This file collects various known factors beyond the limits of the Cunningham project. Some day some of them might be added to the project. Some Base 10 number appear first. 9999 10, 401- c389 25630835501493582366342771676602359. c354 Granlund ecm 9999 10, 402+ c244 411108592242640071999067201. p217 Granlund ecm 9999 10, 403- c999 1613.195053.2877743575868875117. c333 Granlund ecm 9999 10, 403+ c352 35065183927133465514193983196961. c321 Granlund ecm 9999 10, 405+ c202 115690846857912397278375911371. X Linus Nordberg ecm 9999 10, 406+ c326 512592628798218592009. c305 Granlund ecm 9999 10, 409+ c404 1358791302758702868906124409. C377 Granlund ecm 9999 10, 411- c272 910370210237485953333456541012399. p239 Granlund ecm 9999 10, 411+ c252 36497963117203265504917. c229 Granlund ecm 9999 10, 412+ c403 38450569246994805922293218161. c374 Granlund ecm 9999 10, 415- c305 2583267906383511978058229561. c278 Granlund ecm 9999 10, 417+ c269 1036412737512256032518509357. c242 Linus Nordberg ecm 9999 10, 419- c411 481154717070862987053019025329. c381 Granlund ecm 9999 10, 425+ c314 165564988462016408581266824201. c285 Granlund ecm 9999 10, 426+ c276 9234177915412657069. c257 Granlund ecm 9999 10, 429+ c222 80216851991399964961367677. c196 Granlund ecm 9999 10, 432+ c264 789462081785833165384754689. p237 Linus Nordberg ecm 9999 10, 433- c999 5197.71879.10267736058618833778601. c402 Granlund ecm 9999 10, 435+ c202 70350656881.1174705187104089640352756731. c164 Granlund ecm 9999 10, 437- c387 2152970896196020817900437. c363 Granlund ecm 9999 10, 438+ c237 111956960338863707579494311481. c208 Granlund ecm 9999 10, 439+ c438 307331935589859872028943. c415 Granlund ecm 9999 10, 445+ c328 332073601264920920030201. c304 Granlund ecm 9999 10, 449+ c424 149875511372280830299739.1979498820250457412915603811. p373 Granlund ecm 9999 10, 452+ c412 23496896216135822356297. c390 Granlund ecm 9999 10, 453- c999 38959.49831.5367478277103625776110671.1988743444617710279595999836107. p236 Granlund ecm 9999 10, 456+ c289 7865110274657230201779070033. c261 Granlund ecm 9999 10, 459+ c275 236186599173787727067007. c252 Granlund ecm 9999 10, 462+ c159 3925277248426748966984537733816767395325307476622633188305245093834818012069881. p81 fwjmath gnfs 9999 10, 464+ c412 363050401891291226709889. p388 Granlund ecm 9999 10, 465- c228 151063549389365288761.474226535398761166999927321. c181 Granlund+Norberg ecm 9999 10, 468+ c249 22088303808535743236641. p227 Granlund ecm 9999 10, 469+ c393 82807833384684209867899. c370 Granlund ecm 9999 10, 473- c399 4296523694502213981194071003. p371 Granlund ecm 9999 10, 473+ c393 18065356669522314875053. c371 Granlund ecm 9999 10, 475- c999 433201.16891951.34261457162552911201. c328 Granlund ecm 9999 10, 475+ c355 37536220395103028946001.430980650733675562214801.3605627469350067392124001. c284 Granlund ecm 9999 10, 479- c999 8409713172345994955133083761. c Granlund ecm 9999 10, 483- c999 14461987.176686231.4828646712337104427.450663669979084462369440511.575760557843831535447049. c180 Granlund ecm 9999 10, 483+ c260 5342512091349500920639852868215477. p226 Linus Nordberg ecm 9999 10, 485- c380 146750482675162900202561.14139374177495543227906481.381114663987976481223016831. c305 Granlund ecm 9999 10, 486+ c307 729719975272091111399590489. c280 Granlund ecm 9999 10, 487- c460 414975787613882010952043.37906492483728091425671519. c411 Granlund ecm 9999 10, 487+ c480 46031771059124302914419. c458 Granlund ecm 9999 10, 488+ c460 7849115417706986501273297. c435 Granlund ecm 9999 10, 489- c314 5378079413673378180277027.11120952524491214120396599. c264 Granlund ecm 9999 10, 493+ c410 865788741404845009303. c389 Granlund ecm 9999 10, 495- c205 16860090181450569942798606214497570829921. c164 Granlund ecm 9999 10, 497- c999 6482999209.125570206399417189187.1520363337723230705884649. c366 Granlund ecm 9999 10, 499+ c467 90423008276017153733438983. c441 Granlund ecm 9999 10, 513- c324 241321710362499305354071. p301 Granlund ecm 9999 10, 517+ c517 16771138093862687229221870527968178411115969. c IvanleFou@yoyo ECMNET 9999 10, 543- c321 3923435197184939035671283. c296 Granlund ecm 9999 10, 545- c376 170571534068289207623071. p352 Granlund ecm 9999 10, 546+ c251 798407634963349034989. p230 CWI ecm 10/31/97 9999 10, 603- c393 2056773747750522256947853. c368 Granlund ecm 9999 10, 615- c310 5440907236518498609451112390256369995629321. x Granlund 9999 10, 720+ c373 3427762485430544075935398346603780801.c336 Brent ecm 9999 10, 889- c749 153288409997816784961649. c726 Granlund ecm 9999 10, 903- c469 8812951362399248896808929. c445 Granlund ecm 9999 10, 983- c946 534106849805517421445196089. c919 Granlund ecm 9999 10, 415- c278 96357627407011709976598813958321. c246 Koide Yousuke 1/16/03 9999 10, 442+ c368 6219342207515923652594221. c343 Granlund ecm 5/1/01 9999 10, 455- c280 36942048382668980544619913561. c252 Yousuke 2003.01.22 9999 10, 533- c480 325701010363.1368176150329. c457 Fransen 12/6/02 9999 10, 552+ c341 11266057249. c331 Fransen 12/6/02 9999 10, 560+ c385 48102033281.555204874561. c362 Fransen 12/6/02 9999 10, 567- c320 1915010942511169366290219191029597. c287 Yousuke 2002.01.14 9999 10, 577+ c572 4085803565117909125465863327515767. c538 Yousuke 2001.05.26 9999 10, 667+ c612 37832309369. c602 Fransen 12/6/02 9999 10, 759+ c435 272168891611. c424 Fransen 12/6/02 9999 10, 805+ c517 46688538121. c506 Fransen 12/6/02 9999 10, 930M c224 295188553361058681059167605734159744284801. c182 Yousuke 2001.10.22 9999 10, 990L c198 565535931528718738579019314877232841. c162 Yousuke 2001.10.02 9999 10,1155- c471 383230071841. c460 Fransen 12/6/02 9999 10,1227+ c792 1070453760938027595699552600393152583819019423. c747 Kruppa ecm 9999 10,1230L c296 11596877881. c286 Fransen 12/6/02 9999 2,1295+ c216 1297011327466713096225068755289464647661446011. c171 Kruppa ECMNET 9999 6, 512+ c400 80897. c Riesel 1969 9999 6, 512+ c400 3360769. c Riesel 1969 9999 6, 512+ c400 12581314681802812884728041373153281. c353 Nestor Sergio de Araujo Melo 1/19/04 9999 7, 512+ c400 13313. c Bjorn + Riesel 1998 9999 7, 512+ c400 943558259713. c Bjorn + Riesel 1998 9999 7, 512+ c400 1338330888777063359811677099009. c387 Nestor Sergio de Araujo Melo 1/21/04 9999 7, 512+ c400 275102002206713516320479233. c360 Nestor Sergio de Araujo Melo 1/21/04 > From nestor.melo Mon Oct 25 06:52:34 2004 Date: Mon, 25 Oct 2004 08:51:20 -0200 From: Nestor Sergio de Araujo Melo To: Wilfrid Keller CC: Samuel S Wagstaff Dear Wilfrid, Dear Samuel, A new divisor of a Generalized Fermat Number, which is also a Cunningham Number, was found by ECM (Elliptic Curve Method). Cofactor is composite. In Keller tables syntax: 10 1 10 154212497694640843097187 11 In Cunningham tables syntax (as its latest page 95) 10,1024+ c1006 315827195278624446663038977 c980 Melo ECM The details are below: Elliptic curve number 43 GMP-ECM 5.0.3 [powered by GMP 4.1.4] [ECM] Input number has 1006 digits Using B1=1000000, B2=839549780, polynomial Dickson(6), sigma=2475100344 Step 1 took 1880810ms Step 2 took 712340ms ********** Factor found in step 2: 315827195278624446663038977 Found probable prime factor of 27 digits: 315827195278624446663038977 Composite cofactor 17058785296895076325275806258952596422969217277427372881529090790198283625542936538883750689057732086692066474057578443572379521760109290433730741987932666202560083503791569433619494802218784558160638637453019484866945293026732116576717688982572826141109623138902299694616560019032749193286113507300935718260623800673161383440239689686064922603258706788627731379600742139017796501228719364598010776077636203957691244792264823330934141618536732066360784390192019882207638321261412859029250828316101077917473926222816083578856872740855532409501625129969510048982913534467962091401257127295866097485120947209871500082859744791130620986293024180260564799450598718355940180110246689615346948766251020204506744812841984196934410126244284970859564288684172478341290812089699724838918304850506470815869746239456549667532486174395130951748674632997937385416439524136118265854557564368041180651435153869285425844774452150517436161541398117570236641067129543090150797325402244689341664862209 has 980 digits Regards, Nestor -- Nestor Sergio de Araujo Melo - nestor.melo Software Engineer - Cyclades Brasil Phone: +55 11 5033-3365 - Fax: +55 11 5033-3388 http://www.cyclades.com.br From alexander.kruppa Sat Feb 25 17:40:50 2006 here is the factorisation of 2,1295+. 390960945481 413080055666248475387722988636881 1297011327466713096225068755289464647661446011 21948435716309838454791940755133614083294130821081 p122 Using B1=110000000, B2=680270182898, polynomial Dickson(30), sigma=147709473 Step 1 took 597647ms Step 2 took 238812ms ********** Factor found in step 2: 21948435716309838454791940755133614083294130821081 Found probable prime factor of 50 digits: 21948435716309838454791940755133614083294130821081 Probable prime cofactor 18537610443658574018802790288646767074781206524363322642736904920191987329300133108669959550738487862434105722782510889601 has 122 digits Alex From: "Alfred Reich" zehnp at gmx.de, Date: Fri, 30 Nov 2007 13:11:18 +0100 The ecm program (option -pp1) has found a 38-digit factor of 10^1655+1. factor: 18802215938788787651629737655497612041 Input number has 1288 digits Using B1=20000000, B2=24395748312, polynomial Dickson(12), x0=3319294994 Step 1 took 4147438ms Step 2 took 1340156ms [factor found by P-1] ********** Factor found in step 2: 18802215938788787651629737655497612041 Found probable prime factor of 38 digits Yours sincerely Alfred Reich Here is the complete factorization of 5^462+1 5^462+1 = c323 = c156 * c168 c156 = lcm(5^154+1, 5^66+1, 5^42+1) (algebric part) c168 = p4 * p6 * p11 * p18 * p29 * p49 * p55 p4 = 8317 p6 = 285517 p11 = 12168544081 p18 = 537684328029194809 p29 = 17757087562354803087936135241 p49 = 1373095119406080811642424383401401449810674535237 p55 = 1436674768394682949553079043634568862786037502040560613 Mille grazie al Professor Carlo Guidi, Direttore della Scuola del Corso d'Arezzo, per il permesso di usare i propri computer e per l'appoggio. From: Tom Womack Sat Mar 8 20:44:32 2008 Subject: M1575 factored M1575 = 2,1575- The C149 of M1575 splits as 745832506848141808511611576240568244832258614550704416204357517716551 * 46988139879538892325015289211281843797083431443099045770269959929002737021425551 Minute and tedious detail at http://www.mersenneforum.org/showpost.php?p=128220&postcount=1 Tom From kwgc3qck at Wed Jun 11 18:54:11 2008 Date: Wed, 11 Jun 2008 16:34:42 -0600 Subject: Factors of 3150M I'm not sure if you are collecting factors of this size, and I am not even completely certain these have not been previously discovered, but the primitive factors of 2,3150M are P39 * P179, where P39 = 246679299928227037139131842857636793001 and P179 = 22185599869144823915412207002704827855775211943971023799304994441106716920626982761384224391655931873668961649859968095546417404113781428614070798854718147768828551173388173058201 These factors are also factors of M3326400, so I have also reported the factors to the ElevenSmooth project. I discovered these factors using the ECM program, as logged here: GMP-ECM 6.2 [powered by GMP 4.2.2] [ECM] Input number is 547272824420841052662292954105619461782338031488108274055834482156 8372827743183540592213262334440320898430555427835631711532445975732990129670420677 733590610873167134937231324792608486913842821989126573179896162451201 (217 digits) ... Run 887 out of 1200: [Wed Jun 11 12:35:15 2008] Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1200923835 Step 1 took 105182ms Step 2 took 28135ms ********** Factor found in step 2: 246679299928227037139131842857636793001 Found probable prime factor of 39 digits: 246679299928227037139131842857636793001 Probable prime cofactor 2218559986914482391541220700270482785577521194397102379930 4994441106716920626982761384224391655931873668961649859968095546417404113781428614 070798854718147768828551173388173058201 has 179 digits Note that I have not undertaken to prove the primality of these factors. The factors of 3150M are: {5, 5, 5, 29, 109, 181, 421, 1321, 2521, 14449, 54001, 63901, 268501, 695701, \ 13334701, 47392381, 40388473189, 146919792181, 307116398490301, \ 6269989892198401, 743689627597081157353277424901, \ 1038213793447841940908293355871461401, \ 246679299928227037139131842857636793001, \ 15169173997557864184867895400813639018421, \ 3065581111593982777238141477447662979750101, \ 221855998691448239154122070027048278557752119439710237993049944411067169206269\ 827613842243916559318736689616498599680955464174041137814286140707988547181477\ 68828551173388173058201} The above assumes that I understand the definition of 3150M correctly. The above are also factors of 2^6300-1. Cheers! -- Rocke Verser From: Rocke Verser Hi, folks! I believe this is a new factor of 2,3850L, 2^3850+1, 2^7700-1. C312=P31*C282, where P31 = 2342831546513139086564683339201 GMP-ECM 6.2 [powered by GMP 4.2.2] [ECM] Input number is 374202023964420989779799023648225263488829721663509548490189020932862597004053243741671002989619828190305060865455179861573719096003203373588519413635484406914594648947364048146360366345000266675306596678846320309005945464550226260221714949636726069917597882568387925376128893743664941995784612357581018063624401 (312 digits) ... Using B1=1000000, B2=974637522, polynomial Dickson(3), sigma=4172036749 Step 1 took 61616ms Step 2 took 13666ms ********** Factor found in step 2: 2342831546513139086564683339201 Found probable prime factor of 31 digits: 2342831546513139086564683339201 Composite cofactor 159722121089478161935151975597817221328879126981740458056580240173157023840855331295646389662273776270817434844232147040536177070118128943878556790589750200007186455059123299059942783895002625571775357149605018405109711838435233314251806738683172496226856547597158248752445168445201 has 282 digits Cheers! -- Rocke Verser Date: Thu, 10 Jul 2008 19:42:28 -0600 From: Rocke Verser [2008-07-10 22:48:00 GMT] c406.of.2^2700+1: probable factor returned by kwgc3factors342 Factor=1069706648965401676185970737247201 Method=ECM B1=1000000 Sigma=702858004 [2008-07-10 22:48:01 GMT] c406.of.2^2700+1: Composite factor returned by kwgc3factors342 Factor=4648559337038035487046614127520441697623933562172941774261091888728893505590172929778011011135732798082671332219836136031571811887908513049244820549331733013257000349170299128097431307671488040564735306365850509952467684341830532762626620615602386247877591487331697587732062758086420776898277645027997861098489659166331176926356457971273778401430226424843949561712576971201 Method=ECM B1=1000000 Sigma=702858004 Cheers! -- Rocke Verser From: Rocke Verser Subject: A p37 factor of 2^3600+1 As shown below, p37=7565547348716503942322031561007953601 >A factor was found for c547.of.2^3600+1 using GMP-ECM using factor method ECM > Candidate number: 1064769037766716574732516751197172735743457808921176788272319707661576829180232131309407741179300459455952495670589833293251671845994644112213078953151672312426860065742972940362841642761760822891165840516996704871259422031752432278494792499760153106302920108969630853707397410586406537038590765182270610841426337537716904358208714792538291280610141387435571539148134541721956347758370733495153756142210214479615275846316471143258280053179092008503980415643778962119873422913170472801390511470590137918921748280201331243964296875891244677223840001 > Factor: 7565547348716503942322031561007953601 > Factor Type: probable > Factor Length: 37 > Co-Factor: 140739194229926374816410492294572885003517344415511808365111433694907747585845768045223602055853390736923642789269636752400984802129319611696427129634660614800261226272684321994236254553989809867533527141460969432960946545244149995464482565237535125761159054715559829733835658981079613649343256404164078392182912933382065989570650645722259654930784265956297404136967941384112127867957074709597222275435142149211206060525022551621906520768820334560731144692637984499307110625727114360273879419492707427488846401 > Co-Factor Type: Composite > Co-Factor Length: 510 > B1: 250000 > Sigma: 811462153 > Found on machine: hydra-4 Date: Tue, 22 Jul 2008 16:40:04 -0600 From: Rocke Verser Today, I found a P29 for 2^9900+1. [Details at the end.] 2^9900+1=((2^1980+1)(2^3300+1)(2^900+1)(2^60+1)/((2^660+1)(2^300+1)(2^180+1)))*P8*P22*P29*C1385 P8=71319601 P22=537692111855716991184001 P29=42801590153358583348623069601 The P22 was previously known from the ElevenSmooth Web Site. --------------------- Earlier today, I found a P37 for 2^3600+1. The small P12 may not have been previously reported. 2^3600+1=((2^720 + 1)(2^1200 + 1)/(2^240 + 1))*P5*P7*P10*P12*P37*C510 P5=43201 P7=2116801 P10=2885961601 P12=337965120001 P37=7565547348716503942322031561007953601 The P10 was previously known from Brent's factors.gz file. >A factor was found for c1414.of.2^9900+1 using GMP-ECM using factor method ECM > Candidate number: 2292116128116875622007696354377873946933804097263599120137910838198291508030175761580955700758601960174602081376771939791473933768622387681907399622833745809445252795973455564778263774699411897985610740169673331581847144788359370037236797809067230580961466314774476465995453200626251038985150873254779154130829745176162173747621062729497961485498761310013667674921857901438729267914768454427289452580083027704137881995375043941289428998001487298782357304493959021630889878399225958418568089016346378744906579601759264399112497743881603403010122746195912732143651184724920126345341289631063972075160838786362258061085383182704455820014389778694827700323058638162680924510142271371966227291900135646805147185212558377955850130877715265322970212250099883198584755526566206221068388313979815801325118244688279274754026653076417871362936340221496866263690458165766628896834935731353877748961741003940155341892425272883005053420121647155353172292822543592645434704321922313550! >043622332946400864212273301314007779548792360747065217876892920122011519743325296881494376712359010768127678698016743574456248370162843797106101326220740068965501424379837191924749467139485056893214651135850954753590025454301767173220305762234331186969752114937519746813112607961036889134863164980744744781998871850622053539755552527239697082674638368398032203846499995806947630598846729589289638978929022977002018866367386678632244692584760401 > Factor: 42801590153358583348623069601 > Factor Type: probable > Factor Length: 29 > Co-Factor: 53552125514594142829317471837338141222443844255833281194147736350632692118212997723059426368371078798226339190195326375404154489569568772818870691030740170043935680693818502972909119990738239772001451554544814989980949108540480239882654157250152542264041582653390189187132787633697783447880892195713680783130134900519493114158432637656148654269709664411639098367043815573908953103843994439665766965540582910007983019271785113400754236773770331692902660297261102789613845537901342030788635387218466346378560931261689099298653004606386566439819162239295635368164571722102959027237235018835676191187415924237360754733160557499832327922059858313777249516648343821804083709241276169393629827517469027847180723976122196991610158385338029336172347742500790518502290014548324223598779165412503229019051322092713925543253238734269454225115322044077310721042561837354107113857407372312918586430526343702055709121045920572422933559640872643020150123033019387481523374272276516143945809300! >275163736140915376546895142752406622204827376845279488083412142216766400012772401192061756622477476300108567954728682262649278510498402266393411083863131125513551863436617145900185275653299679575715520563421864531315143121435521834371419199910935187682988023183562228177795571461084646362233151230749515421854445154966520753088227614858246668957379053432734876127888645387367352453030594617228165038810010801 > Co-Factor Type: Composite > Co-Factor Length: 1385 > B1: 250000 > Sigma: 1754125892 > Found on machine: hydra-2 Date: Thu, 24 Jul 2008 05:42:31 -0600 From: Rocke Verser Subject: p31 factor of c715.of.2_11550M Folks: c723=p8*c715 is the primitive part of "2,11550M", where p8=73388701 As detailed below, c715=p31*c685, where p31=1303433852539848606260235967801 Cheers. -- Rocke Verser >A factor was found for c715.of.2_11550M using GMP-ECM using factor method ECM > Candidate number: 3130796309281540350316207516232619052574178380464856562650543596695696334818792603590351510089554876170661492486454246868221885910144245409011890765341899338833905001458376582194730577642289137081856976229023100801912073612725597295890275868366604298227404055423842216708952343512525844450353205362699147831674072686929033169654554504366893767835293007994575802174207276057549298488710145836857212858852622417277493100995097256892735398560897092926549975926475109703300367931354866349005068388871662710242822091950129214966855103650476024971716746385213482156661938335415226968856818090152652317191577921889281266218075817038780164917213874527595234002042417271810277023954874087765733213562230491721045603663990701 > Factor: 1303433852539848606260235967801 > Factor Type: probable > Factor Length: 31 > Co-Factor: 2401960255352371693789451439592780575865653566294353308781929593538196627414859029065545034169073321480229278979186896530124544058845838490531833611691046743117470773935407282362078608597054768976276779622288041978755366762850737361097672923529944387039057243911073864962454839552283114517726582854870889100291245340936772621454217600195990211596256924800538528984373062946602588081929970147569320142709717338696363947107435258276022098197054353494928306012136424659587608698131818917584340765505688204164857192697138648750423994235297921381430517030821924491073661247306698794223258267314096061561395165949099309594579826524266887673069399417314543906543081281530598535677544201402901 > Co-Factor Type: Composite > Co-Factor Length: 685 > B1: 250000 > Sigma: 1407580306 > Found on machine: hydra-2 Date: Mon, 11 Aug 2008 23:43:12 -0600 From: Rocke Verser Subject: Factorization of 2^1400+1 The primitive part of 2^1400+1 is: p8*p36*p246, where p8=93066401 p36=360331676468322643689649236464624801 P246=290603255797351401875116431105308935146605837548258511190636927073898933282060156929948561409424354753832009502803515204770684767519584519775733130437326293577505983245830359516593313618581244690715744519479189583012346061661878459292767559889601 I believe the p36.p246 is new. This would also complete the factorization of the complete 2^1400+1. Cheers! -- Rocke Verser >A factor was found for c282.of.2^1400+1 using GMP-ECM using factor method ECM > Candidate number: 104713558348612432018445240716001629068616984540641699860380663342382179494201667597334527089024639980044882512392049141643845966342681073833735938816238243076002628354080495485286091461460190799680741215996041407488909051891153378526874725575314756952332984973979302247797446594401 > Factor: 360331676468322643689649236464624801 > Factor Type: probable > Factor Length: 36 > Co-Factor: 290603255797351401875116431105308935146605837548258511190636927073898933282060156929948561409424354753832009502803515204770684767519584519775733130437326293577505983245830359516593313618581244690715744519479189583012346061661878459292767559889601 > Co-Factor Type: Probable > Co-Factor Length: 246 > B1: 3000000 > Sigma: 2934396240 > Found on machine: hydra-1 Date: Fri, 22 Aug 2008 17:41:11 -0600 From: Rocke Verser Subject: p32 factor of c643.of.2,9450L As shown below, p32 is a factor of 2,9450L, where p32=49596501886925196143952480445201 Cheers. -- Rocke Verser >A factor was found for c643.of.2,9450L using GMP-ECM using factor method ECM > Candidate number: 1724607978268970240168799208546483116238602772640974786706983710553736124973745498665410353265901222500385022272547111954870912333666538069737420134752713313751335114738335204482649976020564252041776397915545304466949185426498050733396487660603831760015944767341037117366934586312981054646004693572542917243988440305679758214035907917369114387804458439121454458507857974855296856990327133087455612839465123138756821909094087637426577629814080478359649831154135564104269807374635233763280757959606498925476072437035310132098977202045484101393245819044125242139471093321931350496387051781312361316104700656565488500497748413990780037551397262801 > Factor: 49596501886925196143952480445201 > Factor Type: probable > Factor Length: 32 > Co-Factor: 34772774543674368430768377801235606451642116618833671435557447763593277003835260131258297270005084974656600308110446206160076146588015056300532881454503944871805251736687595029847076067155711104409836262820547379336358473352764493845946744879769417842028414764877103340910131164342419043785898310441141425910111746356794468170854258073956707648772134545962261320261088983950040412536238740087443284683728646957334604721544722401980563046846454602350072651005024512971260261073522483784544742627978290900976805204849919962257683658267480601211653773884613816044625937425801101356586115257484770055964608425297601 > Co-Factor Type: Composite > Co-Factor Length: 611 > B1: 3000000 > Sigma: 2358325136 > Found on machine: hydra-1 Date: Fri, 10 Oct 2008 06:58:32 -0600 From: Rocke Verser A factor was found for primitive.of.5^525+1_1_1 using GMP-ECM using factor method ECM Candidate number: 537386061881894041650440476042939424009787446609687392603124436070471682278332187655377136545397801658766007701 Factor: 51221911570075178880293450950123975334401 Factor Type: probable Factor Length: 41 Co-Factor: 10491331647135271392301566145772262812230267268018148395744407227153301 Co-Factor Type: Probable Co-Factor Length: 71 B1: 11000000 Sigma: 2718529410 Date: Wed, 25 Mar 2009 Subject: Factors from Valerio Sisti to Sam Wagstaff Dear Professor A logical extension of Cunningham Tables (except the 10 table, with an upper bound of 400 digits) should have entries with upper bound of about 361 decimal digits, as table 2 has, so I have been working to fill the gaps of Tables, obtaining, mainly using GMP-ECM and Msieve, some complete factorizations I submit. The notation is not the standard one, but it is convenient because on the left hand side of all expressions there are algebraic parts (little interesting) partially decomposed, while primitive parts, totally factorized, are on the right hand side. I must thank all the experts of Mathematics and Informatics who have posted online their powerful programs, and in particular Jeff Gilchrist for his very useful instructions on GGNFS, helping me to decompose a c120=p58*p63 completing 7,435- factorization. Hoping my results are new and without any errors, sincerely yours. Valerio Sisti, Scuola del Corso Arezzo Italy (3^609-1)/(3^203-1)/(13*74821*368089*32234893*150224123975857)=2947561*2138662632071226913*50984930600938790172697*P113 (3^639-1)/(3^213-1)/757=2557*7669*499396023937*8141739904937449*P166 (3^645-1)/(3^215-1)/(13*4129*4561)=59341*2199072289*8871459380575801*912851565662857110894244969*13433188106347598163359915928450709921*2751196228592109040664179235751038501334842281*P58 (3^673-1)/2=1826415879755569*4989166368238892867*15964393398656515639633*162738636085359957907179241*518665099640854360708523609062187*P206 (3^717-1)/(3^239-1)/13=2457614587537*4981944496429*75933466677818671998613*P179 (3^719-1)/2=1439*17257*221502813314677*1356659247133798853032285643723*P291 (3^602+1)/(3^86+1)/(29*16493)=87055168229*3814981632127391377*50980291773584318209*P192 (3^606+1)/(3^202+1)/73=1713769*24486768049*126137668609*67806608440582630609*P144 (3^611+1)/(3^47+1)/398581=730193881*1301510755766131*13899889487378851435792249*1284890634316033967801323291*P188 (3^612+1)/(3^204+1)/282429005041=883139339233*129518276313630399553*211063205771765084788013164175857*P119 (3^618+1)/(3^206+1)/73=1031923418880386386777*P174 (3^623+1)/(3^89+1)/547=3739*194377*5686556044639*P231 (3^629+1)/(3^37+1)/(103*307*1021)=71707*877960444290871*51299425811678957273668061329*P227 (3^641+1)/4=3847*373063*4815193*27960421*29952649*4629299333299489283052223*929226972019509722561571755952299851*P214 (3^649+1)/(3^59+1)/(67*661)=27259*21494881*47553529*129058843*707960031891619453*P232 (3^656+1)/(3^16+1)=70849*1172929*88715334003841*P281 (3^665+1)/(3^133+1)/(61*39901*29574984661*374857981681*25349956307509384561)=415916600266344649243171*P183 (3^666+1)/(3^222+1)/530713=516969654193*P195 (3^691+1)/4=8913901*1494719989680433*P307 (3^698+1)/(3^2+1)=76331348023949*657201002395733*P304 (3^708+1)/(3^236+1)/6481=201073*34731649*8558556049*P199 (3^728+1)/(3^104+1)/(113*19489*36214795668330833)=4151057*5863313*13348609*9779184352353998401*210589810325079730354486769*P209 (3^739+1)/4=1258271653*P343 (3^744+1)/(3^248+1)/(97*577*769)=4901473*1435169229601*3861475587087073*4581839443268580361402809889*P167 (5^453-1)/(5^151-1)/31=2719*2002231009*116001942358474281709*28725827491802417627821*287517948889766478099872061872161*P122 (5^467-1)/4=2437741*10589749341418789*9086916876831004249*P285 (5^468+1)/(5^156+1)/(73*543097*1503418321)=937*85873160400449918797155817*P173 (5^473+1)/(5^43+1)/(23*67*5281)=947*11446601*99270403*85223951417067562768043*P253 (5^480+1)/(5^160+1)/(193*5207826497153857*539344757336151926206665601)=13441*15361*4385281*2796282170881*218142099567361*P138 (5^482+1)/(5^2+1)=28921*934844161474657373*P314 (5^483+1)/(5^161+1)/(3*7^2*43*127*7603*66163549*253592389*403316413944121)=967*712909*98351423022563612754061645927*P147 (5^491+1)/6=983*1394441*65203052535938640122309*P311 (5^495+1)/(5^165+1)/(3*5167*60081451169922001*874300184250616439267985523227691404297001)=754381*1863181*50448760561*p145 (5^498+1)/(5^166+1)/601=3653329*6227157528556681*6381497944213050625875889*P183 5,915L:((5^183+1)^2-(5^183+1)*5^92+5^183)/(71*181*1831*2441*1786560207910631*117369445599178322177831741*282652835579996912219434560073594541)=23289087777421*P155 5,915M:((5^183+1)^2+(5^183+1)*5^92+5^183)/(11*1741*1884901*907108630550049150277513478107544348139630852447868173192872357776247941286941)=5923711*10780641615218004138391*121282650064473713751122581*P113 5,935M:((5^187+1)^2+(5^187+1)*5^94+5^187)/(11^2*1531*103511*190295821*34563155350221618511)=192611*920448828120750970042200015191*P189 5,945L:((5^189+1)^2-(5^189+1)*5^95+5^189)/(11*211*541*631*1171*1741*4201*169831*1732501*21226783250214361*26941244373060650224561*150048981833350001935801890061854363895992901)=4545451*P145 5,945M:((5^189+1)^2+(5^189+1)*5^95+5^189)/(71*181*11071*11971*23311*34651*1736701*85280581*297315901*119461537021*1312315694449748688331*17982707297185911173328698426234220871)=21025419411528634804787037331*1325545554645456657650354760481*P93 5,955L:((5^191+1)^2-(5^191+1)*5^96+5^191)/11=3821*284591*1288176748081*5531619057121*77270071023861971*P216 5,975L:((5^195+1)^2-(5^195+1)*5^98+5^195)/(1989151*9384251*49892851*1641395317366745868848220671801*476966369362409096031576235949383293162379490336802701)=1951*17551*1761111219840080597767580940301*P130 5,985L:((5^197+1)^2-(5^197+1)*5^99+5^197)/71=35461*170572300709456235387703271*P243 5,995L:((5^199+1)^2-(5^199+1)*5^100+5^199)/11=41469611*1490619451*269644492391794455719338841735437621*P225 (6^403-1)/(6^31-1)/(3433*760891)=195053*594023*806807*6691284581879*p251 (6^413-1)/(6^59-1)/55987=4506155564597*p259 (6^417-1)/(6^139-1)/43=224530109318798267990497*p192 (6^419-1)/5=839*1479620699964596873622221*225066688766683908874389829009469*p266 (6^423-1)/(6^141-1)/(19*2467)=2539*239105827*25961228334094267*901282995018904681*23384328601493048110561*1962056758780675866460803833449*p116 (6^433-1)/5=1733*31177*542117*15237429272039731*p307 (6^443-1)/5=887*315367271*6080975059*331317534439063458789618961*p297 (6^403+1)/(6^31+1)/(53*937*37571)=1613*8867*860809*160663942225879*5543173075200321107*60877952441030437680144841*p209 (6^405+1)/(6^135+1)/(1783*149862151*3920344350409644507093715799617)=5891765185545693031801*p147 (6^408+1)/(6^136+1)/(5953*473896897)=6529*70177*2823361*380776609*158141084859073*p162 (6^418+1)/(6^38+1)/(58477*70489*863017)=178069*93714790877401*p192 (6^422+1)/(6^2+1)=164581*635533*2475022074841*194945778982624777*7182382972736028583822349020404781*p253 (6^423+1)/(6^141+1)=46441*187931374492447*p201 (6^424+1)/(6^8+1)=1828522365423361*445214738087767889*40592127272306287833159196885729*p260 (6^428+1)/(6^4+1)=857*154081*178540528582082489*45120213087522758245045677588529*p273 (6^433+1)/7=6649607265258689507977*1722823570857721499847173811539*p285 (6^435+1)/(6^145+1)/(31*68209*92569*1439329*1950271*380675809*519258631*24378360481)=1243596271*p166 (6^447+1)/(6^149+1)/31=17334857534194004624977*p209 6,810L:((6^135+1)^2-(6^135+1)*6^68+6^135)/1047532535514129255363516988891792003940353=1572593941*326587879716262741*p142 6,810M:((6^135+1)^2+(6^135+1)*6^68+6^135)/(39661919912737*26411543817830547235357966561)=1621*320435243187841*178880165276055876541*1141474040947210592672032861*310079312179893621392715264037923541*p68 6,834L:((6^139+1)^2-(6^139+1)*6^70+6^139)/13=1669*11677*241861*51797935791539645260219370581*p174 6,846M:((6^141+1)^2+(6^141+1)*6^71+6^141)/55117=3300192135812809*p200 6,882L:((6^147+1)^2-(6^147+1)*6^74+6^147)/(73*541*12185192600132570384611238029)=42337*3814295437*319550543929*14068970619229*90886564008812535191945719129*p129 6,894L:((6^149+1)^2-(6^149+1)*6^75+6^149)/13=1789*25033*4205688901*2127099636560937932152252309*p187 (7^411-1)/(7^137-1)/(3*19)=575401*9712753*109781389*329437051*27500724319*8350989090751*21597040515507988471*p158 (7^415-1)/(7^83-1)/2801=11621*58704241*3332338781*239838191551978888291*472147873240510126308071*p212 (7^427-1)/(7^61-1)/(29*4733)=165649067659909*p290 (7^435-1)/(7^145-1)/(3*19*31*159871*2576743207*196915704073465747*358475907408445923469)=76561*84391*59796922604452021*87163539657316351*144975423216697187157750841*3018134674629431661103715628858892719721420190476720595671*p63(ggnfs 19-23 marzo 2009) (7^441-1)/(7^147-1)/(3*39331)=3186701281*7973534017*216238581721*479133961673103577*2643999917660728787808396988849*c165 I am now working on the cofactor c165 (snfs difficulty 213) but it needs time. Thank you very much. Valerio (7^410+1)/(7^82+1)/(5*281*4021)=419338981*215733452138918239324341601*p236 (7^420+1)/(7^140+1)/(73*193*409*3361*4894546210513*2232059760329037670187857)=18481*12913561*14562241*79419989041*85560261859655897641*p140 (7^423-1)/(7^141-1)/(3*37*1063)=4904535443967721*74344711992811394446323372079*123073308832989689693844493084849*156035321945212360260109221423643393*5719374442762619138354952842044488751*236797435223187931175815185235335037279*p47 (7^424+1)/(7^8+1)=4241*103457*1044737*129143176241617*100941848531314056778097*918670131104163860047361*881100735006644311209917728729921*p243 (7^433+1)/8=759942972667*509586366687974529787*2084523936688829692709*5761806214962941486129716857597161*p278 (7^435+1)/(7^145+1)/(43*6568801*5406066031*1284564941030772067*34720058992462423813)=195458551*27841766971*430783787382438799452691*276643923707698106990518186402292641*p112 (7^437+1)/(7^23+1)/(351121*4058036683)=772616187911*p323 7,847M:((7^121+1)^3+7^61*(7^242+7^121+1))/(911*258576319*32817262777539703) =3159704810685347*4782096685998787*106738675233569048375019161*p222 7,875L:((7^125+1)^3-7^63*(7^250+7^125+1))/(421*911*12128131*518511805672937017706047048027197369743872095240751)=494592001*28023084251*476856731468823464501*p214 (11^305-1)/(11^61-1)/(5*3221)=99431*23907106086511*p232 (11^321-1)/(11^107-1)/(7*19)=998311*111525083440182079*565907075298149659147*297571581361738410622071889*2829934760722845283610290789677553*8094394036023237528697722819032319787*p81 (11^333-1)/(11^111-1)/1772893=2657295303701652382339*11781861706172482362289*14919583772234049458190757699987*p151 (11^345-1)/(11^115-1)/(7*19*195019441*139*8209475377*5283012903770196631383821046101707)=4831*138213632971*355201733241601*116563335563581*279365907858391*868298599610923233331*p105 (11^303+1)/(11^101+1)/(3*37)=1213*35759258032327*p192 (11^315+1)/(11^105+1)/(3*590077*181*631*86306335830799838011*3304981*468843103*71596275661*278853374647)=390943731740941*652173369161401023151532831652601*p103 (11^322+1)/(11^46+1)/(29*1933*55527473)=17161957*77119626524711597*p251 (11^330+1)/(11^110+1)/(13*1117*9863099401*46266666682081629547022793157801) =169786321*46329453543600481*p159 (11^335+1)/(11^67+1)/13421=160362548659171*56073052565336146651*1556839871447009376471730140581*p211 (11^339+1)/(11^113+1)/(3*37)=553249*68894480469960903562541911*p202 (11^342+1)/(11^114+1)/3138426605161=2053*47881*59373696615049*1797862738052870017281253*p179 (11^350+1)/(11^70+1)/(101*2248313994601*1993099906542710819727884501)=701*322001*458501*56956081489652801*14903525246049041675501*p197 (12^302+1)/(12^2+1)=68302133*120323603034409*22440488732337254955872775557*p274 (12^306+1)/(12^102+1)/(73*122138321401)=11293220089*p198 (12^308+1)/(12^44+1)/79493013628273739882868481=617*7383259577*110613781433*1851671052617*1217372772042875183569681*p199 (12^310+1)/(12^62+1)/(5*85403261)=316201*2776950660064804328381*p233 (12^314+1)/(12^2+1)=1021129*54195773*2727836693*795165844829*42801421835309*p288 (12^316+1)/(12^4+1)=3793*113761*34880894473637521*p312 (12^317+1)/13=5182951*552367429*5950562514894050197*198062718216351406927*p287 (12^334+1)/(12^2+1)=60847235569*246573441033636701*267148186898890490634673*p307 12,609L:(12^203+1-2^203*3^102)/(7*7*43*17011*2032959451*1390046661396154093141)=223392163*1160863969736521*p158 12,615L:(12^205+1-2^205*3^103)/(7*35671*2631304807*31383200376667*305115772972736748643)=6151*78721*8249098321*2884308215671*281244358113238895941*p121 12,615M:(12^205+1+2^205*3^103)/(19*31*421*6768262271978677*1371514197393197319841009039)=3691*55351*356701*1591621*171466377571*25050543163651*20180587175658253004616750165991*p97 12,621M:(12^207+1+2^207*3^104)/(271*487*39097)=4969*33231611842309*162867909058707122777800081*70119412232223755484393713461*p142 12,633M:(12^211+1+2^211*3^106)/7=80829037*48905430935845333*49891472380880789396701818619*p174 12,651M:(12^217+1+2^217*3^109)/(19*1885339*5209*24221034391*1188277798029874021)=24990802831*36028936189*561132068323*360479288619067687307617*411875176065360161587300408902901*p106 12,657M:(12^219+1+2^219*3^110)/1801=1646867935776737809275643*3877144229695685240495907541*p182 12,687M:(12^229+1+2^229*3^115)/19=17863*496117051*507278904810174576049*p213 12,693L:(12^231+1-2^231*3^116)/(127*1801*2971*79277059*2537121133*76659283352997582300893022139)=117811*5907133*853926587452519813*210079688110361883223974683653843*p133 from Valerio Sisti, Scuola del Corso Arezzo, Italy Mon May 11 04:11:25 2009 Dear Sam I completed some more entries from extended Cunningham tables, mainly with GMP-ECM, GGNFS and Msieve. (6^420+1)/(6^140+1)/(13441*1678321*1176362433121*592575109627400042641* 19100900655540830489319601)=32182332471663935745292081* 181133707436328143240762088473323830615494216665374481*p71 (ggnfs 4th-13th April 2009) (11^345+1)/(11^115+1)/(3*31*37*7537711*691*394648951*18013255921* 932225927887*1577386579003)=10493015204281*82093337481199195111* 4653540256149079393531* 268329760256288474139750611836167259046916142267161253213874311*p67 (ggnfs 18th April-5th May 2009) (11^343+1)/(11^49+1)=1373*80764846592083051952741744555923*p272 (12^311+1)/13=108713161*16233257671*3322500172913625684217*30507907277117 231118739*142237120015583282646410101*p247 Best regards Valerio Sisti Date: Tue, 5 Jan 2010 06:09:05 +0000 (GMT) Subject: An Aurifeuillian from the extended Cunningham tables from Valerio Sisti, Scuola del Corso Arezzo Italy Dear Professor Wagstaff I submit the complete factoring of 11,693M (with primitive part c188): c188 = p15 * p32 * p70 * p71 p15 = 714386046101113 (ECM) p32 = 62374753101477731854227222815497 (ECM) p70 = 9612514200467663770065345284443055909719868124964766522328421150545733 p71 = 60150653588398421957391619139283963646277351554269738918804268286919877 Best regards, Valerio Sisti Date: Tue, 5 Jan 2010 06:11:47 +0000 (GMT) Subject: 3,615- factorized from Valerio Sisti, Scuola del Corso Arezzo Italy Dear Professor Wagstaff The primitive part c153 of 3^615-1 had the known factor 1195561. I completed the cofactor c147: c147 = p58 * p90 p58 = 1362086797533369884718343037628515311025580176953784595301 p90=421633347816774477312568512935355512995267621932928675226625496883164556883743599102159141 done with GGNFS + Msieve, snfs mode, in almost 4 days: N=c147=57430121646102382079246764968171887055701372190577435801908712508257361\ 1123677046144769077525732805190112278443849406848562906182290859253982796441 SNFS difficulty: 156 digits. Best regards, Valerio Sisti Fri Apr 23 22:18:03 2010 From: Juno Fukos Subject: New factors of 10,420+ Dear Sam Wagstaff, I have factored 10,420+ using GGNFS/Msieve. Here are the results: Number: c150 N = 191413141591299314411353617644492718709042398621746359743575335167576218516274501587918765785208170431266534615378694736680781077885837943706833300081 (150 digits) Divisors found: r1=1146780383632163283649175272843774050715065531735480891145232027761 (pp67) r2=166913512232431273140362987966641859731500109846278942036790211593884632236221381121 (pp84) Date: Wed, 26 May 2010 00:06:48 -0700 (PDT) Subject: 3,651- completed from Valerio Sisti, Scuola del Corso, Arezzo, Italy Dear Professor Wagstaff I have decomposed the cofactor c153 of 3,651- from the extended Cunningham tables: C153 = p62 . p91 p62 = 96204592550401464761305884120719794990493457611613148273892749 Using GGNFS and Msieve, snfs difficulty 177 9993 3, 775- c282 10739917689782934291348634826555020368414408001. c236 9993 3, 705- c163 17925163261886613890595611153971449075737880597365455065081252926739721. p93 Batalov 9993 3, 793- c253 16697555282285598006569362183247214662839081861. c207 9993 3, 711- c179 3297217946493332412969462353064559561775620666597919718037. p121 Patel 9993 3, 621- c162 56037810170128607485215702998215395873753992381472041909493199033. p97 Sisti 9993 3, 771- c179 6349458818586896189136555241554887684748673593241. p130 Patel 9993 3, 713- c232 3746121650449359706373304838111671353932176369894346189979. c175 Patel 9993 3, 601- c267 280046742341301374601452645724586373020825738763. p219 Zimmermann 8883 3,1545L c183 47226070700056986973989716338395248861101. p142 Batalov 8883 3,1467M c233 1467369063868139907894170198267347695043. p193 Batalov 8883 3,1227L c176 1884829770214494850445830337981704304388104953. p131 Batalov 8883 3,1317M c150 15625305790155774800504213544664082865394459261063. p100 Batalov 8883 3,1551M c196 24323442816253703577801984883577228485909. c155 Batalov 8883 3, 737+ c314 14263424804201470751933276338500698101637395259181896676103. c256 Patel 8883 3, 601+ c225 99662693768317340925902417065182211496514913533377563. c172 Zimmermann 8883 3, 614+ c247 3700423355888888433267275227637393533393. p207 Zimmermann 8883 3,1497L c211 4325949238806739927299209368953885473640314221453. c162 Batalov 8883 3, 751+ c292 14438399185507795836391026829363711126699381. p248 Patel 8883 3, 800+ c292 828612745984947326236664694266987201. p256 Zimmermann 8883 3, 745+ c243 123638783293460451899415516617326147238701. c202 Crombie 8883 3, 734+ c239 19346193355268919991963502211565571652210317. c196 Crombie 8883 3, 754+ c298 404394435255301288048281718492833550420133. c256 Patel 8883 3, 643+ c261 509187561404661757367729674058316068477384580347881. c210 Wagstaff 8883 3, 655+ c213 17829644652744215879033807026959425807505451. p170 Wagstaff 8883 3, 664+ c238 31675278328982904528911989463021073249761534129. c192 Wagstaff 8883 3, 678+ c185 20519399520866300834222618426550131918931481. c142 Crombie ecm 8883 3, 710+ c208 1587739069088177069703605488276164333544784041. c163 Wagstaff 8883 3, 736+ c239 11896026625793266610838943451786977052993729. c196 Wagstaff 8883 3, 738+ c192 28326013908267967686705873444514300194671894689. c146 Timofeev 8883 3, 742+ c210 160083013525563915840629955214963515462459001. c166 Wagstaff 8883 3, 756+ c202 235659123611028760889174187672411908116033. p161 Timofeev 8883 3, 768+ c207 40954545504988911659715489116607926436750337.165456058625467287980204466925838136186989569. c119 Wagstaff 8883 3, 768+ c119 91730834648442264377552298732808331695683871942657. p69 Crombie 8883 3, 770+ c212 43096959793032445548903348494877685833802855201. c166 Zimmermann 8883 3,1551L c220 251732260937427449284221399869569351765747869364693. c169 Wagstaff 8883 3,1563L c197 122709649224812489003719050561751333767918697. p153 Wagstaff 8883 3,1593M c203 651801120376464912317703961852338147792701829163. c155 Wagstaff 8883 3,1491M c186 1336666262860734148823336429211753277097394853. p141 Wagstaff 8883 3, 613+ c287 582664694022060378487303494994260032536305143468203. p236 Crombie 8883 3, 640+ c199 13076941325455482829912264905750890970035910385026138881. p144 Wagstaff 8883 3, 736+ c196 1247036742297703166908159202955583952202290499340646473620161. c136 Wagstaff 8883 3,1419L c189 11703406430266218978257490461953503553682840367379. p140 Wagstaff 8883 3,1521L c181 431270705707474469926387253492102092723171. p139 Wagstaff 8883 3, 782+ c180 3396702861857272322078479657554031154429684440074961. p129 Wagstaff 8883 3,1257L c179 41331010257787158945317134169652726706443368869. p133 Wagstaff 8883 3,1383L c176 1182718958128495494468566947747280615372427102019. p128 Wagstaff 8883 3, 601+ c172 86902355074724783760880315140535804855654542209233. p122 Wagstaff 8883 3, 770+ c166 3901270012592353889488393715434456266067911442114901. p114 Wagstaff 8883 3,1353L c163 83613362115293179644194965306446000845497946511165006709. p107 Wagstaff 8883 3,1497L c162 18121221314230958534921272566638481354835724027233. p113 Wagstaff 8883 3,1593M c155 89984026679224734202841571611513508860907497599083631. p102 Wagstaff 8883 3, 678+ c142 4958516442623153717590015032806345495942226285172417. p90 Wagstaff 8883 3,1389L c148 95994604310948122947970710957774523366749829616603023. p95 Wagstaff 8883 3, 680+ c197 67755248611875460378079722752844769046697142426312561. p145 Crombie 8883 3, 736+ c136 452706629830083000089483652685969343006665451735378081077678465217. p71 Sisti gnfs 8883 3,1227M c166 239824552005056235492614325111551457389894619409731643096859591929672237. p95 Becker snfs 8883 3,1233L c183 13353572643988247658608034704873943700955712637. c136 te Riele Reported by Raman: p55 factor = 5198395892876421104415109549087087419559080537214372111 from M2269 p56 factor = 10788426156438350117334292343137689257142387557947087583 from M1657 p57 factor = 112493750443412941745410571996247741731544451845539488817 from M1669 by Dmitry Domanov about one year ago 9993 3, 647- c282 442835641420911902056735643278356653800144245791. p235 CWI 9993 3, 649- c151 15085422068047701255996957660890445982732633519169170463921377. p90 Shi Bai gnfs 9993 3, 753- c203 520007425071396254516306885057657287480573719509149. p152 Zimmermann 9993 3, 793- c207 281917997457114791804117679712996794806843175202151. p157 Zimmermann 9993 3, 781- c254 7780641680178781705992580957454350040047182204553. p205 Zimmermann 9993 3, 773- c353 51753676317054169356502097758181015861805520123259. c303 Zimmermann 9993 3, 701- c311 23637385035979072308469324277209913925678054439921. c261 Zimmermann ECMNET 8883 3,1449L c163 32066039581084608234530436622210937908724090089606941026078750243892289807051. p86 Sisti snfs 8883 3,1233L c136 55689495605155319991104394339716588666292932422482577. p84 Sisti gnfs 8883 3, 652+ c236 232583871442577064636968324408043794796584298649722896548157321. p174 Batalov ECMNET 8883 3,1401L c147 272274988033889335721484807373062503985916595364448604887. p90 te Riele ECMNET 8883 3,1515L c173 27061274672708699326609768156777363988042527261853049427552775878973839531215357631. p90 Sisti snfs 8883 3, 617+ c286 17236983499017921972849595101062911347678496967884099. c234 Crombie ECMNET 8883 3, 738+ c146 4798828679466307055106930246665859446886573362311480873. p91 Crombie ECMNET 8883 3, 636+ c183 2043251484963900577270976557432899165759873259654116392674129. p123 Sisti snfs Here it is: 2538207129840687799335203259492870476186248896616401346500027311795983 divides 2^1237-1. This is the first factor of this number, but, unfortunately, the cofactor is composite. We (Joppe Bos, Thorsten Kleinjung, Arjen Lenstra, Peter Montgomery) did roughly 66k curves with B1=3*10^9 on PS3s and stage 2 on PCs as before. Best regards, Thorsten GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Resuming ECM residue saved by jwbos@node-13-2.ps3 with GMP-ECM 5.0 on Fri Oct 8 05:00:09 2010 Input number is 2366489796864789032480357565728828726290717497082983937916449656405258806369911394088430697987024401491549182072567647944966567194643054087496217699862727559530896885323550201467965814495433630889456121746591136618847867145529671430941221247948819903224909668395221348996168804894354162721862128794536784391099950472185019186030884950180952280079066183529036357120894697471 (373 digits) Using B1=3000000000-3000000000, B2=103971375307818, polynomial x^1, sigma=3000086787 Step 1 took 0ms Step 2********** Factor found in step 2: 2538207129840687799335203259492870476186248896616401346500027311795983 Found probable prime factor of 70 digits: 2538207129840687799335203259492870476186248896616401346500027311795983 Composite cofactor 932346997627937198512116805585638652223533192516806816522982865866804199262267590070758266268742758283545150004345986721379992894347882545052483695173645594473520682900937642680132877292150643356579486299211525438560741941531670625397281199369604215535391846857906233364905825622441048803673998858526737 has 303 digits > From Serge Batalov Tue Dec 7 17:45:04 2010 On Dec 6, 2010 (Yousuke Koide) found a factor for 10^466+1 -- Phi(932,10): c450(3733444597......) = 31306780512964774446383151831688280696877739051661 * c401(1192535462......) Forwarding a bit of news from the repunit site: http://homepage2.nifty.com/m_kamada/math/Phin10changes.htm "-- Dec 7, 2010 (Polybius) -- Factor of 10,501+ Phi_1002(10): c247(6679009732......) = 3991682749552894902673962957124418797917278009299 * p199(1673231604......) # Phi_1002(10) is the 1010th factorized number of the form Phi_n(10) (n<=100000, L and M are combined)." The p47 for the same composite was already known; now a p49 finishes it. This is only relevant for the http://homes.cerias.purdue.edu/~ssw/cun/xtend/other page, and possibly for the records site. --Serge I've now read that 10^522+1 is now fully factored by ECM with a p50: credit nenym@yoyo "n=1044: c269(1791140799......) = 60567370378102931159842571650342558304322238516849 * p219(2957270207......) # Phi_1044(10) is the 1012th factorized number of the form Phi_n(10) (n<=100000, L and M are combined)." Ref.: http://www.rechenkraft.net/yoyo/y_factors_ecm.php http://homepage2.nifty.com/m_kamada/math/Phin10changes.htm -S ________________________________ > From: Serge Batalov 8883 3, 748+ c254 183162281447510307948409550311054675916423719399249. c204 Zimmermann ECMNET 8883 3, 742+ c166 13473362672263926237309242100811578883708481789425002001. p111 Wagstaff ECMNET 8883 3,1443L c154 362466230088787245203725150695608196446507416763500471557553488672973. p86 Wagstaff ECMNET 8883 3,1551L c169 9566060032790010874483547376656893826943127817285473. p117 Wagstaff ECMNET 8883 3,1287M c147 229137440902743554855001003266555708431363896185295129440398260574501. p79 Sisti gnfs 8883 3, 733+ c320 14823684702981475009592461845932731578396587316265543. p268 Zimmermann ECMNET 8883 3, 634+ c302 472401162592505264461751488855196441634426625661. c254 Zimmermann ECMNET 8883 3,1575L c167 320646300022948794802147545696597591103896898277711821386517638335251. p99 Becker snfs 8883 3, 726+ c186 23191950196768230363778981723034199011516405519886553. p134 Zimmermann ECMNET 8883 3, 654+ c177 768798186873372583863320060009556072338616327096617569. c123 Zimmermann ECMNET 8883 3, 654+ c123 146721718871925945765916800880087575792414767765049463049929. p64 Zimmermann GNFS CADO-NFS 8883 3,1251M c162 335381883455915280694509000726623090162099379489326453135770648145268654661. p87 Sisti snfs 8883 3, 757+ c334 17554598519995405810046176003170689881127776042411117087. c279 Wagstaff ECMNET 8883 3, 632+ c274 594548574449554037511134980694607790101788345550302129. c220 Zimmermann 8883 3, 628+ c298 126170538473855459870995755264812959134139669176057183246713. p239 Wagstaff ECMNET 8883 3,1539M c232 161691714495465128664479087883100410975673390632829. p182 Zimmermann ECMNET 8883 3,1347L c214 228988172224679462242791599307571660953770400768266015782650669023522386399550060982667297. p125 Becker snfs 8883 3,1293M c166 1378336345766620653207902647162085597271536812015328316153926217078504281624475739. p84 Sisti snfs 8883 3, 688+ c269 207559527409737613969927087202358711000070985004550657. c215 Wagstaff ECMNET 8883 3, 688+ c215 6391497281666786260897813852145132751366501900615904106113. c158 Wagstaff ECMNET 8883 3, 631+ c277 3527519602384687600760560181416106278756256864901236966389. c219 Wagstaff ECMNET 8883 3,1545M c173 120827206310996826267591035767856760692282690273958361228231. p113 Sisti snfs 8883 3, 703+ c268 364412904077207703548678842096328173270446766681001630691841. c208 Wagstaff ECMNET 8883 3, 620+ c215 887475966429509881965989304017966887321042613117385401. p161 Zimmermann ECMNET 8883 3, 616+ c216 360305320299000552852773132726625211676479337783057. c165 Zimmermann ECMNET 8883 3, 634+ c254 8337154692872113830290689381191142463833018052450178581. c199 Wagstaff ECMNET 8883 3, 634+ c199 7213820902434963364151186560559158420921586339845038328468305677. p136 Wagstaff ECMNET 8883 3,1509L c151 27459510724289498116813774473856506741721424907963276819187958030449. p84 Sisti gnfs 8883 3,1581L c226 82460484027281186047102892108013807301830647372983199436523. p167 Wagstaff ECMNET 8883 3, 644+ c240 23338277219334749889268159571245434765900455868304561. p187 Wagstaff ECMNET 8883 3,1311M c180 2565529198795631969709544404900654938238819298341757226219744091905156200806131899. p98 Sisti snfs 8883 3, 622+ c289 614601335704406847014819901955802334466227429378451201. p235 Zimmermann ECMNET 8883 3, 700+ c193 411400277307233545355500531285558665653225531422721617201. c136 Wagstaff ECMNET 9993 3, 777- c170 2571962138124987934147419817293123173577059740948079871281409261069982357. p97 Becker snfs 9993 3, 769- c347 54881494789070208618554690004702274737120782891528221. c294 Wagstaff ECMNET 9993 3, 657- c196 223246955099680367178517299116228058686491827406406309030993178576248812126197773842306861. p106 Sisti snfs 9993 3, 695- c242 1415085487923782842786280300887039057567659793736322663601. p185 Wagstaff ECMNET From Mon May 2 21:32:31 2011 From: Serge Batalov Hi Sam, These two factors are for the http://homes.cerias.purdue.edu/~ssw/cun/xtend/other webpage. ___________________ #1. I have read that 10^411+1 was now fully factored. (I am quoting from M.Kamada's pages, verbatim) -- May 1, 2011 (Yousuke Koide) -- n=822: c188(2756648081......) = 135238230631321944924974183810091904866809004766932500659 * p132(2038364498......) (Phi(822,10) pertains to the 10,411+ cofactor) So, this was done by ECM, not by SNFS! A fairly large p57. By Yousuke Koide. ______________ #2. I have reduced 5^457-1 cofactor from a c213 to c161, but this p53 factor may be already known. If not, here it is: Input number is Phi(457,5)/13711/455162861/137015205580881761325799/476936039068611477153641752340911/26628842186290124810309584480767097781 (213 digits) Using B1=11000000, B2=46843330180, polynomial Dickson(12), sigma=2916844944 Step 1 took 45448ms Step 2 took 20310ms ********** Factor found in step 2: 36725891754169847010253630086789677124279381501342379 Found probable prime factor of 53 digits: 36725891754169847010253630086789677124279381501342379 Composite cofactor 16843894005221105437716198112357240078989243121219959292084137021577729111446498281956648873916336318219657046004620998275788511023411721467310781529960292872301 has 161 digits This is practically the 5th hole in 5- table, and it has been a gnfs c213 even before the factor. Now, it is a practical (for the Lehigh cluster) gnfs c161. I'd propose that we reserve it for Batalov+Dodson gnfs, as soon as it is officially added. Best regards, --Serge Batalov Date: Mon, 3 Oct 2011 12:36:35 -0700 (PDT) From: Serge Batalov Subject: Fw: 10^651+1 is fully factored Hi Sam, For the extended tables: 10^651+1 is fully factored. Input number is Phi(1302,10)/1303/10439437 (350 digits) >Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=4183461552 >Step 1 took 388800ms >Step 2 took 89448ms >********** Factor found in step 2: 25540795299896197421506059449931706821324283570117 >Found probable prime factor of 50 digits: 25540795299896197421506059449931706821324283570117 >Probable prime cofactor (Phi(1302,10)/1303/10439437)/25540795299896197421506059449931706821324283570117 has 301 digits Best regards, --Serge Date: Mon, 21 Nov 2011 07:59:22 +0000 (GMT) From: Dagobert Dexter Subject: 7,441- c165 (file "other.txt") completed from Valerio Sisti to Sam Wagstaff By ggnfs & msieve, snfs difficulty 193, I have completed the cofactor c165 of 7,441- c165 = p48 . p118 p48 = 148604037346679149806473694800108374797541959361 Sincerely yours Valerio 9993 3, 723- c168 844419612452198561310720080038799341972811718390811373415844777. p105 Wagstaff ECMNET 9993 3, 731- c321 83409037264696307690489614635052488166993297850365365503. c265 Zimmermann ECMNET 9993 3, 687- c218 1045963705876214920796627188811335128227156263690344876782164668343294332064615217521. p134 Sisti snfs 9993 3, 681- c216 17912376123853772222915593610277542408026048271683746540522410033644069. c146 Sisti snfs 9993 3, 681- c146 1297599233219531151503255035280818381563769714974946578770599377350713429. p74 Sisti snfs 8883 3, 694+ c316 1699056397186614791135374117017333664675788452845338373009. p259 Zimmermann ECMNET 8883 3, 700+ c136 4345812429269618584351954732947672774394903738484010733210801. p76 Sisti gnfs 8883 3, 696+ c185 5273401289202779683808904079887693969121468228193849819329. p127 Wagstaff ECMNET 8883 3, 688+ c158 1388239215502726549524438440497854225949903590564939687586177. p97 Wagstaff ECMNET 8883 3,1551M c155 5210457042762754918650165277316177454890893470999329279279079799. p92 Sisti gnfs 8883 3,1341L c185 2611483851240732754723755400040767425960184479694677504793092352664077819. p113 Sisti snfs 8883 3,1377M c207 4149318348880416504275030292599179694974631641579671025045152106665845347. p134 Sisti snfs 8883 3,1413L c224 3399257905066384711028775506606457340148614808185831222197895970158237266603378649324399. p136 Sisti snfs 8883 3, 798+ c163 142790206314095560201908548053753693328675245014044946751986351525783246421172209. p82 Sisti snfs From: Raman Date: Mon, 9 Apr 2012 22:11:40 +0530 Subject: the 10^455-1 factors To: Samuel S Wagstaff , Sun Jan 29 00:17:21 2012 prp75 factor: 139397282236319122569927698220829009751930337603755594300386510230285560351 Sun Jan 29 00:17:21 2012 prp92 factor: 32647385051525041661479792654516355809315046496410663779745524799749707387460867800164362111 Chris K Dear Michael, > Date: Thu, 12 Apr 2012 14:07:59 +0200 > From: michael > > Finally I found a nice factor: > > 56486824832476092597936178673369952799696200730531645364799743 | 2^2161-1 > > Sigma=5333535472170270 > B1=44000000 > > Kind regards, > Michael Kenn > http://www.kenn.at congratulations! This is the 7th largest so far in 2012, and the 44th largest ever found. Did you report your factor to Will Edgington? See http://www.garlic.com/~wedgingt/mersenne.html. Best regards, Paul PS: congratulations for your cycling records!