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, 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, 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 at cyclades.com.br 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 (at) cyclades.com.br Software Engineer - Cyclades Brasil Phone: +55 11 5033-3365 - Fax: +55 11 5033-3388 http://www.cyclades.com.br From alexander.kruppa at mytum.de 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 mail.verser.org 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