Factorization of 388...887

Table of contents 目次

About 388...887 388...887 について
Prime numbers of the form 388...887 388...887 の形の素数
Factor table of 388...887 388...887 の素因数分解表
Related links 関連リンク

1. About 388...887 388...887 について

1.1. Classification 分類

Quasi-repdigit of the form ABB...BBC ABB...BBC の形のクワージレプディジット (Quasi-repdigit)

1.2. Sequence 数列

38w7 = { 37, 387, 3887, 38887, 388887, 3888887, 38888887, 388888887, 3888888887, 38888888887, … }

2. Prime numbers of the form 388...887 388...887 の形の素数

2.2. Known (probable) prime numbers 既知の (おそらく) 素数

35×10¹-179 = 37 is prime. は素数です。 (Makoto Kamada / December 1, 2004 2004 年 12 月 1 日)
35×10⁶-179 = 3888887 is prime. は素数です。 (Makoto Kamada / December 1, 2004 2004 年 12 月 1 日)
35×10¹⁰¹⁷⁶-179 = 3(8)₁₀₁₇₅7_<10177> is PRP. はおそらく素数です。 (Serge Batalov / PFGW / October 13, 2008 2008 年 10 月 13 日)
35×10⁵⁶⁸⁹⁸-179 = 3(8)₅₆₈₉₇7_<56899> is PRP. はおそらく素数です。 (Serge Batalov / PFGW / February 28, 2009 2009 年 2 月 28 日)

2.3. Range of search 捜索範囲

n≤30000 / Completed 終了
n≤50000 / Completed 終了 / Erik Branger / May 1, 2013 2013 年 5 月 1 日
n≤100000 / Completed 終了 / Bob Price / March 30, 2015 2015 年 3 月 30 日

2.4. Prime factors that appear periodically 周期的に現れる素因数

Cofactors are written verbosely to clarify that they are integers. 補因子はそれらが整数であることを明確にするために冗長に書かれています。

35×10^3k+1-179 = 37×(35×10¹-179×37+35×10×10³-19×37×k-1Σm=010^3m)
35×10^3k+2-179 = 3×(35×10²-179×3+35×10²×10³-19×3×k-1Σm=010^3m)
35×10^6k+3-179 = 13×(35×10³-179×13+35×10³×10⁶-19×13×k-1Σm=010^6m)
35×10^18k+12-179 = 19×(35×10¹²-179×19+35×10¹²×10¹⁸-19×19×k-1Σm=010^18m)
35×10^21k+2-179 = 43×(35×10²-179×43+35×10²×10²¹-19×43×k-1Σm=010^21m)
35×10^22k+3-179 = 23×(35×10³-179×23+35×10³×10²²-19×23×k-1Σm=010^22m)
35×10^28k+25-179 = 29×(35×10²⁵-179×29+35×10²⁵×10²⁸-19×29×k-1Σm=010^28m)
35×10^33k+14-179 = 67×(35×10¹⁴-179×67+35×10¹⁴×10³³-19×67×k-1Σm=010^33m)
35×10^35k+15-179 = 71×(35×10¹⁵-179×71+35×10¹⁵×10³⁵-19×71×k-1Σm=010^35m)
35×10^46k+33-179 = 47×(35×10³³-179×47+35×10³³×10⁴⁶-19×47×k-1Σm=010^46m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 4.82%. 捜索難易度 (周期的に現れる素因数で割り切れない項の割合) は 4.82% です。

3. Factor table of 388...887 388...887 の素因数分解表

3.2. Range of factorization 分解範囲

n≤100 / Completed 終了 / December 1, 2004 2004 年 12 月 1 日
n≤150 / Completed 終了 / December 9, 2008 2008 年 12 月 9 日
n≤200 / Completed 終了 / March 26, 2021 2021 年 3 月 26 日
n≤300 / Remaining 55 残り 55

3.3. Terms that have not been factored yet まだ分解されていない項

n=214, 224, 228, 230, 231, 233, 234, 235, 237, 238, 239, 240, 243, 246, 247, 251, 252, 253, 254, 255, 256, 259, 260, 261, 262, 263, 265, 266, 267, 269, 270, 271, 273, 274, 275, 276, 277, 278, 279, 280, 282, 283, 285, 287, 288, 289, 291, 292, 293, 294, 295, 297, 298, 299, 300 (55/300)

3.4. Factor table 素因数分解表

35×10¹-179 = 37 = definitely prime number 素数

35×10²-179 = 387 = 3² × 43

35×10³-179 = 3887 = 13² × 23

35×10⁴-179 = 38887 = 37 × 1051

35×10⁵-179 = 388887 = 3 × 129629

35×10⁶-179 = 3888887 = definitely prime number 素数

35×10⁷-179 = 38888887 = 37 × 1051051

35×10⁸-179 = 388888887 = 3 × 277 × 467977

35×10⁹-179 = 3888888887_<10> = 13 × 14891 × 20089

35×10¹⁰-179 = 38888888887_<11> = 37 × 2063 × 509477

35×10¹¹-179 = 388888888887_<12> = 3³ × 383 × 419 × 89753

35×10¹²-179 = 3888888888887_<13> = 19 × 61 × 3355382993_<10>

35×10¹³-179 = 38888888888887_<14> = 37 × 691 × 1663 × 914647

35×10¹⁴-179 = 388888888888887_<15> = 3 × 67 × 129361 × 14956367

35×10¹⁵-179 = 3888888888888887_<16> = 13 × 71 × 1413371 × 2981039

35×10¹⁶-179 = 38888888888888887_<17> = 37 × 6043 × 8783 × 19802879

35×10¹⁷-179 = 388888888888888887_<18> = 3 × 51769 × 872747 × 2869103

35×10¹⁸-179 = 3888888888888888887_<19> = 135007 × 860399 × 33478759

35×10¹⁹-179 = 38888888888888888887_<20> = 37 × 1051051051051051051_<19>

35×10²⁰-179 = 388888888888888888887_<21> = 3² × 6047 × 33199 × 215237557231_<12>

35×10²¹-179 = 3888888888888888888887_<22> = 13 × 16487 × 17390353 × 1043355109_<10>

35×10²²-179 = 38888888888888888888887_<23> = 37 × 391381481 × 2685489993971_<13>

35×10²³-179 = 388888888888888888888887_<24> = 3 × 43 × 283 × 10652447171470920341_<20>

35×10²⁴-179 = 3888888888888888888888887_<25> = 7129 × 15439 × 108179809 × 326611553

35×10²⁵-179 = 38888888888888888888888887_<26> = 23 × 29 × 37 × 109 × 14456776901242741717_<20>

35×10²⁶-179 = 388888888888888888888888887_<27> = 3 × 4187021 × 30959870903353393649_<20>

35×10²⁷-179 = 3888888888888888888888888887_<28> = 13 × 9101317 × 32868352914781360247_<20>

35×10²⁸-179 = 38888888888888888888888888887_<29> = 37 × 10739 × 97872339235594659749609_<23>

35×10²⁹-179 = 388888888888888888888888888887_<30> = 3² × 600293 × 71981310032284028871251_<23>

35×10³⁰-179 = 3888888888888888888888888888887_<31> = 19 × 157 × 797 × 33526061 × 48790068661048217_<17>

35×10³¹-179 = 38888888888888888888888888888887_<32> = 37 × 2587472639_<10> × 406207600114859050709_<21>

35×10³²-179 = 388888888888888888888888888888887_<33> = 3 × 929168476471_<12> × 139511437282036829099_<21>

35×10³³-179 = 3888888888888888888888888888888887_<34> = 13 × 47² × 135421140400769192077476369011_<30>

35×10³⁴-179 = 38888888888888888888888888888888887_<35> = 37 × 197 × 4881785049241_<13> × 1092896239651373063_<19>

35×10³⁵-179 = 388888888888888888888888888888888887_<36> = 3 × 487 × 1447 × 142873 × 1287527826266780084671957_<25>

35×10³⁶-179 = 3888888888888888888888888888888888887_<37> = 233 × 24412859797_<11> × 683676979736435603413987_<24>

35×10³⁷-179 = 38888888888888888888888888888888888887_<38> = 37 × 8039 × 130744004360125768261108477553309_<33>

35×10³⁸-179 = 388888888888888888888888888888888888887_<39> = 3³ × 113 × 1451 × 87844770960948255690226609139887_<32>

35×10³⁹-179 = 3888888888888888888888888888888888888887_<40> = 13 × 299145299145299145299145299145299145299_<39>

35×10⁴⁰-179 = 38888888888888888888888888888888888888887_<41> = 37 × 30567917507971241_<17> × 34384123510440870431411_<23>

35×10⁴¹-179 = 388888888888888888888888888888888888888887_<42> = 3 × 293 × 14269722653_<11> × 31004242681298086898913978701_<29>

35×10⁴²-179 = 3888888888888888888888888888888888888888887_<43> = 260921 × 14904468742986915153969549744516113647_<38>

35×10⁴³-179 = 38888888888888888888888888888888888888888887_<44> = 37 × 313 × 899604927804071_<15> × 3732739199900441898877637_<25>

35×10⁴⁴-179 = 388888888888888888888888888888888888888888887_<45> = 3 × 43 × 22922381620933_<14> × 146286139905713_<15> × 899027353938107_<15>

35×10⁴⁵-179 = 3888888888888888888888888888888888888888888887_<46> = 13 × 427342820031409_<15> × 700012461010372079987843302211_<30>

35×10⁴⁶-179 = 38888888888888888888888888888888888888888888887_<47> = 37 × 1051051051051051051051051051051051051051051051_<46>

35×10⁴⁷-179 = 388888888888888888888888888888888888888888888887_<48> = 3² × 23 × 67 × 4992233 × 5616755768372936599299318666510766331_<37>

35×10⁴⁸-179 = 3888888888888888888888888888888888888888888888887_<49> = 19 × 8521 × 269383 × 1535341 × 58077289039361967990946906383071_<32>

35×10⁴⁹-179 = 38888888888888888888888888888888888888888888888887_<50> = 37 × 126903927546410754881_<21> × 8282257857359577872575294571_<28>

35×10⁵⁰-179 = 388888888888888888888888888888888888888888888888887_<51> = 3 × 71 × 61450644007_<11> × 29711152110875455680488887904403238957_<38>

35×10⁵¹-179 = 3(8)₅₀7_<52> = 13 × 97 × 227³ × 1061 × 4329205573932973_<16> × 57399655242681513715433_<23>

35×10⁵²-179 = 3(8)₅₁7_<53> = 37 × 59 × 257 × 975827 × 71033930414244429563797334988236765586251_<41>

35×10⁵³-179 = 3(8)₅₂7_<54> = 3 × 29 × 174631 × 25596756753428190087044550416480075451633015671_<47>

35×10⁵⁴-179 = 3(8)₅₃7_<55> = 1075259 × 810979564187437_<15> × 1056434632774559_<16> × 4221433068785948471_<19>

35×10⁵⁵-179 = 3(8)₅₄7_<56> = 37 × 883 × 3581 × 2677281553618036187_<19> × 124155150448689990611594499751_<30>

35×10⁵⁶-179 = 3(8)₅₅7_<57> = 3² × 109471 × 110909 × 389352920123_<12> × 9140579165853068513932931852927119_<34>

35×10⁵⁷-179 = 3(8)₅₆7_<58> = 13 × 21893 × 1568070979_<10> × 1020298662479868305959_<22> × 8540511287473581063163_<22>

35×10⁵⁸-179 = 3(8)₅₇7_<59> = 37 × 11200361 × 49135109 × 1909852670788927486496409925951002935384599_<43>

35×10⁵⁹-179 = 3(8)₅₈7_<60> = 3 × 44101 × 2939380731267536555398508642199261459595692379529480729_<55>

35×10⁶⁰-179 = 3(8)₅₉7_<61> = 569 × 1027553176423_<13> × 6651337150713954651762457616061396287971116601_<46>

35×10⁶¹-179 = 3(8)₆₀7_<62> = 37 × 1571 × 3217 × 473642747 × 439082040369250022550290766146991650219547019_<45>

35×10⁶²-179 = 3(8)₆₁7_<63> = 3 × 25505755335937361_<17> × 247725245785280129_<18> × 20516147975616759937033021741_<29>

35×10⁶³-179 = 3(8)₆₂7_<64> = 13 × 179 × 1019 × 6273000062199006360569_<22> × 261444599782618946915537977434121771_<36>

35×10⁶⁴-179 = 3(8)₆₃7_<65> = 37 × 1879 × 559367243773843028765860059101144785019186296461442815886669_<60>

35×10⁶⁵-179 = 3(8)₆₄7_<66> = 3⁴ × 43 × 80449 × 4791681658428493_<16> × 289643277356740962894138693605554089140777_<42>

35×10⁶⁶-179 = 3(8)₆₅7_<67> = 19 × 7304333 × 28021499372098645448486311148889216196013840356552667465281_<59>

35×10⁶⁷-179 = 3(8)₆₆7_<68> = 37 × 349 × 3266047 × 188235763067478377089_<21> × 4898620716697953378326841371537291353_<37>

35×10⁶⁸-179 = 3(8)₆₇7_<69> = 3 × 13997 × 23329001 × 765983849 × 1815132604169_<13> × 285525700390971452020902366242363897_<36>

35×10⁶⁹-179 = 3(8)₆₈7_<70> = 13 × 23 × 1931 × 3499 × 197063 × 9768391123613035201576593886627118296030124433941910379_<55>

35×10⁷⁰-179 = 3(8)₆₉7_<71> = 37 × 6473 × 13309 × 23839414723309_<14> × 511772787997464102720491482864783498179576664427_<48>

35×10⁷¹-179 = 3(8)₇₀7_<72> = 3 × 15013 × 92177774957_<11> × 93672168656692612743693008827024987251334027102456710269_<56>

35×10⁷²-179 = 3(8)₇₁7_<73> = 61 × 285023 × 7850279 × 65611669401559_<14> × 366810423312499695437_<21> × 1183880711999215588426897_<25>

35×10⁷³-179 = 3(8)₇₂7_<74> = 37 × 2312805991_<10> × 55016304698121461936243_<23> × 8260249980392413088836655030853426871727_<40>

35×10⁷⁴-179 = 3(8)₇₃7_<75> = 3² × 2143 × 20163264835842219572193129511530507019696629278212728204950945657120801_<71>

35×10⁷⁵-179 = 3(8)₇₄7_<76> = 13 × 299145299145299145299145299145299145299145299145299145299145299145299145299_<75>

35×10⁷⁶-179 = 3(8)₇₅7_<77> = 37 × 4969 × 55609 × 58747627 × 1046693452290120727_<19> × 61858572344952549059377667528148629908039_<41>

35×10⁷⁷-179 = 3(8)₇₆7_<78> = 3 × 223 × 277 × 1865809219_<10> × 8083114276341451_<16> × 67138637873408734948993_<23> × 2072531637329074122520247_<25>

35×10⁷⁸-179 = 3(8)₇₇7_<79> = 724223556227_<12> × 196989965577980783456848331_<27> × 27258928717185166323598602972953799817751_<41>

35×10⁷⁹-179 = 3(8)₇₈7_<80> = 37 × 47 × 28373693 × 788152191547118267113380117258055372488163933994453010632705001395881_<69>

35×10⁸⁰-179 = 3(8)₇₉7_<81> = 3 × 67 × 5903 × 240041 × 571279 × 12147382647167_<14> × 778805957426480341261_<21> × 252645187464425107740979189853_<30>

35×10⁸¹-179 = 3(8)₈₀7_<82> = 13² × 29 × 5779 × 365985173 × 375167013892553262178180192522015471456512660493388150587777815461_<66>

35×10⁸²-179 = 3(8)₈₁7_<83> = 37 × 149 × 11877953 × 384782799851_<12> × 1543406374145756026914842957758122524702797174257951181487933_<61>

35×10⁸³-179 = 3(8)₈₂7_<84> = 3² × 1556483670437_<13> × 438627784438601_<15> × 2383718331186959881_<19> × 26551397361086662033526540919687608419_<38>

35×10⁸⁴-179 = 3(8)₈₃7_<85> = 19 × 374047 × 1021291 × 235899743 × 135557087661033457_<18> × 42855056889267617366783_<23> × 390970941236974453826153_<24>

35×10⁸⁵-179 = 3(8)₈₄7_<86> = 37 × 71 × 229 × 739 × 19646688697_<11> × 1994821204479040181_<19> × 2231989779491144599744431071094097908746907071743_<49>

35×10⁸⁶-179 = 3(8)₈₅7_<87> = 3 × 43 × 5261 × 26003 × 2260501 × 55525511 × 549981984894985072986224141021_<30> × 319226058168816209959240250796311_<33>

35×10⁸⁷-179 = 3(8)₈₆7_<88> = 13 × 19892113 × 4493185217264055429451_<22> × 3346932421996840445665309686707126086760176285213754776073_<58>

35×10⁸⁸-179 = 3(8)₈₇7_<89> = 37² × 476390012251_<12> × 75686850236339_<14> × 17966900250475949_<17> × 245929601849367959_<18> × 178301519211623930079156077_<27>

35×10⁸⁹-179 = 3(8)₈₈7_<90> = 3 × 13999 × 7541717 × 242020579 × 344160375539_<12> × 14740895671311839148818059334000828739894479286018702381823_<59>

35×10⁹⁰-179 = 3(8)₈₉7_<91> = 18415673 × 227699236847_<12> × 927419803118345939876261601514176044017398028251631179975368971047640577_<72>

35×10⁹¹-179 = 3(8)₉₀7_<92> = 23 × 37 × 304013 × 1139741 × 1240758109_<10> × 106294434586125448493999701671321866541536503893958460595100251198521_<69>

35×10⁹²-179 = 3(8)₉₁7_<93> = 3³ × 4253 × 21091703 × 2122058966825531219_<19> × 75665393169761249530940321980418660702301133222275358362583861_<62>

35×10⁹³-179 = 3(8)₉₂7_<94> = 13 × 857 × 3697 × 9833 × 23027 × 20409534982741_<14> × 20431271750198050440705544796336640147483426820251555633658037101_<65>

35×10⁹⁴-179 = 3(8)₉₃7_<95> = 37 × 433 × 12613 × 25469 × 243001883 × 447353677 × 427552756373_<12> × 162575562180004870499476866335110230389420151507033857_<54>

35×10⁹⁵-179 = 3(8)₉₄7_<96> = 3 × 18382028773831_<14> × 34646494137151803813491821_<26> × 297870479163389415097513103_<27> × 683319917002979925270474129193_<30>

35×10⁹⁶-179 = 3(8)₉₅7_<97> = 463 × 1327 × 1044021156131_<13> × 283216829162672429_<18> × 21406480298385236016941461190423667356459214705576049711622513_<62>

35×10⁹⁷-179 = 3(8)₉₆7_<98> = 37 × 245339 × 2260331 × 5888091301_<10> × 321892340871780823033090352904711682332534032777152102632511154848143540439_<75>

35×10⁹⁸-179 = 3(8)₉₇7_<99> = 3 × 116803 × 514074427 × 9724842980735429_<16> × 221994229085424269824897112482875609573627985902120228797373832241321_<69>

35×10⁹⁹-179 = 3(8)₉₈7_<100> = 13 × 829 × 6155351 × 10163921 × 2006844185222771_<16> × 2874086890990148730609979510734432506809852467364651805449201393891_<67>

35×10¹⁰⁰-179 = 3(8)₉₉7_<101> = 37 × 389 × 701 × 465901 × 1418867 × 7183373 × 741539762586953938609_<21> × 1094606441152900940606972149779873736037760656067845761_<55>

35×10¹⁰¹-179 = 3(8)₁₀₀7_<102> = 3² × 168540033858042417413_<21> × 3282521659900311650270457149507_<31> × 78103833080810711077856871100699017964197145933073_<50> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=2144918086 for P31 / November 29, 2008 2008 年 11 月 29 日)

35×10¹⁰²-179 = 3(8)₁₀₁7_<103> = 19 × 269 × 9587 × 357080865133_<12> × 765347640290657_<15> × 11131955940267077_<17> × 26087960125763987737148727800617637758551831086477243_<53>

35×10¹⁰³-179 = 3(8)₁₀₂7_<104> = 37 × 131 × 1481 × 38299 × 202254561854416559848922039163312240405477011_<45> × 699377564266339266150223417648152119745082832369_<48> (Serge Batalov / Msieve-1.39 snfs / 0.20 hours on Opteron-2.6GHz; Linux x86_64 / December 7, 2008 2008 年 12 月 7 日)

35×10¹⁰⁴-179 = 3(8)₁₀₃7_<105> = 3 × 26437 × 2385547020076158193_<19> × 2055436801448573127426306730806807930825825689721063357772785209530948328124160169_<82>

35×10¹⁰⁵-179 = 3(8)₁₀₄7_<106> = 13 × 881 × 128311 × 309933853 × 58185333763_<11> × 146743826416260880896331548960991103601781894767931943701592603823123300625651_<78>

35×10¹⁰⁶-179 = 3(8)₁₀₅7_<107> = 37 × 19577330153_<11> × 53687149516145315785187139202200644986540675777050683477384121277583842923459076583058687463667_<95>

35×10¹⁰⁷-179 = 3(8)₁₀₆7_<108> = 3 × 43 × 9366053 × 26289495769153_<14> × 5575601063534743139797_<22> × 4954252202983322157449227_<25> × 443227964789192786941942083579088385693_<39>

35×10¹⁰⁸-179 = 3(8)₁₀₇7_<109> = 157 × 39283896658167869_<17> × 96410699435316947342251_<23> × 6540125603159563632570389186961146942883272045827514496599236333789_<67>

35×10¹⁰⁹-179 = 3(8)₁₀₈7_<110> = 29 × 37 × 787 × 1277 × 82890577453_<11> × 435065873047993755402704675173982262799812238344641638281261074646443256760425788912022277_<90>

35×10¹¹⁰-179 = 3(8)₁₀₉7_<111> = 3² × 59 × 220988543189_<12> × 9712674854191_<13> × 341210513662893320456436287440226706707981312708248229277564741428524952122743879223_<84>

35×10¹¹¹-179 = 3(8)₁₁₀7_<112> = 13 × 443 × 1153 × 687885491316509_<15> × 851398733007703092024010773571573075012343482250389524033456768818799104336172259126903709_<90>

35×10¹¹²-179 = 3(8)₁₁₁7_<113> = 37 × 371549 × 1742453 × 4076085617_<10> × 398293614612009779912117884384930538943320773203252998151504053454389457156139992975495899_<90>

35×10¹¹³-179 = 3(8)₁₁₂7_<114> = 3 × 23 × 67 × 2361307315329023_<16> × 510712342028689440749924324396136884587_<39> × 69754587631347514921265069039903044640326990855644594869_<56> (Sinkiti Sibata / Msieve 1.39 for P39 x P56 / 6.77 hours / December 8, 2008 2008 年 12 月 8 日)

35×10¹¹⁴-179 = 3(8)₁₁₃7_<115> = 4110160586637253424951061483322223671294257236029_<49> × 946164707416116073991311909742053789197323995598219236310578275203_<66> (Sinkiti Sibata / Msieve / 0.88 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / December 7, 2008 2008 年 12 月 7 日)

35×10¹¹⁵-179 = 3(8)₁₁₄7_<116> = 37 × 25329121 × 622865946841_<12> × 923997155153_<12> × 72100532161897219634576760152926250799482144426455238703638046538413856232466876947_<83>

35×10¹¹⁶-179 = 3(8)₁₁₅7_<117> = 3 × 9675037 × 71748853691923987_<17> × 186739709453078377894693993432873131582331275066717190541135343441193500915239365019697741691_<93>

35×10¹¹⁷-179 = 3(8)₁₁₆7_<118> = 13 × 773 × 507715096573_<12> × 762223986716963541797558739356029658495340673270111555668479691753587903870112602590407826938984838531_<102>

35×10¹¹⁸-179 = 3(8)₁₁₇7_<119> = 37 × 1324063952129_<13> × 96892031191566013687_<20> × 8192695026945701591818189959762947542991776015513428294070996175180764561667611645037_<85>

35×10¹¹⁹-179 = 3(8)₁₁₈7_<120> = 3³ × 378817 × 2449991 × 34668139379_<11> × 35056709309_<11> × 1749478901804010401266390472714651_<34> × 7298900286002683161226083211619276827777195861547743_<52> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=2191944760 for P34 / November 29, 2008 2008 年 11 月 29 日)

35×10¹²⁰-179 = 3(8)₁₁₉7_<121> = 19 × 71 × 571 × 1669 × 620509472709735843259609_<24> × 4874978722258739818226938401081903574588596565322465454061645481206893729499852843061893_<88>

35×10¹²¹-179 = 3(8)₁₂₀7_<122> = 37 × 1286419914980909_<16> × 817035743003596986774518895041797756431883295291718283948880910173035634718982467208983736335065801248439_<105>

35×10¹²²-179 = 3(8)₁₂₁7_<123> = 3 × 1667 × 200131 × 19180783 × 1127206542851648414760167029508360310343210538429_<49> × 17971506403106683410565933523865358418769645819039526418711_<59> (Serge Batalov / Msieve-1.39 snfs / 1.10 hours on Opteron-2.6GHz; Linux x86_64 / December 7, 2008 2008 年 12 月 7 日)

35×10¹²³-179 = 3(8)₁₂₂7_<124> = 13 × 32514646135566929765652027227651_<32> × 11000509236102085663313836629757193677_<38> × 836354428344066072261132208793124499586090114853277237_<54> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=3527436879 for P32 / November 29, 2008 2008 年 11 月 29 日) (Sinkiti Sibata / Msieve 1.39 for P38 x P54 / 0.96 hours / December 7, 2008 2008 年 12 月 7 日)

35×10¹²⁴-179 = 3(8)₁₂₃7_<125> = 37 × 16878444893867_<14> × 62271794449082448727683064516087692754693109832386506985194915580833603237245129123541199460012410701373748353_<110>

35×10¹²⁵-179 = 3(8)₁₂₄7_<126> = 3 × 47 × 64763 × 116707776113553593_<18> × 3449974226317333002857_<22> × 629410769386852770078232639202039_<33> × 168046569134019683224017285754042553776304278751_<48> (Makoto Kamada / Msieve 1.39 for P33 x P48 / 19 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 7, 2008 2008 年 12 月 7 日)

35×10¹²⁶-179 = 3(8)₁₂₅7_<127> = 1088661307159_<13> × 3572175169004066603624815241929548310310334844618066001122805032980163488666216456419866562152125891167270880320993_<115>

35×10¹²⁷-179 = 3(8)₁₂₆7_<128> = 37 × 1649510569739_<13> × 390752729727494409677256101481138223351378730947_<48> × 1630672275638178028977091023427467641772116201128430345768992206347_<67> (Sinkiti Sibata / Msieve / 2.68 hours / December 8, 2008 2008 年 12 月 8 日)

35×10¹²⁸-179 = 3(8)₁₂₇7_<129> = 3² × 43 × 2557 × 1744978463_<10> × 479702072115780301_<18> × 614114184448342236450430905615224850081743454187_<48> × 764492180582182386904576547379784128078297585553_<48> (Sinkiti Sibata / Msieve 1.39 for P48(6141...) x P48(7644...) / 4.77 hours / December 8, 2008 2008 年 12 月 8 日)

35×10¹²⁹-179 = 3(8)₁₂₈7_<130> = 13 × 4483 × 56167 × 58946617 × 1688818162261_<13> × 11934121068745823705470067537198986946830775083159544896858186101829030689053715431095496660222758307_<101>

35×10¹³⁰-179 = 3(8)₁₂₉7_<131> = 37 × 1613 × 86467 × 127277577316998781516401903357718924380855137_<45> × 59208921733784673577031498471236697681202219803320125271724133270956593801213_<77> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 1.96 hours on Core 2 Quad Q6700 / December 8, 2008 2008 年 12 月 8 日)

35×10¹³¹-179 = 3(8)₁₃₀7_<132> = 3 × 2237 × 806685229963_<12> × 71834684854509942822720521264871071791072380336683344635303252710780784121758885496152411080689090256809836840833059_<116>

35×10¹³²-179 = 3(8)₁₃₁7_<133> = 61 × 167 × 197 × 1087 × 917117 × 349527261719_<12> × 381821911376033779003_<21> × 2618098890081871199911145483496466417_<37> × 5563278048469018825873033722128510859501955470983_<49> (Sinkiti Sibata / Msieve 1.38 for P37 x P49 / 5.17 hours / December 7, 2008 2008 年 12 月 7 日)

35×10¹³³-179 = 3(8)₁₃₂7_<134> = 37 × 109² × 1907 × 46389545965991584482274384899468719894373400186840205356282481357849674498956597120494504034924337340356148086204231600279553_<125>

35×10¹³⁴-179 = 3(8)₁₃₃7_<135> = 3 × 969728384217945564797275207754143001546059800826738657962986323_<63> × 133676224950527476034793786904878991749286703030637898637843016107605423_<72> (Erik Branger / GGNFS, Msieve snfs / 5.12 hours / December 7, 2008 2008 年 12 月 7 日)

35×10¹³⁵-179 = 3(8)₁₃₄7_<136> = 13 × 23 × 16553 × 24509 × 69682502333_<11> × 460074647142703802157326262302662064268882040417649148449612080261392286668264775381359053679467017332639128955893_<114>

35×10¹³⁶-179 = 3(8)₁₃₅7_<137> = 37 × 29167 × 919157593 × 3381050409557332073873_<22> × 1739713428667749607136125403_<28> × 667797102844306534452219112505627_<33> × 9980864916516622911910034512582936494917_<40> (Makoto Kamada / Msieve 1.39 for P33 x P40 / 5.5 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 7, 2008 2008 年 12 月 7 日)

35×10¹³⁷-179 = 3(8)₁₃₆7_<138> = 3² × 29 × 231289 × 4934234473825097501_<19> × 2290855432503787895839_<22> × 4737214230912425154616835065391_<31> × 120306628818978905183746027272026885894951791519872734798447_<60> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=871361795 for P31 / November 30, 2008 2008 年 11 月 30 日)

35×10¹³⁸-179 = 3(8)₁₃₇7_<139> = 19 × 1049 × 309769 × 470663 × 38057395340621219550760269513883685643294306836546403397_<56> × 35164898775576928212777153301681488449949331239308314024794822219503_<68> (Sinkiti Sibata / Msieve / 5.90 hours / December 8, 2008 2008 年 12 月 8 日)

35×10¹³⁹-179 = 3(8)₁₃₈7_<140> = 37 × 23957 × 13997909 × 531167603 × 5324940143_<10> × 3808548267229_<13> × 1234471249886739306632069758085923_<34> × 235690164383998395752830997318697209446208726758860398731520089_<63> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1486614879 for P34 / December 7, 2008 2008 年 12 月 7 日)

35×10¹⁴⁰-179 = 3(8)₁₃₉7_<141> = 3 × 971 × 1609 × 11810587 × 23506146256163387_<17> × 56265065521646473_<17> × 16118358280917512747_<20> × 329546311446076246738389023345713223515705096554495970421434677032515809949_<75>

35×10¹⁴¹-179 = 3(8)₁₄₀7_<142> = 13 × 2879 × 24457822001458490363244626531_<29> × 73820734517195491206986826554621892806273334976028047_<53> × 57549873803153056003497272592233619822725268242612595233_<56> (Sinkiti Sibata / Msieve / 8.16 hours / December 8, 2008 2008 年 12 月 8 日)

35×10¹⁴²-179 = 3(8)₁₄₁7_<143> = 37 × 24851 × 1638208606894922829008039249_<28> × 226680845566547999740279589713872828602549663480669_<51> × 113892706687805799382922156923032816068749972971507800267021_<60> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 6.50 hours / December 9, 2008 2008 年 12 月 9 日)

35×10¹⁴³-179 = 3(8)₁₄₂7_<144> = 3 × 1844111 × 499536635714987177_<18> × 1238949422381688869_<19> × 113578544684960287777606565290817980766861311566139761828425074629467840747124186003566657590793198303_<102>

35×10¹⁴⁴-179 = 3(8)₁₄₃7_<145> = 107590361 × 376107998117_<12> × 21426550966873432966355113684930427555362915856005664850821_<59> × 4485257002846199926844351970859416404519415299681016964991792241031_<67> (Sinkiti Sibata / Msieve / 7.82 hours / December 8, 2008 2008 年 12 月 8 日)

35×10¹⁴⁵-179 = 3(8)₁₄₄7_<146> = 37 × 10691 × 8039823463319470838095139_<25> × 12228099631385930101044998721368207669254068571470242415081680517021197523808839114266921707309896536964498256862899_<116>

35×10¹⁴⁶-179 = 3(8)₁₄₅7_<147> = 3⁴ × 67 × 193 × 277 × 49727897 × 62936791 × 254784924128927_<15> × 1602143318448769417_<19> × 1839174664159673259192831667_<28> × 570460897910764821717261694521329661663649867302217618412202091_<63>

35×10¹⁴⁷-179 = 3(8)₁₄₆7_<148> = 13 × 97 × 362069557 × 299602865702474536357_<21> × 28429712943812056436003142307749281212081993818847792578352098888840623706096266066550129725820841479403674793209083_<116>

35×10¹⁴⁸-179 = 3(8)₁₄₇7_<149> = 37 × 9323 × 15956226879511_<14> × 673341962260369_<15> × 9516173471923224352619_<22> × 1102655614680336542342660077476811151182251144573749983124620564476876883299059608469512949797_<94>

35×10¹⁴⁹-179 = 3(8)₁₄₈7_<150> = 3 × 43 × 61841047 × 7722230965619_<13> × 6312715308925637435525544017254861633184650885534737104652572655797794968450579016377783932625241216522539771346516982790593371_<127>

35×10¹⁵⁰-179 = 3(8)₁₄₉7_<151> = 113 × 60913 × 504602257803587_<15> × 2416659974789463349472870748049_<31> × 463310735504271124456267885096630252609292561519115467233046597648340168340147876833280198456259021_<99> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=2961914480 for P31 / November 30, 2008 2008 年 11 月 30 日)

35×10¹⁵¹-179 = 3(8)₁₅₀7_<152> = 37 × 7607 × 549302680970858401_<18> × 118123717349038913397400950983195020461774566916898370759_<57> × 2129421183757089787810934958106849683297394566265161960072723588038834827_<73> (Sinkiti Sibata / Msieve / 18.97 hours / December 9, 2008 2008 年 12 月 9 日)

35×10¹⁵²-179 = 3(8)₁₅₁7_<153> = 3 × 32348688376499948062857708229_<29> × 42240598854390378377688655800680354702163772637296451470451_<59> × 94867517757021778096754297616255666172836797900280601682198483651_<65> (Sinkiti Sibata / Msieve / 19.04 hours / December 9, 2008 2008 年 12 月 9 日)

35×10¹⁵³-179 = 3(8)₁₅₂7_<154> = 13 × 4231849 × 87825499 × 203512357 × 3954946468484526589275761596493495138902006960928303212200544026514704064950563794533058311023957376947233831497031656463639637357_<130>

35×10¹⁵⁴-179 = 3(8)₁₅₃7_<155> = 37 × 431 × 26701 × 225569 × 255801659 × 1582837179513282796126693998165711282849105957495954517165337083800488840072824252426671307805858408444681019879906829018836017277851_<133>

35×10¹⁵⁵-179 = 3(8)₁₅₄7_<156> = 3² × 71 × 1283 × 471571 × 40050877 × 25115330666467130164309942539605254581185349076599425398832746532733003321447893642452148451703511218836920235306148060620593527337502053_<137>

35×10¹⁵⁶-179 = 3(8)₁₅₅7_<157> = 19 × 58096309927_<11> × 1859651820102671746966417186881408253_<37> × 1076928618506846748863383858027045833094779104071139_<52> × 1759157919925246744872768718883007727648687170851865993997_<58> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3652731674 for P37 / December 7, 2008 2008 年 12 月 7 日) (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 gnfs for P52 x P58 / 25.17 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / December 9, 2008 2008 年 12 月 9 日)

35×10¹⁵⁷-179 = 3(8)₁₅₆7_<158> = 23 × 37 × 2069 × 1151733944305984141_<19> × 53292721252355927483_<20> × 951140256289141598794249013986046916487726837_<45> × 378330066980404354259155145077482265252602731240864591664915709201643_<69> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2131351972 for P45 / December 7, 2008 2008 年 12 月 7 日)

35×10¹⁵⁸-179 = 3(8)₁₅₇7_<159> = 3 × 948971 × 386565619457279237_<18> × 34682497186158503087676784739_<29> × 10188676042364521961635131645399710654664381239786308129036220781773959022172956380401411958245387864579193_<107>

35×10¹⁵⁹-179 = 3(8)₁₅₈7_<160> = 13² × 65257 × 14268157 × 900723308910475183047680333245858277_<36> × 93911989316878837694411058288113772487947233_<44> × 292167163732202035035400549617558221929515408022408002322526037047_<66> (Serge Batalov / Msieve-1.39 snfs / 20.00 hours on Opteron-2.6GHz; Linux x86_64 / December 9, 2008 2008 年 12 月 9 日)

35×10¹⁶⁰-179 = 3(8)₁₅₉7_<161> = 37 × 1051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051051_<160>

35×10¹⁶¹-179 = 3(8)₁₆₀7_<162> = 3 × 192799 × 242197863343_<12> × 13253282881361993_<17> × 186251389998046129_<18> × 2113037716029191144429_<22> × 28742297975313337803187625016407_<32> × 18517291741272127549515342256010461522539595944240811661567_<59> (Sinkiti Sibata / Msieve 1.39 for P32 x P59 / 1.32 hours / December 7, 2008 2008 年 12 月 7 日)

35×10¹⁶²-179 = 3(8)₁₆₁7_<163> = 2589231713141_<13> × 12349029638342801933_<20> × 11781950893253965807469256867841699660786517244589420402301_<59> × 10322967879635049910907388130429762547909825198231377987413088190570273779_<74> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 23.59 hours on Core 2 Quad Q6700 / January 13, 2009 2009 年 1 月 13 日)

35×10¹⁶³-179 = 3(8)₁₆₂7_<164> = 37 × 859433 × 307872788703161951907149258898808205952508429619_<48> × 3972285727489072042775156135135899166170668429731548228973478147815338273608566491300580895913110250732250113_<109> (Sinkiti Sibata / GGNFS-0.77.1-20060513-nocona snfs / 64.73 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / December 12, 2008 2008 年 12 月 12 日)

35×10¹⁶⁴-179 = 3(8)₁₆₃7_<165> = 3² × 227 × 283 × 607 × 721641441052677560056142789_<27> × 2164226505067740336545299545138264786212773_<43> × 709508928632527276438580379581169517506057775727086708484652773434018533527897889599737_<87> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 20.65 hours on Core 2 Quad Q6700 / January 29, 2009 2009 年 1 月 29 日)

35×10¹⁶⁵-179 = 3(8)₁₆₄7_<166> = 13 × 29 × 200041 × 6591395639_<10> × 10664333440055130067457_<23> × 109280386502103256471935743911750090597_<39> × 6712925841213146837839103821365744689243652680605247737247853841651220452334798552144461_<88> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=3000000, sigma=2491864470 for P39 / February 16, 2009 2009 年 2 月 16 日)

35×10¹⁶⁶-179 = 3(8)₁₆₅7_<167> = 37 × 9967 × 37307 × 2354535121_<10> × 132127952267_<12> × 141133482721793_<15> × 8226444157972988141710931167_<28> × 7825767400812519208912071922939339970412517548592436550077410265971108080505948124839410842387_<94> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3714132238 for P28 / December 7, 2008 2008 年 12 月 7 日)

35×10¹⁶⁷-179 = 3(8)₁₆₆7_<168> = 3 × 219943721724751_<15> × 25906357094181540237749_<23> × 996244817379145944395119476840665614982629783547816089009_<57> × 22836013332760580540298944200610015633803921232860776910122536509987443319_<74> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 49.98 hours, 1.24 hours / June 26, 2009 2009 年 6 月 26 日)

35×10¹⁶⁸-179 = 3(8)₁₆₇7_<169> = 59 × 1499 × 185642217629222800749008039_<27> × 236861864009682601838908983097974720710874871660466663971126833693835014463603604917945661043647366977470655115617239332136955669043654713_<138>

35×10¹⁶⁹-179 = 3(8)₁₆₈7_<170> = 37 × 9283 × 616717 × 7261187 × 2690791161620814877_<19> × 1203662182305387631696435974379_<31> × 111228175619580244012703383781260734185184707_<45> × 70184707899453055525548085720106885156447759916870224213803_<59> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=2478242797 for P31 / December 2, 2008 2008 年 12 月 2 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P45 x P59 / 4.67 hours on Core 2 Quad Q6700 / December 9, 2008 2008 年 12 月 9 日)

35×10¹⁷⁰-179 = 3(8)₁₆₉7_<171> = 3 × 43 × 148439 × 2560157 × 1078133780824366391_<19> × 7357809711078414297597466488448434130955952087297435284641955934147587418493000897012507473936672861100165849172617738786404425090867522771_<139>

35×10¹⁷¹-179 = 3(8)₁₇₀7_<172> = 13 × 47 × 1213 × 199049 × 15678749 × 1681326724702380830986666063449803648950939206956016549535035586664552823503150409396267413111947352238806053923341126953458709356836651108158560349012909_<154>

35×10¹⁷²-179 = 3(8)₁₇₁7_<173> = 37 × 181 × 1611593 × 3948653 × 912516851139781217445055215436213953397738920484889878625026756217671221753172693728767268331061170865183185527178464294755286866684501254719775087344078499_<156>

35×10¹⁷³-179 = 3(8)₁₇₂7_<174> = 3³ × 509 × 134369 × 337724536741041059203277713140298669_<36> × 35379397955005834588592053197139791721891_<41> × 17625110578008454198749170325730853946484306159435410277383328749926110210790680918234559_<89> (Ignacio Santos / GGNFS, Msieve snfs / 82.53 hours / October 7, 2009 2009 年 10 月 7 日)

35×10¹⁷⁴-179 = 3(8)₁₇₃7_<175> = 19² × 15061 × 2410693 × 149519191 × 3186866803970929_<16> × 622675483614331819639166554319447008180707834866422273685261008001969015232450449361682210461896358375812225574418483890467829486051043361_<138>

35×10¹⁷⁵-179 = 3(8)₁₇₄7_<176> = 37 × 1314351100496114977_<19> × 313688834308281490428375074251862115800219_<42> × 2549255455539678047077216900839145161405584904522655217565465200669353745545342141581455200486427802677811159135377_<115> (Wataru Sakai / May 21, 2011 2011 年 5 月 21 日)

35×10¹⁷⁶-179 = 3(8)₁₇₅7_<177> = 3 × 379 × 577 × 16633 × 8626865492539519_<16> × 16287071657624667201329691914058751_<35> × 72485366745861100910529372318687451_<35> × 3499228437398053869070314749177548455789874474953667584190158156018462102243163469_<82> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=641671 for P35(7248...) / December 3, 2008 2008 年 12 月 3 日) (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1452233116 for P35(1628...) / December 8, 2008 2008 年 12 月 8 日)

35×10¹⁷⁷-179 = 3(8)₁₇₆7_<178> = 13 × 12163 × 4682863 × 274791901 × 631983238333223786693_<21> × 87804349006598114590032075861927015852744947_<44> × 344432804335628402026565030270795649116570161185464758048714173624074822263981761587630166101_<93> (Alfred Reich / Msieve 1.50 snfs / June 16, 2013 2013 年 6 月 16 日)

35×10¹⁷⁸-179 = 3(8)₁₇₇7_<179> = 37 × 32969 × 189583 × 517981 × 3942871 × 10985291 × 22070273 × 6669335981879766458758192517_<28> × 50920232656772421298875597231096960594307229219521852623019622483583930275126623970795438847629543847126898487473_<113> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=4196366601 for P28 / December 7, 2008 2008 年 12 月 7 日)

35×10¹⁷⁹-179 = 3(8)₁₇₈7_<180> = 3 × 23 × 67 × 83982433896533_<14> × 1001643517536920173363658716426708995017263593335003809313829111434875501861873862126171437222002796711603818679033771423646064216124903532925645249010186183528693_<163>

35×10¹⁸⁰-179 = 3(8)₁₇₉7_<181> = 2549 × 1525652761431498191011725731223573514668061549191404036441305958763785362451506037225927378928555860686107841855193757900701800270258489167865393836362843816747308312628045856763_<178>

35×10¹⁸¹-179 = 3(8)₁₈₀7_<182> = 37 × 5783 × 8291 × 6221154558239353306655743_<25> × 1259634470484335012059329643_<28> × 100287270379262073062534543329774973_<36> × 27893458439383066549646630630840407002770488829451805100233906262131129518370132230671_<86> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=730062768 for P36 / December 8, 2008 2008 年 12 月 8 日)

35×10¹⁸²-179 = 3(8)₁₈₁7_<183> = 3² × 16111 × 2682010833791190897101972350767170041785728790466754176848729224952509251021654555472030075303201324760094130917377974254228573223876639762266559692748838880881170827998047496113_<178>

35×10¹⁸³-179 = 3(8)₁₈₂7_<184> = 13 × 349 × 103331658487_<12> × 130324752158322141231839320712765346334485533_<45> × 4144779491795801904255085377603295114012730452396597_<52> × 15356598071106482204301771137351504752162708969590162450779723636170886473_<74> (Jo Yeong Uk / GMP-ECM v6.4.4 B1=11000000, sigma=4312673018 for P45, GGNFS/Msieve v1.39 gnfs for P52 x P74 / June 25, 2014 2014 年 6 月 25 日)

35×10¹⁸⁴-179 = 3(8)₁₈₃7_<185> = 37 × 367 × 653 × 4385757001018360244902174624979870941707111804461700769247994170902900680786022386933712152467759579768292437966255308974513150585856312099891304651560189822078985904715820301401_<178>

35×10¹⁸⁵-179 = 3(8)₁₈₄7_<186> = 3 × 3242017 × 78781626947123_<14> × 5308091521661172993909954169669_<31> × 523319167282656102031457080236046027_<36> × 663463264282258883675390613253776805699_<39> × 275386167394865512719650839806880906553023554612593681877187_<60> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2815757366 for P31 / December 7, 2008 2008 年 12 月 7 日) (Ignacio Santos / GMP-ECM 6.3 B1=3000000, sigma=829203093 for P36 / July 13, 2011 2011 年 7 月 13 日) (Warut Roonguthai / Msieve 1.48 gnfs for P39 x P60 / July 15, 2011 2011 年 7 月 15 日)

35×10¹⁸⁶-179 = 3(8)₁₈₅7_<187> = 157 × 24359 × 61381 × 8547631 × 741825421 × 12281370259_<11> × 1354976246545216979406271187005039_<34> × 5120353883635458429190544130895666258719013_<43> × 30662425523328166855980476520758336325858134810791000702868819091594477883_<74> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=968099289 for P34 / December 4, 2008 2008 年 12 月 4 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona/Msieve v1.39 gnfs for P43 x P74 / 22.72 hours on Core 2 Quad Q6700 / December 22, 2008 2008 年 12 月 22 日)

35×10¹⁸⁷-179 = 3(8)₁₈₆7_<188> = 37 × 293 × 44819 × 22323411871_<11> × 23575219891_<11> × 5405268658708132199635096286107_<31> × 28135874568677300735640012694914520710640214152856963017290900531616339376629182034845122781934860626430793955513760673461885739_<128> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3147506786 for P31 / December 8, 2008 2008 年 12 月 8 日)

35×10¹⁸⁸-179 = 3(8)₁₈₇7_<189> = 3 × 7793 × 10613324850502783_<17> × 6526424009733342375314748209_<28> × 335241822265248988722904072946366191004800819556311355137_<57> × 716332521153925054417233718466933575588240593452508432822778353535040469371508397027_<84> (Jason Parker-Burlingham / CADO-NFS-3.0.0-dev for P57 x P84 / March 1, 2019 2019 年 3 月 1 日)

35×10¹⁸⁹-179 = 3(8)₁₈₈7_<190> = 13 × 26431 × 2334785669_<10> × 166578567949_<12> × 29100633594265181858603448913808343945934796157637238185084201140102333787189364173340647908256812547120081543238833247158631952704674355847515473769901627037636909_<164>

35×10¹⁹⁰-179 = 3(8)₁₈₉7_<191> = 37 × 71 × 14557 × 188376405871_<12> × 100052775801257540571316324434644431_<36> × 53955774591906532584355748338849107591740690677796168764881239745263680448494857784509088189650964104515962241950495581815296128962436833_<137> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=395137034 for P36 / July 4, 2013 2013 年 7 月 4 日)

35×10¹⁹¹-179 = 3(8)₁₉₀7_<192> = 3² × 43 × 21787 × 4269252338874813405012089_<25> × 10803520776432982148259968468094055168337455070613406705438119922597683672405072236690732709660149626609212790754431769517757346428634360589789802032962219409407_<161>

35×10¹⁹²-179 = 3(8)₁₉₁7_<193> = 19 × 61 × 3355382993001629757453743648739334675486530533985236314830792829067203527945546927427859265650464960214744511552104304477039593519317419231137954175055124149170741060301025788515003355382993_<190>

35×10¹⁹³-179 = 3(8)₁₉₂7_<194> = 29 × 37 × 25973008709_<11> × 1395415529154957458668405429378130607621716795428987238353097640327233602487205112577173129984623513548621241551533838925718827552455992861569823756121799403323706114190878783788091_<181>

35×10¹⁹⁴-179 = 3(8)₁₉₃7_<195> = 3 × 252111793534021_<15> × 809221524714549477197717_<24> × 635394852261075823589269556330886357753134789625671477835319774409779927400715436402325112931913989338040463848866324636290138334793592806751228303251521397_<156>

35×10¹⁹⁵-179 = 3(8)₁₉₄7_<196> = 13 × 1193 × 664661 × 3552417074375311274670072482413541784449969509003_<49> × 106198307043959791062345096304590412359250542611025595111143325949237408731508993362407227381993672181492911190602141078104514422281843821_<138> (Robert Backstrom / Msieve 1.44 snfs / March 13, 2012 2012 年 3 月 13 日)

35×10¹⁹⁶-179 = 3(8)₁₉₅7_<197> = 37 × 12653 × 27697 × 2999145750239692587400188978811257065669296024198349662102293321808225641578643425488166806162166877401972713291192686525559283627313624196975429526367492747138175787040277010620609369511_<187>

35×10¹⁹⁷-179 = 3(8)₁₉₆7_<198> = 3 × 89318587 × 350496642709302609130811_<24> × 102966821696114315724575719581427638907291_<42> × 40214369716199723535550822887937804979629563992829757871795582887810320282113336768678171862585955063703187609279073314007967_<125> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4255581934 for P42 / July 4, 2013 2013 年 7 月 4 日)

35×10¹⁹⁸-179 = 3(8)₁₉₇7_<199> = 448053902349583_<15> × 20238072233250682389213815154482772094455110917839250801884669783496214190110681_<80> × 428870455461498198509058395083442468511570122193284627886336617185389415952071761337132184100341301207169_<105> (Bob Backstrom / Msieve 1.54 snfs for P80 x P105 / March 26, 2021 2021 年 3 月 26 日)

35×10¹⁹⁹-179 = 3(8)₁₉₈7_<200> = 37² × 10733 × 1474787 × 40926981270737_<14> × 67943981069963573_<17> × 104941293006996173973083_<24> × 1686572485286955083300811181135965507389483535419645649892384754773_<67> × 3646359901272172895247095198305474811423225197938307378270234332707_<67> (Ignacio Santos / GGNFS, Msieve gnfs for P67(1686...) x P67(3646...) / October 16, 2010 2010 年 10 月 16 日)

35×10²⁰⁰-179 = 3(8)₁₉₉7_<201> = 3³ × 1787 × 4122401 × 20445349807322515409363909003914189838150076566150095981197666672869250064033604839_<83> × 95629621748264414527368452183626638813707018983807568135851517900290950981370561857545087648852317825526617_<107> (matsui / Msieve 1.47 snfs / September 6, 2010 2010 年 9 月 6 日)

35×10²⁰¹-179 = 3(8)₂₀₀7_<202> = 13 × 23 × 826697 × 473407660679_<12> × 11517434171970608719_<20> × 18811864491025991729_<20> × 49401864156353199188963792945581316751711196051132601_<53> × 3104858310386415307331038040853093800859655758201420510011090679981342218414849937443371501_<91> (Eric Jeancolas / cado-nfs-3.0.0 for P53 x P91 / May 10, 2020 2020 年 5 月 10 日)

35×10²⁰²-179 = 3(8)₂₀₁7_<203> = 37 × 36118644455111721394476564262279362183697261549_<47> × 3293898399544187326777054807794959505060276762759732491_<55> × 8834503942940752249432849357854950544490744137172844219578502235694939623388905000315383980972142789_<100> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 97.20 hours, 19.87 hours / March 5, 2009 2009 年 3 月 5 日)

35×10²⁰³-179 = 3(8)₂₀₂7_<204> = 3 × 3248461725714870617_<19> × 39904927493366962632476799659732791100899013732476051392602756257771819068527174438818189602429451951667339597165592090531813595772267314090308483876921163367008871102859677529325010437_<185>

35×10²⁰⁴-179 = 3(8)₂₀₃7_<205> = 11939 × 163110981887066305100933083_<27> × 42096697097429856724820552216243556133006809151_<47> × 47437998624730658434576463708970302556634751601496116999652796989317812345235766334534769147859140929141031941270890292273170201_<128> (Bob Backstrom / Msieve 1.44 snfs for P47 x P128 / October 22, 2023 2023 年 10 月 22 日)

35×10²⁰⁵-179 = 3(8)₂₀₄7_<206> = 37 × 823 × 1093 × 1870717 × 22659502517583351991924459_<26> × 27564197306960726458401030495190610558916488162554892087689455038609230772605204141150573095968580851594737932261094280186719366675049466966865880397643197265299488503_<167>

35×10²⁰⁶-179 = 3(8)₂₀₅7_<207> = 3 × 263 × 29599 × 2557932239_<10> × 325399028281_<12> × 700191085537147901094744735774752940309741476990420852082470723_<63> × 28572591255720584333860116095811560615943315370790426733845711699612014987103377564117869663718219254256901196014081_<116> (Bob Backstrom / Msieve 1.44 snfs for P63 x P116 / July 12, 2024 2024 年 7 月 12 日)

35×10²⁰⁷-179 = 3(8)₂₀₆7_<208> = 13 × 729209022392163521704999_<24> × 410232580726930298077335108382417607670186809008605558038065516475005448462958680909626574470952242034926408884224548141965914689668384222316083096733073627285844635645389019011059701_<183>

35×10²⁰⁸-179 = 3(8)₂₀₇7_<209> = 37 × 60323497724744884875369974819393878626950842517_<47> × 17423576063957356823345711519320730260795494443038332196035444035682033667862668082657368321510695121744816307840912698899608570639861326699893248489890992045503_<161> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs / December 1, 2013 2013 年 12 月 1 日)

35×10²⁰⁹-179 = 3(8)₂₀₈7_<210> = 3² × 506251 × 23174132382601_<14> × 3683101164153892552107908537912441744425441764421902414868020071989582900374685023904751505531364564090490782654767798373393305788423411568901921910855023530481946963732376536279047818373493_<190>

35×10²¹⁰-179 = 3(8)₂₀₉7_<211> = 19 × 23279 × 283675864393_<12> × 271456045436707034688138377_<27> × 123687021432754625399716260751_<30> × 544609522563567980369661523570783_<33> × 1695025931935939119406403350228658799999331316866860085759209709550278333939030848721819831507420985441699_<106> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1069749333 for P30 / June 15, 2013 2013 年 6 月 15 日) (Ignacio Santos / GMP-ECM 7.0 B1=1000000, sigma=1 for P33 / June 28, 2013 2013 年 6 月 28 日)

35×10²¹¹-179 = 3(8)₂₁₀7_<212> = 37 × 17041 × 61677780121533422396047828827595273226398160380907872252276923364300865621210671383783290361542811516404615401153163021597972598500736520805765568396869376858814098412713517460891441291652546860574558479611_<206>

35×10²¹²-179 = 3(8)₂₁₁7_<213> = 3 × 43 × 67 × 5281 × 184983619 × 10044414370877445547_<20> × 4585502789780947999243922755674860406722249281793659056953091830581720458236451041518664773288571307179998558758615618036819939510114383273807989459762662090018232165223612060573_<178>

35×10²¹³-179 = 3(8)₂₁₂7_<214> = 13 × 6664811 × 21028730272229982031_<20> × 140135511472534184092714474871216338249_<39> × 15231163877574868259124606825354362696136268161511976364508210007382270940386316719572392975817030105414890120521573638569775675156312028521824766911_<149> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1011915595 for P39 / July 2, 2013 2013 年 7 月 2 日)

35×10²¹⁴-179 = 3(8)₂₁₃7_<215> = 37 × 2621 × 43933 × 212677328162641636725629328225737717_<36> × [42918519646020111655426543838594475053000462801283573036133121834799904012921164228457829468442812370264260174437569021197475742463890043186068246848740291509505564009671_<170>] (Serge Batalov / GMP-ECM B1=3000000, sigma=2319367285 for P36 / January 9, 2014 2014 年 1 月 9 日) Free to factor

35×10²¹⁵-179 = 3(8)₂₁₄7_<216> = 3 × 277 × 491 × 53233 × 404369311 × 15600491033_<11> × 10874624346767_<14> × 5233663479641575844891_<22> × 12181189361625660196297_<23> × 501219381216306534139619162509_<30> × 1111003976493038221982495717504483767_<37> × 7351778246842343676745907802148004276777055775690900574072419459_<64> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1897419310 for P30 / June 15, 2013 2013 年 6 月 15 日) (Dmitry Domanov / Msieve 1.50 gnfs for P37 x P64 / June 21, 2013 2013 年 6 月 21 日)

35×10²¹⁶-179 = 3(8)₂₁₅7_<217> = 94238192149_<11> × 43498615491516945087740181693737987446935217277697911832878675047_<65> × 948687448469732730953841610361028043098747079583267063506168193264244583638168754158412424161562817528549597489754769627358074388967829571629_<141> (Bob Backstrom / Msieve 1.54 snfs for P65 x P141 / March 26, 2020 2020 年 3 月 26 日)

35×10²¹⁷-179 = 3(8)₂₁₆7_<218> = 37 × 47 × 3748344674981199661_<19> × 320148088301956325041_<21> × 18635262766786460989487314096088690149673391917162908447282775254964564173925632032553480090192297955234990769428535115342531982795622241339256790861260360165330920053032172233_<176>

35×10²¹⁸-179 = 3(8)₂₁₇7_<219> = 3² × 887 × 2087 × 781087 × 2506632233708389789384184631319254669881229885303113028925373600639682062620831_<79> × 11921939861266920732939411037893589455428392309203975493914485028060345476629609037177615694753543445722892285140617405094913951_<128> (Bob Backstrom / Msieve 1.54 snfs for P79 x P128 / June 24, 2020 2020 年 6 月 24 日)

35×10²¹⁹-179 = 3(8)₂₁₈7_<220> = 13 × 4009344532120776253466279143387784372087_<40> × 6309181086403325179419707486500146582146655868283891536611137420324917932511638913_<82> × 11825943836037934373839900866084632062445357474839119147738132951113784687146613684621797171709829_<98> (Ignacio Santos / GMP-ECM 7.0 B1=3000000, sigma=1 for P40 / June 29, 2013 2013 年 6 月 29 日) (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P82 x P98 / December 28, 2020 2020 年 12 月 28 日)

35×10²²⁰-179 = 3(8)₂₁₉7_<221> = 37 × 50387 × 3243941 × 922881391587673969289_<21> × 27683806577204444421501530520148072786887607813931_<50> × 251686932102387544766479594491421176527332074973626658966862187972031674303840623866468875689624856998366094241422025914035944069072695367_<138> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P50 x P138 / January 10, 2019 2019 年 1 月 10 日)

35×10²²¹-179 = 3(8)₂₂₀7_<222> = 3 × 29 × 223403 × 6387016189_<10> × 38482151683_<11> × 119686523905883842387_<21> × 6542900822440917239864079779_<28> × 103954747130791973402327291022476083870802804960500485816184884238198268261230116677685232387187313790477006298979981061364388472009932841868936317_<147>

35×10²²²-179 = 3(8)₂₂₁7_<223> = 28009357 × 8928997060615668960712956375683_<31> × 88337339725762949449827394477272846847_<38> × 176025424181242748443305933556781612061021634440548966014685378988863288342736230545361893869116197536170851549288410263809732252404839269774331791_<147> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=745844492 for P31 / June 16, 2013 2013 年 6 月 16 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2153262541 for P38 / July 2, 2013 2013 年 7 月 2 日)

35×10²²³-179 = 3(8)₂₂₂7_<224> = 23 × 37 × 258703 × 195800793521_<12> × 13921553562472088521_<20> × 64802589370000608552603768996822095510211591459535533153663651932274143620576321972588800803004736415581145802656384166276210075224363450008884592773763405045050822458835016002080817019_<185>

35×10²²⁴-179 = 3(8)₂₂₃7_<225> = 3 × 7231979 × 920171078996329_<15> × 1255608582268826707_<19> × [15514017216206078492479780928176308957490121921564091855495125785760575528385668152088795852605312773369139238988526318770341660353022969719787837938221158652874649018158445353703259717_<185>] Free to factor

35×10²²⁵-179 = 3(8)₂₂₄7_<226> = 13 × 71 × 11164556233193677208833108879_<29> × 79299264491273801589352780751_<29> × 4758972653124621788979370896305735839196292979266926335601553225392110243355177766017485852300356706396285807900729545787276261792582906170197962297781927611388505461_<166> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4219947191 for P29 / July 2, 2013 2013 年 7 月 2 日)

35×10²²⁶-179 = 3(8)₂₂₅7_<227> = 37 × 59 × 8707 × 49697 × 73859 × 453843527 × 1904288000639_<13> × 3978244973773277099_<19> × 1826904268589891920852452726569665399_<37> × 1696386014920937314220850261232646756648962923396239_<52> × 52311706201971339938469734158288323777449909283084453174717452492893502419334845547_<83> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1150061551 for P37 / July 4, 2013 2013 年 7 月 4 日) (Erik Branger / GGNFS, Msieve gnfs for P52 x P83 / May 22, 2014 2014 年 5 月 22 日)

35×10²²⁷-179 = 3(8)₂₂₆7_<228> = 3⁵ × 340527983189644621511451120275327492976901_<42> × 4277245960404427518869975708367822896958543225535976351_<55> × 1098758455601742860153081809409757491267458530853668975108903130205028689749980688616405271618024241012111877035457575619825075159_<130> (matsui / Msieve 1.52 snfs / November 17, 2013 2013 年 11 月 17 日)

35×10²²⁸-179 = 3(8)₂₂₇7_<229> = 19 × 62981 × 103242749 × 2916215993_<10> × 63420224984843_<14> × 67984029233467_<14> × [2503504958622057374175629779655513581527912128837563065667971262784285266373680381160807300443853828410702617600289659443545330427754134186197315346009687985713217529576510830749_<178>] Free to factor

35×10²²⁹-179 = 3(8)₂₂₈7_<230> = 37 × 797 × 40009 × 32961562665058174051711986228790211382208483989817819568108187296849772510440202743938794795357087661896244331570285363680595048393002761676334589179512747995912056896704234365682120865686370223257202858687129494077479087_<221>

35×10²³⁰-179 = 3(8)₂₂₉7_<231> = 3 × 149 × 197 × 1439 × 112997 × 2044024963_<10> × [13287334949127609119215412627750264889563715424671234303743170122138288079808984279021092609372026476087795339034782646562691996182872365072601966071333226618488075066485563620514039889344442262981452840931717_<209>] Free to factor

35×10²³¹-179 = 3(8)₂₃₀7_<232> = 13 × 8040077301908128219_<19> × [37206769028738549488522212453494930342065044248537947717869129394127393396236183814430072031018933027013219868797814298078273231460158787473062944624565243707019831391586550620382339200355156697525498893970073321_<212>] Free to factor

35×10²³²-179 = 3(8)₂₃₁7_<233> = 37 × 33251947 × 77499093892384070295953_<23> × 407859052886890848042735431042672149130778511096980103407989048408156213757551091332197781473063446643100390801907875199013785852848250244368820475270335013221383079900626430855719666756864159156522161_<201>

35×10²³³-179 = 3(8)₂₃₂7_<234> = 3 × 43 × 131 × 110943451620983_<15> × [207425839107836520307597797297560114643021663784744294349166000853519813796917923345097248207114418676059385179935136969140374691113102229910149208367622974700359524836640737297281850792801827879996599450144006940011_<216>] Free to factor

35×10²³⁴-179 = 3(8)₂₃₃7_<235> = 2327332382622043483_<19> × 4543165183499514703_<19> × [367797349395598987314863890543426588927103313513645106439221560264365840410764550784071023514746490496511658622763429939582334890984473811303572222392155881468156853857686132355965163079603864820763_<198>] Free to factor

35×10²³⁵-179 = 3(8)₂₃₄7_<236> = 37 × 121115221 × 624076043273593_<15> × 159780552587709597954097_<24> × 177076187913894672515771_<24> × [491477330516213514973968738483574273699397782419499350840747601316273309839416667866177936918246814397419482266119239270708554648896127892606714054799165087335759941_<165>] Free to factor

35×10²³⁶-179 = 3(8)₂₃₅7_<237> = 3² × 346863856906526911787389_<24> × 124573015270524714797548279483433003495186705112005789962398948257798370542002342743879015858433187367277239406321912236529888870609023247883075317133292725262445686577023363887938623566240764971546628331158913387_<213>

35×10²³⁷-179 = 3(8)₂₃₆7_<238> = 13² × 601 × 134257 × [285185486411404588943244241190437461780786066267865060396762345730756988811485427353962876383960156155153590212314334974827121229749227037040412302330544814148709980379606261209699900393339309315186184986209122918617237564913639_<228>] Free to factor

35×10²³⁸-179 = 3(8)₂₃₇7_<239> = 37 × 1097009 × 3315943 × 3878991491776700938118225724427_<31> × 537031563338145447445719958568507_<33> × [138703661306215476664383700124719847491442961695384884733987961917550946663525254330993476732733302761888380275285964831612132825743296392934889505873744249124357_<162>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=4276365167 for P33 / June 19, 2013 2013 年 6 月 19 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1603332319 for P31 / July 2, 2013 2013 年 7 月 2 日) Free to factor

35×10²³⁹-179 = 3(8)₂₃₈7_<240> = 3 × 1534295061253_<13> × [84488070712921461812136081555931698978452821721024275482700317401664665416666207517181780935018364797480100430217812074925608572152896124635929405560890018417861839789830741143735228461551188444356974276414825230084396945352793_<227>] Free to factor

35×10²⁴⁰-179 = 3(8)₂₃₉7_<241> = 2861 × 13425403 × 71173448729_<11> × 3750588799851035456797207_<25> × [379282568560713244812137712694408585946146134356095914403796875879290596207958607824152818514207733333964565395107646252730208227363257326270065862728517569431035395012064160750944473884796207063_<195>] Free to factor

35×10²⁴¹-179 = 3(8)₂₄₀7_<242> = 37 × 109 × 179 × 4240741 × 387278062046519618883316194693740165949311_<42> × 32800437497728807998665178781374071822563644071645140937173116443542757003426654212244714958560488905741082231171161970023605671193331146100782267642340860692969553439196054909048409375191_<188> (Serge Batalov / GMP-ECM B1=3000000, sigma=701587485 for P42 / May 19, 2014 2014 年 5 月 19 日)

35×10²⁴²-179 = 3(8)₂₄₁7_<243> = 3 × 233333560541_<12> × 6849381236309_<13> × 277850812826453642232801662225507_<33> × 135338909350196405779093889246735548501_<39> × 26922432975725172397305711249005743115609_<41> × 2797992619636601938214046310624770104779163681537_<49> × 28633901015641102298627640869481829115572199640455609362811_<59> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4017413759 for P33, B1=3000000, sigma=112492743 for P39, B1=3000000, sigma=4165603284 for P41, Msieve 1.50 gnfs for P49 x P59 / July 2, 2013 2013 年 7 月 2 日)

35×10²⁴³-179 = 3(8)₂₄₂7_<244> = 13 × 97 × 691 × 19246462812061351_<17> × [231889709266649916701899041219123445710271359167563677827246460668003168392221785080262478210700155919708555863281472987697477454070176814512362038728549778450580562991450970861729703385916595489014873909555988514663406487_<222>] Free to factor

35×10²⁴⁴-179 = 3(8)₂₄₃7_<245> = 37 × 17713 × 11510730503730073950959_<23> × 2049532358924236850577163_<25> × 11871561844242057283324218631_<29> × 381420741911021724853886037343618716141602299353311188702811651688176303231_<75> × 555471596666011262587496295980192365276905889510689325860783813712947176121673227759496471_<90> (NFS@Home Greg Childers and Caleb Birtwistle / Msieve 1.54 for P75 x P90 / November 15, 2023 2023 年 11 月 15 日)

35×10²⁴⁵-179 = 3(8)₂₄₄7_<246> = 3² × 23 × 67 × 3457 × 75202052599753427483_<20> × 11023406675423263347293_<23> × 9784428927037834567659835790174921347733266701910041096551974835924543667979890834294525544829244722018423099302355726827532178489972288415818449206159087894758695038798526338976994707961449473181_<196>

35×10²⁴⁶-179 = 3(8)₂₄₅7_<247> = 19 × 637849874351_<12> × 897457216434745688401_<21> × [357552406651117389166448942851060608716293416958647451019665664006889487801891214933820307324657827325242726181517396905646920062198076878375515479016128258287404645021109825677054697779825356860142673314737674323_<213>] Free to factor

35×10²⁴⁷-179 = 3(8)₂₄₆7_<248> = 37 × 911 × 71059 × 3983789 × 4301633645609717_<16> × 4630341404709037598403661_<25> × [204617879811490321948267447307278733769369783814234669338538971039403165041345562025324685839781813245514387374793080661006080263852398411276646507057571816925721818991338457024217062962044243_<192>] Free to factor

35×10²⁴⁸-179 = 3(8)₂₄₇7_<249> = 3 × 155473 × 31066177 × 2220008756303218033644039911372396081884957_<43> × 12089457188983341758679999533148330509437727476723798325989120468425924296136075271084700509734805810673856085497303305521793325690608568868920405364935207427963747858393201564330919381598637457_<194> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3576119425 for P43 / July 3, 2013 2013 年 7 月 3 日)

35×10²⁴⁹-179 = 3(8)₂₄₈7_<250> = 13 × 29 × 66949 × 1421779 × 2586347750538017931611774266081_<31> × 41900680555093156907133542244676440215071017225763240638629190470798250778450489181504588315202687782907593706108150699862512455198686764131448771740191878105869132082235244578443873348357811733321011297681_<206> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1032999084 for P31 / June 20, 2013 2013 年 6 月 20 日)

35×10²⁵⁰-179 = 3(8)₂₄₉7_<251> = 37 × 463 × 296489 × 469541 × 22072405627_<11> × 41182078837_<11> × 84417643253_<11> × 42590145846579499578827_<23> × 14312713061154484321800020883553_<32> × 270399701782080630931844339928269_<33> × 3484255452040458920651707402196078289661578709_<46> × 370017502649695145595230510819448274243451723682592900390081836310004009_<72> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2838392438 for P33 / June 20, 2013 2013 年 6 月 20 日) (Ignacio Santos / GMP-ECM 7.0 B1=1000000, sigma=1 for P32 / June 28, 2013 2013 年 6 月 28 日) (Dmitry Domanov / Msieve 1.50 gnfs for P46 x P72 / July 1, 2013 2013 年 7 月 1 日)

35×10²⁵¹-179 = 3(8)₂₅₀7_<252> = 3 × 188827 × 12433367819_<11> × [55214278972510526636901019703975150657022178006894869270907879887786354026459985877549559737232832807109433605634488605678414800634136186140639113086684938367183060782380466160495696280152146106178146806643895573987203420543936355398133_<236>] Free to factor

35×10²⁵²-179 = 3(8)₂₅₁7_<253> = 61 × 11763253 × 67879484149790993_<17> × [79841691442798187517289451596555475430991466154647095510794236113961157637059429898658639617933953252071869124762619895847719425904192124194231176403877889627458201834955499652136703410396956179038671339775744073870100597560423_<227>] Free to factor

35×10²⁵³-179 = 3(8)₂₅₂7_<254> = 37 × 455610492671_<12> × [2306907035633227757496759371754602860646397343187870295515473078175224761056370133772570565143298328256887185097308404062734165316272888034878580407335140117293813401353589238113490749631153704968995566978415908842884979517713191281524525781_<241>] Free to factor

35×10²⁵⁴-179 = 3(8)₂₅₃7_<255> = 3³ × 43 × 2027 × 1289921 × [128108059647706460292955924891212885808760541599212554995377994694129754143590084084558165690152978793993490194120833971106392709383534810144370215651849444556634323124452052054949470157526519947569075150364820119697800521439828211441554835901_<243>] Free to factor

35×10²⁵⁵-179 = 3(8)₂₅₄7_<256> = 13 × 16724583470641276271_<20> × [17886561998415433034386424832149054652047663370707480897191798054612134066553143009889733291302919059129659307054288193843486337757984418668589929950907351966002428603984634189938262013450098253175752680967604672565046604958853196920669_<236>] Free to factor

35×10²⁵⁶-179 = 3(8)₂₅₅7_<257> = 37 × 13376063 × 242452760967680092201_<21> × [324092044995733908159909507573785745052504306574045313240172728264421540039818519703640236130602533641949442325392682926289989611999883201492702772641225899207219939508358216490263029728766239469142205317231089713491480627064077_<228>] Free to factor

35×10²⁵⁷-179 = 3(8)₂₅₆7_<258> = 3 × 507358237844751869_<18> × 43932856189799793864711149843971_<32> × 12651368625597699868255533730192821285133_<41> × 320580981880810725409197026039818934828343191_<45> × 704279702000165596323029082688300972263425876535324232962683_<60> × 2036008976946167318764258451132690002144214829850439285577358579_<64> (Jason Parker-Burlingham / GMP-ECM for P32 / January 2, 2021 2021 年 1 月 2 日) (Ignacio Santos / GMP-ECM B1=3000000 for P41 / April 15, 2024 2024 年 4 月 15 日) (Bob Backstrom / GMP-ECM 7.0.4 B1=52280000 for P45 x P60 x P64 / April 24, 2024 2024 年 4 月 24 日)

35×10²⁵⁸-179 = 3(8)₂₅₇7_<259> = 52913629 × 4608714905965690521437_<22> × 6778637732075222213765540923795553_<34> × 2352532969930504909448150303852530555903855537560816354390720107286493531328170863307167325291949341928836014302481884054865014265510923780567423301696352508646491419556836059892676766351900121823_<196> (Jason Parker-Burlingham / GMP-ECM for P34 x P196 / January 2, 2021 2021 年 1 月 2 日)

35×10²⁵⁹-179 = 3(8)₂₅₈7_<260> = 37 × 121571 × 127627283350219542553272733_<27> × [67740796181115069456051267255629344488052732485362697462736943096796521358900829786449834834219441049126248758625194636408131493281326500020031600959830714267941032286875608219285460340017907279059639865621514563570527957603757_<227>] Free to factor

35×10²⁶⁰-179 = 3(8)₂₅₉7_<261> = 3 × 71 × 113844082434923_<15> × [16037455723242389223322815657273978728343475335254401232627116995830313873783697186201812542014621808833914307517178546583794233702220843655394650868593162964297772954141915580483541748467990874378100715937678729299309431123443592115109935352913_<245>] Free to factor

35×10²⁶¹-179 = 3(8)₂₆₀7_<262> = 13 × [299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299145299_<261>] Free to factor

35×10²⁶²-179 = 3(8)₂₆₁7_<263> = 37 × 113² × [82312714468717288045348191013474121000160627382806096879242779469892008070408884881435590183338636623936960690034540766782915737414915110897568411860838832410607804139012534344980112072288436921532700372076987317021775475843922864049733812440367378107216779_<257>] Free to factor

35×10²⁶³-179 = 3(8)₂₆₂7_<264> = 3² × 47 × 1061 × 5583932593_<10> × 864979903094429271741611_<24> × 2057654902580240127769633211_<28> × [87186864641161079310741491692816456868270472229303327369187774021890607056007893730401345783630015510778166400155073856425432729045357057026990084586279130160100930939166130059950690768480781525093_<197>] Free to factor

35×10²⁶⁴-179 = 3(8)₂₆₃7_<265> = 19 × 157 × 50587 × 309167 × 30949019 × 321617517246189617_<18> × 8374398867197338791847105005051935773337936888561961514428718279613094686370834440309985344887032052707426019880249486307419725997078894298179434681540738416135974625962399493550032732292052781620534904265021177968099361107367_<226>

35×10²⁶⁵-179 = 3(8)₂₆₄7_<266> = 37 × 735533 × 2109286723_<10> × 44741119679719680723929_<23> × 7562094793622685224111017078679_<31> × [2002336499824245559748683622154804352416482998822048699533728397130774988922186411220989258369088233141928279825172052762906218270065632046323048569659862525911429002069748695336315321312010568579_<196>] (Jason Parker-Burlingham / GMP-ECM for P31 / January 2, 2021 2021 年 1 月 2 日) Free to factor

35×10²⁶⁶-179 = 3(8)₂₆₅7_<267> = 3 × 5867 × 1114344672677_<13> × [19827531603807989553738662277545344861096609654965551751329789046489188336913063613539738710351520326123885286555450787624983853193638951873892235375906339995259902180831879315931919064280033620431432106152946864785592502842509193494710372386362401131_<251>] Free to factor

35×10²⁶⁷-179 = 3(8)₂₆₆7_<268> = 13 × 23 × [13006317354143441099962839093273875882571534745447788926049795615013006317354143441099962839093273875882571534745447788926049795615013006317354143441099962839093273875882571534745447788926049795615013006317354143441099962839093273875882571534745447788926049795615013_<266>] Free to factor

35×10²⁶⁸-179 = 3(8)₂₆₇7_<269> = 37 × 233 × 39719 × 16416989 × 700189292068859_<15> × 9880083431953583956771805941952500190828323473870460588605789944151937778652588307895572753139890325303561670665776965193325395498170139971656815761239458593467154704171926826199483282930116293264974030535358100018222280904846028551323963_<238>

35×10²⁶⁹-179 = 3(8)₂₆₈7_<270> = 3 × 12703 × 8094929 × 102482788532253328725618782689_<30> × [12300818322485379994386893612180709095763516564888313165628229064905521752338023741568839295288131298266749464808486691985540327963857614920073948732140512140747186433135716655980515078109070032197861927039829625869141309178147603_<230>] (Jason Parker-Burlingham / GMP-ECM for P30 / January 2, 2021 2021 年 1 月 2 日) Free to factor

35×10²⁷⁰-179 = 3(8)₂₆₉7_<271> = 1180174399_<10> × 41212336341791_<14> × 15869759813851237159331861_<26> × 269242354094827872729109319_<27> × [18712782810471696964705640114968034748868286187367042026439060770906757652089380371207388272569948090069840470198052178392007773975239568161429905003821835151534236593882996257452841013045665274477_<197>] Free to factor

35×10²⁷¹-179 = 3(8)₂₇₀7_<272> = 37 × 1619 × 4091 × 2227561508959771702185664326577_<31> × 6492343307985278499543017742461_<31> × [10972770627740465738763505620418306720488767420143173452258819756770253187552930224410624765367053074167907914478822047455410647363643909011965102921273017134796708273024538344155545748462030244060707927_<203>] (Jason Parker-Burlingham / GMP-ECM for P31(2227...) x P31(6492...) / January 2, 2021 2021 年 1 月 2 日) Free to factor

35×10²⁷²-179 = 3(8)₂₇₁7_<273> = 3² × 299843 × 28036219 × 243644813288057_<15> × 340953989536861_<15> × 1192800733578817057_<19> × 102617213772383833623817313_<27> × 34589358319565687867012359519_<29> × 14614571914784555226033698119308469551142809866615884786566407150662824621361993419924532235512205745578380378409287999489968553359518025884775654681265504013_<158>

35×10²⁷³-179 = 3(8)₂₇₂7_<274> = 13 × 186191878365469279370023111_<27> × [1606650632516407060645159772688713248880328122889052969355856836622096723396307337422426720970896271300074907564649792441006518759759471760332966289267933605321052642133491813618373685627605169180091612545610557343724930896107035385567364853964309_<247>] Free to factor

35×10²⁷⁴-179 = 3(8)₂₇₃7_<275> = 37 × 1429 × 332121617 × 23261136905904017_<17> × [95205820664645302795629709831650769381607900863234105674233228485349575657073980390707098636748148820496582704498594524623373614226802579783570062166783888807520285992085186577546016922740938070055389458100007762491797671631220459236110995384671_<245>] Free to factor

35×10²⁷⁵-179 = 3(8)₂₇₄7_<276> = 3 × 43 × [3014642549526270456503014642549526270456503014642549526270456503014642549526270456503014642549526270456503014642549526270456503014642549526270456503014642549526270456503014642549526270456503014642549526270456503014642549526270456503014642549526270456503014642549526270456503_<274>] Free to factor

35×10²⁷⁶-179 = 3(8)₂₇₅7_<277> = 13627 × 234836857 × 172587244266420394255492202627_<30> × [7041259098128910783933067687215394841090058041444843706882913251865120732078475141980020938230631833421690652532834232447766043752476530385219505522728223090591685472821417132114135592069608661063515071990684618037353898122001799888479_<235>] (Jason Parker-Burlingham / GMP-ECM for P30 / January 2, 2021 2021 年 1 月 2 日) Free to factor

35×10²⁷⁷-179 = 3(8)₂₇₆7_<278> = 29 × 37 × 227 × 20035567 × [7968898925207712257971895098936944411315457003999197263844270697448933532065942700410232762059093434425365202840071445008741900340474155875822210389191075435861548049954052127630417775510269110671614462773848222191424615043061709497317777082508058017499523145853091_<265>] Free to factor

35×10²⁷⁸-179 = 3(8)₂₇₇7_<279> = 3 × 67 × 1350566576088012181785541817_<28> × [1432562174825305668535471524605011206485651438783402276629001332463652603856807203339801733771238041439392362115846929519141022150517584448364246579644665482033873724293505181501896801989492413169690914684133854474367045257796345123872322416022619511_<250>] Free to factor

35×10²⁷⁹-179 = 3(8)₂₇₈7_<280> = 13 × 217933 × 220592549 × 1873249809977749014431517026492197_<34> × [3321793638313866365870163373416106293543051486442854188305595985791387489541748468808316562669703258078566037782452020461580515118248677000577811215373979505146555669939617750976584884659068317982852569942244395050621601973320480951_<232>] (Jason Parker-Burlingham / GMP-ECM for P34 / January 2, 2021 2021 年 1 月 2 日) Free to factor

35×10²⁸⁰-179 = 3(8)₂₇₉7_<281> = 37 × 2180392795653718729_<19> × [482046653770899167381093730941045509476838464174385035661732697654435001929389754921042945713111917169520609209424011538875357275144599991086752721389545654450296489782855862022347689394012398552394998929143843756434159585644900589822440681905195340180939028819_<261>] Free to factor

35×10²⁸¹-179 = 3(8)₂₈₀7_<282> = 3³ × 366383 × 9730657 × 16191896192232307_<17> × 1136058505687278713_<19> × 219627078039617900309813913636197121779775784682056954529026827868657134990799231843894639697160984285187988442366757310282225763473163195900768054654549727676360295080068473346488625381759212277075843427461930628888107350784811429761_<234>

35×10²⁸²-179 = 3(8)₂₈₁7_<283> = 19 × 51834721 × 12480373033_<11> × [316390621980087178108752721304183734090569667145611412895401367468325207909565188634918153091468912191475557391981155928441584663822324172001486321866847308085662826072651788404395443722209862643136601054199815125094131915239132651335938376514070544215135370823461_<264>] Free to factor

35×10²⁸³-179 = 3(8)₂₈₂7_<284> = 37 × 14265389 × 1355437630951_<13> × 55402024104743_<14> × 30358272040796046695304182622100286336771_<41> × [32319004345828505570293042079133500834512165133158659090015917613323347129101025415171149720301087193169773476670485157946138738808851299598705002365817762199609774665261065295125597514351298454784536411477453_<209>] (Seth Troisi / GMP-ECM 7.0.6 dev B1=1e9 for P41 / November 15, 2023 2023 年 11 月 15 日) Free to factor

35×10²⁸⁴-179 = 3(8)₂₈₃7_<285> = 3 × 59 × 277 × 1549 × 16937 × 1235573 × 197116766246899_<15> × 81100369032739810749954557_<26> × 15306284752982717269589034640501218274086128845893940248190903827537078659495551786619804154353719788467302805380023846467856088289481325204412335332394538102630886344772654019214939218263019670899286724993931560254393855898629_<227>

35×10²⁸⁵-179 = 3(8)₂₈₄7_<286> = 13 × 619 × 4517 × 5953 × 914205315373318658021_<21> × [19659017914643266509538762096555501308686159936027346146363339080272310470320805183185798108210952686145787380654738009546063152152498937279431954221744801033791352532045074875324174931114898405121387681643781975305111983981678587597536259653569812780001_<254>] Free to factor

35×10²⁸⁶-179 = 3(8)₂₈₅7_<287> = 37 × 4397 × 11719 × 51593 × 30181947878503_<14> × 2346980883421483778457365473_<28> × 5581220648102349237087797307793732595679427982328162903364161878565473410433284702989938951612890494202095155507732734985341447456483129254798547407946110469367876789615573660946680524653376929523817489034954961834776031397794337071_<232>

35×10²⁸⁷-179 = 3(8)₂₈₆7_<288> = 3 × 510719679857374296965928217531904080639529_<42> × [253817573009582359196581491593594208678839511844616342712812579722252512316335073643786237675635908441634925374812884849353532016320046527387783634585202652151225270125020486504096193524002986121692323239459162910045177250900982483511859000566901_<246>] (Jason Parker-Burlingham / GMP-ECM for P42 / January 2, 2021 2021 年 1 月 2 日) Free to factor

35×10²⁸⁸-179 = 3(8)₂₈₇7_<289> = 2767553 × 10992586960887629_<17> × 555404006995469011637324085035909_<33> × 1827662512923981746468867413362772949_<37> × [125928684207924254450126031789495164793772642309172823976313262793517881081830095643332973488130323897182609415328183002071264793972802335320015790977767203043174253118373980797543216939324364403611_<198>] (Jason Parker-Burlingham / GMP-ECM for P33 / January 2, 2021 2021 年 1 月 2 日) (Marlon Trifunovic / GMP-ECM 7.0.5-dev B1=3000000, sigma=1:135521066 for P37 / February 28, 2022 2022 年 2 月 28 日) Free to factor

35×10²⁸⁹-179 = 3(8)₂₈₈7_<290> = 23² × 37 × 4177 × 36767 × 232753 × 13601279 × 3187673429987_<13> × 1061900972857261261_<19> × [1207292744295224194737944762221899126031756109044622804223505803781274140695713199525668330970782444980940973380362420128061523309562737366106033902796764737405147737497320967052055395624403982064000401838629135439429443273037916361549_<235>] Free to factor

35×10²⁹⁰-179 = 3(8)₂₈₉7_<291> = 3² × 495639593 × 10310685805475769079_<20> × 435649859317905198683_<21> × 19408496908144593128325588275522743716062815758324963385219062597299230494820283191327366510957245824642277405988734097447415189861804090080568275725085145551698766980756015606084788152413546984384903817531870495057964701880602389481607407043_<242>

35×10²⁹¹-179 = 3(8)₂₉₀7_<292> = 13 × 19903738247_<11> × [15029603757494547868244245160832130656744427952650172595446778292094927452908504838483025158080260356093656244068938551154126082451253969472438535889739946362506306484050455433983446071857857330630785959878240620390997204079094886177102123206953430909701570157467781692602518543317_<281>] Free to factor

35×10²⁹²-179 = 3(8)₂₉₁7_<293> = 37 × 1117 × 140867 × 13284560816570399712131197_<26> × 118970128315332917222119089440077_<33> × [4226454916452062328539303293393992501176915701447800763682145905558667634317689287586547111114512809434976500880958264128892380973382084106422917540547534985227899850455816503178028310327837725591449456221905531966211252629461_<226>] (Jason Parker-Burlingham / GMP-ECM for P33 / January 2, 2021 2021 年 1 月 2 日) Free to factor

35×10²⁹³-179 = 3(8)₂₉₂7_<294> = 3 × 2801 × 45184597 × [1024237702237191866485661642000776963954161488421615214678334811011585272132015072666191992917607209421921917683693538021711678256494418936274463644803307332518192380847113692612169892254532913525730378977572432696951923634443017215557522533963873741421729926460335269181654109671257_<283>] Free to factor

35×10²⁹⁴-179 = 3(8)₂₉₃7_<295> = 8423 × 38873 × 113079311 × [105033423733793113251412588517865712654715470449869012314351997380028192042253225537135680218348201307059252509342448008470355910519938413278011595073883721434404737309756252914767244524500005596659180567988666223693355304570596147745231243947921137886011022606705808751426516823_<279>] Free to factor

35×10²⁹⁵-179 = 3(8)₂₉₄7_<296> = 37 × 71² × 27027037979_<11> × 55751585871342957326273701622257281285617_<41> × [138373025225551929910397239612946572718122365144155754356251790804499999346364771180057928251692954866387706090562559816085600233618642275136058527613846124633802552486021816750229810783541765791563588942770760362093980371799754779341196177_<240>] (Ignacio Santos / GMP-ECM B1=3000000 for P41 / April 16, 2024 2024 年 4 月 16 日) Free to factor

35×10²⁹⁶-179 = 3(8)₂₉₅7_<297> = 3 × 43 × 822766167929_<12> × 565220719086545693_<18> × 1184202161117414227400763143759280497_<37> × 49230367216086153324173976707969062139_<38> × 355560353357855198948995972230749088741404501_<45> × 43038695126311231546431609491364079125386829891701_<50> × 7266243990548116771464616648204478273719822933483674152267876952477454447924517785812215379152953_<97> (Jason Parker-Burlingham / GMP-ECM for P37 / January 2, 2021 2021 年 1 月 2 日) (Ignacio Santos / GMP-ECM B1=3000000 for P38 / April 16, 2024 2024 年 4 月 16 日) (Dmitry Domanov / for P45 / May 20, 2024 2024 年 5 月 20 日) (Ignacio Santos / GMP-ECM B1=43000000 for P50 x P97 / May 30, 2024 2024 年 5 月 30 日)

35×10²⁹⁷-179 = 3(8)₂₉₆7_<298> = 13 × 1217 × [245805504638701023253200738821116799752789892477649256613923828385619675677194165279621319062568035452176783318936153775923701971360147202382206490669925345356734017374937670747038043669103652669798931097205542562978881795644326457802217867953282908089810308380563105296055172801269761006819347_<294>] Free to factor

35×10²⁹⁸-179 = 3(8)₂₉₇7_<299> = 37 × 167 × 1291 × 4127 × 97365643 × 509172251711_<12> × 1265044136845763_<16> × 573301320462446678518244266347677_<33> × [32853946391171889347378335406008474806988831717398167674851789865346350199352619415502687615887169600524298088717031980242253537972059230750011932672737355914865598251306134547843867802090472965398337710910479849187217123_<221>] (Jason Parker-Burlingham / GMP-ECM for P33 / January 2, 2021 2021 年 1 月 2 日) Free to factor

35×10²⁹⁹-179 = 3(8)₂₉₈7_<300> = 3² × 223 × 349 × 76369 × 60914476153592971113371_<23> × 81223862634992105611197519739_<29> × [1469371050558555687735307456828893336459449412371788252274998559653304772064512931345418449888549412194512580118780598429705300622080547322338823963285952414351298024842573035084583698113233279346229300482627738540359126034551384335791469_<238>] Free to factor

35×10³⁰⁰-179 = 3(8)₂₉₉7_<301> = 19 × 111827 × 1659038867_<10> × 3997617413_<10> × 47638466110621_<14> × 1459187939585302666836149561_<28> × 35518755804073175833704595068172945181279676187_<47> × [111773982697184844990832200729509720757163226261214326509799819141809143997116657894103617669457927729000552012619521951507251600464368616160016011366275636126633607433239385286277171217127_<189>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1:787723057 for P47 / January 13, 2021 2021 年 1 月 13 日) Free to factor

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4. Related links 関連リンク

A102979 - OEIS (The OEIS Foundation Inc.)