L.M L (3M) 12583.522853.571783.530408191.592541429047. .576645302107129013678909521875060871623139771202369563027849\ 9764519533021621872795434114889.P124 M (3L) 80918570844563675641898786371301488783517392748899.P201 12^3h+1=(12^h+1)L.M, L=12^h-2^h.3^k+1, M=12^h+2^h.3^k+1, h=2k-1.