Factorization of 344...448

Table of contents 目次

About 344...448 344...448 について
Prime numbers of the form 344...448 344...448 の形の素数
1. Last updated 最終更新日
2. Known (probable) prime numbers 既知の (おそらく) 素数
Factor table of 344...448 344...448 の素因数分解表

1. About 344...448 344...448 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

34w8 = { 38, 348, 3448, 34448, 344448, 3444448, 34444448, 344444448, 3444444448, 34444444448, … }

2. Prime numbers of the form 344...448 344...448 の形の素数

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

No prime number of the form 344...448 exists. 344...448 の形の素数は存在しません。

3. Factor table of 344...448 344...448 の素因数分解表

3.2. Range of factorization 分解範囲

n≤100 / Completed 終了 / July 27, 2022 2022 年 7 月 27 日
n≤150 / Completed 終了 / July 28, 2022 2022 年 7 月 28 日
n≤200 / Completed 終了 / February 22, 2023 2023 年 2 月 22 日
n≤300 / Remaining 59 残り 59

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

n=207, 210, 212, 213, 214, 215, 216, 218, 221, 223, 226, 227, 228, 231, 233, 235, 237, 238, 240, 242, 243, 244, 245, 248, 250, 252, 253, 256, 257, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 274, 275, 276, 277, 279, 281, 282, 283, 284, 285, 286, 287, 290, 292, 295, 296 (59/300)

3.4. Factor table 素因数分解表

31×10¹+329 = 38 = 2 × 19

31×10²+329 = 348 = 2² × 3 × 29

31×10³+329 = 3448 = 2³ × 431

31×10⁴+329 = 34448 = 2⁴ × 2153

31×10⁵+329 = 344448 = 2⁷ × 3² × 13 × 23

31×10⁶+329 = 3444448 = 2⁵ × 7 × 15377

31×10⁷+329 = 34444448 = 2⁵ × 17 × 63317

31×10⁸+329 = 344444448 = 2⁵ × 3 × 43 × 181 × 461

31×10⁹+329 = 3444444448_<10> = 2⁵ × 3709 × 29021

31×10¹⁰+329 = 34444444448_<11> = 2⁵ × 1076388889_<10>

31×10¹¹+329 = 344444444448_<12> = 2⁵ × 3 × 13 × 275997151

31×10¹²+329 = 3444444444448_<13> = 2⁵ × 7 × 61² × 83 × 49789

31×10¹³+329 = 34444444444448_<14> = 2⁵ × 109 × 4261 × 2317561

31×10¹⁴+329 = 344444444444448_<15> = 2⁵ × 3² × 1195987654321_<13>

31×10¹⁵+329 = 3444444444444448_<16> = 2⁵ × 149 × 55351 × 13051411

31×10¹⁶+329 = 34444444444444448_<17> = 2⁵ × 71 × 150131 × 100981189

31×10¹⁷+329 = 344444444444444448_<18> = 2⁵ × 3 × 13 × 197 × 1401000766483_<13>

31×10¹⁸+329 = 3444444444444444448_<19> = 2⁵ × 7 × 380819 × 40378720933_<11>

31×10¹⁹+329 = 34444444444444444448_<20> = 2⁵ × 19 × 4861 × 11654401724671_<14>

31×10²⁰+329 = 344444444444444444448_<21> = 2⁵ × 3 × 744573307 × 4818817609_<10>

31×10²¹+329 = 3444444444444444444448_<22> = 2⁵ × 769 × 1153 × 121398566625977_<15>

31×10²²+329 = 34444444444444444444448_<23> = 2⁵ × 179 × 247717 × 24275062866023_<14>

31×10²³+329 = 344444444444444444444448_<24> = 2⁵ × 3³ × 13 × 17 × 131 × 6773629 × 2032920833_<10>

31×10²⁴+329 = 3444444444444444444444448_<25> = 2⁵ × 7² × 139 × 1217 × 25805071 × 503225557

31×10²⁵+329 = 34444444444444444444444448_<26> = 2⁵ × 863 × 1247264065919917600103_<22>

31×10²⁶+329 = 344444444444444444444444448_<27> = 2⁵ × 3 × 1013 × 25583 × 52639 × 2630143262423_<13>

31×10²⁷+329 = 3444444444444444444444444448_<28> = 2⁵ × 23 × 47028314689_<11> × 99513489304687_<14>

31×10²⁸+329 = 34444444444444444444444444448_<29> = 2⁵ × 886411699 × 1214321618389299811_<19>

31×10²⁹+329 = 344444444444444444444444444448_<30> = 2⁵ × 3 × 13 × 43 × 167 × 599 × 64164209763603824029_<20>

31×10³⁰+329 = 3444444444444444444444444444448_<31> = 2⁵ × 7 × 29 × 47 × 151153 × 74637750021778679093_<20>

31×10³¹+329 = 34444444444444444444444444444448_<32> = 2⁵ × 59 × 505935611 × 36059686402847480161_<20>

31×10³²+329 = 344444444444444444444444444444448_<33> = 2⁵ × 3² × 1279 × 39117041 × 42627979 × 560783741341_<12>

31×10³³+329 = 3444444444444444444444444444444448_<34> = 2⁵ × 260921 × 9151619 × 45870949 × 982708053839_<12>

31×10³⁴+329 = 34444444444444444444444444444444448_<35> = 2⁵ × 3169 × 339662003436064654114512113881_<30>

31×10³⁵+329 = 344444444444444444444444444444444448_<36> = 2⁵ × 3 × 13 × 107881 × 632759502059_<12> × 4043160297336469_<16>

31×10³⁶+329 = 3444444444444444444444444444444444448_<37> = 2⁵ × 7 × 60293 × 10195483 × 25014767323806486001033_<23>

31×10³⁷+329 = 34444444444444444444444444444444444448_<38> = 2⁵ × 19 × 13553 × 16007 × 1465993 × 86134907 × 2068040959511_<13>

31×10³⁸+329 = 344444444444444444444444444444444444448_<39> = 2⁵ × 3 × 229 × 6232327 × 94992011 × 4466837593_<10> × 5924817707_<10>

31×10³⁹+329 = 3444444444444444444444444444444444444448_<40> = 2⁵ × 17 × 6331699346405228758169934640522875817_<37>

31×10⁴⁰+329 = 34444444444444444444444444444444444444448_<41> = 2⁵ × 3022405919664584213_<19> × 356136441463938991253_<21>

31×10⁴¹+329 = 344444444444444444444444444444444444444448_<42> = 2⁵ × 3² × 13 × 421 × 4409 × 180731 × 274238546276923019315554363_<27>

31×10⁴²+329 = 3444444444444444444444444444444444444444448_<43> = 2⁵ × 7 × 68791 × 747547 × 140864135141_<12> × 2122758590990321311_<19>

31×10⁴³+329 = 34444444444444444444444444444444444444444448_<44> = 2⁵ × 1034783 × 34679924222744539_<17> × 29994510649150696997_<20>

31×10⁴⁴+329 = 344444444444444444444444444444444444444444448_<45> = 2⁵ × 3 × 3587962962962962962962962962962962962962963_<43>

31×10⁴⁵+329 = 3444444444444444444444444444444444444444444448_<46> = 2⁵ × 523 × 673 × 271333 × 1127067265532557848080119770586127_<34>

31×10⁴⁶+329 = 34444444444444444444444444444444444444444444448_<47> = 2⁵ × 1277 × 8017 × 141707 × 1759516489837_<13> × 421678812301199114419_<21>

31×10⁴⁷+329 = 344444444444444444444444444444444444444444444448_<48> = 2⁵ × 3 × 13 × 32441655793213772741_<20> × 8507492735771050756917011_<25>

31×10⁴⁸+329 = 3444444444444444444444444444444444444444444444448_<49> = 2⁵ × 7 × 2917 × 3265687482370727_<16> × 1614210304605729024374388853_<28>

31×10⁴⁹+329 = 34444444444444444444444444444444444444444444444448_<50> = 2⁵ × 23 × 10331 × 492053 × 1747623034343_<13> × 5267922343910030749739407_<25>

31×10⁵⁰+329 = 344444444444444444444444444444444444444444444444448_<51> = 2⁵ × 3³ × 43 × 191 × 16181843 × 2999684892615529440281874127990082773_<37>

31×10⁵¹+329 = 3(4)₅₀8_<52> = 2⁵ × 71 × 1031 × 711874409 × 2518892443_<10> × 28966596247_<11> × 28310120753420101_<17>

31×10⁵²+329 = 3(4)₅₁8_<53> = 2⁵ × 269 × 883 × 4531648565800472741578384305316401457050730607_<46>

31×10⁵³+329 = 3(4)₅₂8_<54> = 2⁵ × 3 × 13² × 83 × 902821 × 22744494973579535411_<20> × 12456763062904204201799_<23>

31×10⁵⁴+329 = 3(4)₅₃8_<55> = 2⁵ × 7 × 2711 × 5672070869415022863934704583911518621957574373657_<49>

31×10⁵⁵+329 = 3(4)₅₄8_<56> = 2⁵ × 17 × 19 × 11909 × 79783766005157857_<17> × 3507331826644516840870089524311_<31>

31×10⁵⁶+329 = 3(4)₅₅8_<57> = 2⁵ × 3 × 216373 × 374187870448694336693_<21> × 44315451594670671879664229867_<29>

31×10⁵⁷+329 = 3(4)₅₆8_<58> = 2⁵ × 35869091 × 3000881424312896272974659126123070386391695537779_<49>

31×10⁵⁸+329 = 3(4)₅₇8_<59> = 2⁵ × 29 × 10499 × 15359 × 1655222106157_<13> × 2095758039289_<13> × 66353359061158691951837_<23>

31×10⁵⁹+329 = 3(4)₅₈8_<60> = 2⁵ × 3² × 13 × 151303 × 30407511331_<11> × 1082386458007_<13> × 18474495086090853576640699367_<29>

31×10⁶⁰+329 = 3(4)₅₉8_<61> = 2⁵ × 7 × 832477 × 6368983 × 2900205907929048830755649517877631777131194797_<46>

31×10⁶¹+329 = 3(4)₆₀8_<62> = 2⁵ × 647 × 1281950653673_<13> × 3494616567149_<13> × 7522168707923_<13> × 49368623255782438897_<20>

31×10⁶²+329 = 3(4)₆₁8_<63> = 2⁵ × 3 × 113 × 394193582191_<12> × 414348140053009_<15> × 194399240952606374467031022022429_<33>

31×10⁶³+329 = 3(4)₆₂8_<64> = 2⁵ × 2179 × 43377467069_<11> × 364220956849_<12> × 3126675827492937955187219405120482111_<37>

31×10⁶⁴+329 = 3(4)₆₃8_<65> = 2⁵ × 4547 × 236725069032084646775651833932018669208024827114336681083987_<60>

31×10⁶⁵+329 = 3(4)₆₄8_<66> = 2⁵ × 3 × 13 × 1061 × 157874174251991_<15> × 6473362892968592717077_<22> × 254535387053017467920113_<24>

31×10⁶⁶+329 = 3(4)₆₅8_<67> = 2⁵ × 7² × 1891959274193_<13> × 8503988858000894990241589_<25> × 136533322845345914721592693_<27>

31×10⁶⁷+329 = 3(4)₆₆8_<68> = 2⁵ × 223 × 313 × 1399 × 2200207 × 7174399 × 698317977850257342709436204700206401128136873_<45>

31×10⁶⁸+329 = 3(4)₆₇8_<69> = 2⁵ × 3² × 97 × 587 × 1843117 × 11396302178913338344316077144693436003742755655964013567_<56>

31×10⁶⁹+329 = 3(4)₆₈8_<70> = 2⁵ × 1483 × 1754749 × 6299481919_<10> × 31368608149_<11> × 116450940586251787_<18> × 1797504423711860339711_<22>

31×10⁷⁰+329 = 3(4)₆₉8_<71> = 2⁵ × 139 × 1457941 × 288979127 × 1226675503_<10> × 218420863673_<12> × 68600008471786009231970387480047_<32>

31×10⁷¹+329 = 3(4)₇₀8_<72> = 2⁵ × 3 × 13 × 17 × 23 × 43 × 16415699220671563501516514066326711303812356569151906093558386427_<65>

31×10⁷²+329 = 3(4)₇₁8_<73> = 2⁵ × 7 × 61 × 499 × 223283 × 8393773 × 8476685942541031_<16> × 31798147072881563558086840890738126217_<38>

31×10⁷³+329 = 3(4)₇₂8_<74> = 2⁵ × 19 × 15307 × 521319933913_<12> × 2208337822128417649387_<22> × 3214812740011215068547136481790643_<34>

31×10⁷⁴+329 = 3(4)₇₃8_<75> = 2⁵ × 3 × 113145730871_<12> × 40944394986790441_<17> × 774489119789011278615828355039416185359454333_<45>

31×10⁷⁵+329 = 3(4)₇₄8_<76> = 2⁵ × 3793 × 134219 × 245989 × 859521367463652598506797189005984232828111766234197118754303_<60>

31×10⁷⁶+329 = 3(4)₇₅8_<77> = 2⁵ × 47 × 6682606847509_<13> × 2158187909982887_<16> × 1587947651969206739225446442111571889777944589_<46>

31×10⁷⁷+329 = 3(4)₇₆8_<78> = 2⁵ × 3⁴ × 13 × 44695687 × 4873735694951209343459_<22> × 46925968459297527603210472554858929106168761_<44>

31×10⁷⁸+329 = 3(4)₇₇8_<79> = 2⁵ × 7 × 443847777325067_<15> × 82803384460725890666318507_<26> × 418397449449251230099618265972679383_<36>

31×10⁷⁹+329 = 3(4)₇₈8_<80> = 2⁵ × 839 × 29179 × 43968013180772973693094662748863663435554391305259696780514342379515469_<71>

31×10⁸⁰+329 = 3(4)₇₉8_<81> = 2⁵ × 3 × 96481981651660477201337_<23> × 37187907022028017095432920257876304885045314820151353899_<56>

31×10⁸¹+329 = 3(4)₈₀8_<82> = 2⁵ × 4428737 × 5017433821_<10> × 1042553175560399687_<19> × 4646323531146637098546186989433908968494744011_<46>

31×10⁸²+329 = 3(4)₈₁8_<83> = 2⁵ × 1811 × 113047531561044763633_<21> × 5257625788637260451267298726586637226371570975544393431603_<58>

31×10⁸³+329 = 3(4)₈₂8_<84> = 2⁵ × 3 × 13 × 453745967 × 2549704788383876655421205063609_<31> × 238562359504346331235313892874918015934617_<42> (Eric Jeancolas / ECM for P31 x P42 / June 24, 2022 2022 年 6 月 24 日)

31×10⁸⁴+329 = 3(4)₈₃8_<85> = 2⁵ × 7 × 1732469 × 15463229 × 64567913 × 1434260090540833771_<19> × 6198132314873807381714042347480153459769749_<43>

31×10⁸⁵+329 = 3(4)₈₄8_<86> = 2⁵ × 3225518237_<10> × 602800611989_<12> × 30462919485067_<14> × 28828071777152324477_<20> × 630389400841109327046592920647_<30>

31×10⁸⁶+329 = 3(4)₈₅8_<87> = 2⁵ × 3² × 29 × 71 × 580858501370076568392903183254486476115098423662451507683821104575516102147152819_<81>

31×10⁸⁷+329 = 3(4)₈₆8_<88> = 2⁵ × 17 × 2117041 × 2990825093328484785211970217167676873992267533924747654554826868614339511913337_<79>

31×10⁸⁸+329 = 3(4)₈₇8_<89> = 2⁵ × 1021 × 45909350929092018543719_<23> × 11262695711595038824244821171_<29> × 2038918941626992236635584433047241_<34>

31×10⁸⁹+329 = 3(4)₈₈8_<90> = 2⁵ × 3 × 13 × 59 × 947 × 87017042453454157817_<20> × 56767306732694991057428643539049034633383409003747244086575511_<62>

31×10⁹⁰+329 = 3(4)₈₉8_<91> = 2⁵ × 7 × 1968467 × 2964574729023235095166109330574641_<34> × 2635000034884268254249367515776946761940752506741_<49> (Eric Jeancolas / ECM for P34 x P49 / June 24, 2022 2022 年 6 月 24 日)

31×10⁹¹+329 = 3(4)₉₀8_<92> = 2⁵ × 19 × 151901 × 12286784697220704239_<20> × 30354055512169337082017653742004649751641374275801400580869850129_<65>

31×10⁹²+329 = 3(4)₉₁8_<93> = 2⁵ × 3 × 43 × 471481897 × 299354078059241_<15> × 8616920812316692079_<19> × 68608384427212349796298113841682486679325036327_<47>

31×10⁹³+329 = 3(4)₉₂8_<94> = 2⁵ × 23 × 160837904094865087_<18> × 1757520533571755419146947_<25> × 16555890954525712490282973834496355846678396034587_<50>

31×10⁹⁴+329 = 3(4)₉₃8_<95> = 2⁵ × 83 × 619 × 493027 × 40906449414049_<14> × 61054718061489932849819609_<26> × 17014482548757422716205187432599290888534651_<44>

31×10⁹⁵+329 = 3(4)₉₄8_<96> = 2⁵ × 3² × 13 × 1784659 × 32335450155817_<14> × 1594223426166070577447127966752593371929318653954780565556281554015207039_<73>

31×10⁹⁶+329 = 3(4)₉₅8_<97> = 2⁵ × 7 × 1070011 × 16477567563402482362051_<23> × 146486785000782719073481_<24> × 5953760701490853772301603529419845368462647_<43>

31×10⁹⁷+329 = 3(4)₉₆8_<98> = 2⁵ × 1602666291572261_<16> × 2117634323873218511953_<22> × 317157609493235394636665605076207245685475510938122881650933_<60>

31×10⁹⁸+329 = 3(4)₉₇8_<99> = 2⁵ × 3 × 919 × 23719 × 37340438957_<11> × 4408152858779530425149521428239589289266877668826216994268140878902661757165119_<79>

31×10⁹⁹+329 = 3(4)₉₈8_<100> = 2⁵ × 13405967 × 8029177521389459551025963952386940001335889375894248351416118575324621408428716025400397367_<91>

31×10¹⁰⁰+329 = 3(4)₉₉8_<101> = 2⁵ × 55036780742550388875377467170432183897071578801_<47> × 19557628087369292809877606841207392514058008585095689_<53> (Dmitry Domanov / Msieve 1.54 snfs for P47 x P53 / July 27, 2022 2022 年 7 月 27 日)

31×10¹⁰¹+329 = 3(4)₁₀₀8_<102> = 2⁵ × 3 × 13 × 4611067 × 33991396014741169274848307398531069782866017_<44> × 1760897857715108131351930994666553026049065628109_<49> (Eric Jeancolas / ECM for P44 x P49 / June 24, 2022 2022 年 6 月 24 日)

31×10¹⁰²+329 = 3(4)₁₀₁8_<103> = 2⁵ × 7 × 15137 × 471059966553475896551_<21> × 3686717616001725567739675978792891_<34> × 584945338147342118544997472439391267005131_<42> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2741429352 for P34 x P42 / June 24, 2022 2022 年 6 月 24 日)

31×10¹⁰³+329 = 3(4)₁₀₂8_<104> = 2⁵ × 17 × 615555903542972060973541_<24> × 102861483578691919145125883679427583188541801921471131831700977485322757342837_<78>

31×10¹⁰⁴+329 = 3(4)₁₀₃8_<105> = 2⁵ × 3³ × 193 × 49463 × 41760691321196826780450628849560607498663020959823099547551328358835993713100029526824054222173_<95>

31×10¹⁰⁵+329 = 3(4)₁₀₄8_<106> = 2⁵ × 773 × 12970701619_<11> × 570805753421_<12> × 140226681012931821254923_<24> × 134124231456364811282203534713479474757250902613217561609_<57>

31×10¹⁰⁶+329 = 3(4)₁₀₅8_<107> = 2⁵ × 1949 × 3169 × 77682152244401_<14> × 61513678905471603137_<20> × 720640644741489523253603366599_<30> × 50608495165798010857441870690012763_<35> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:113465897 for P30 x P35 / June 24, 2022 2022 年 6 月 24 日)

31×10¹⁰⁷+329 = 3(4)₁₀₆8_<108> = 2⁵ × 3 × 13 × 12703 × 575242033534153267_<18> × 98865491032494588774287_<23> × 382034831022779469460466028297021535309991735244032154895573_<60>

31×10¹⁰⁸+329 = 3(4)₁₀₇8_<109> = 2⁵ × 7² × 4969 × 201570227103017_<15> × 99371671840167766358992352182057427_<35> × 22070651218697970282509087335614044210470426846925891_<53> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3134649830 for P35 x P53 / June 24, 2022 2022 年 6 月 24 日)

31×10¹⁰⁹+329 = 3(4)₁₀₈8_<110> = 2⁵ × 19 × 258782251200947101499758515060720599777_<39> × 218917821916754365094922789690321420145553264463005680892271091023203_<69> (Dmitry Domanov / Msieve 1.54 snfs for P39 x P69 / July 27, 2022 2022 年 7 月 27 日)

31×10¹¹⁰+329 = 3(4)₁₀₉8_<111> = 2⁵ × 3 × 727 × 85743253 × 7455693117031763140847991477624235146952936823339_<49> × 7720146835709248131531819990754235818380434152307_<49> (Dmitry Domanov / Msieve 1.54 snfs for P49 x P49 / July 27, 2022 2022 年 7 月 27 日)

31×10¹¹¹+329 = 3(4)₁₁₀8_<112> = 2⁵ × 311 × 73471 × 341315827 × 13801822532962888233517117157975830172392247276351395725020147880027919530927403396204802788747_<95>

31×10¹¹²+329 = 3(4)₁₁₁8_<113> = 2⁵ × 389651 × 9219488471379682289_<19> × 584364273075224061993609710857386034272523_<42> × 512746765226201316259626256297986667743849337_<45> (Dmitry Domanov / for P42 x P45 / July 27, 2022 2022 年 7 月 27 日)

31×10¹¹³+329 = 3(4)₁₁₂8_<114> = 2⁵ × 3² × 13 × 43 × 585870661 × 3651851749626232110806539147232102206138993658953903071211212317364474826605753626471160977738556179_<100>

31×10¹¹⁴+329 = 3(4)₁₁₃8_<115> = 2⁵ × 7 × 29 × 174617 × 1096445002204776621062269_<25> × 42330680667447487581112795705753_<32> × 65425122037823492473429005025240706226763922114327_<50> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1188543084 for P32 x P50 / June 24, 2022 2022 年 6 月 24 日)

31×10¹¹⁵+329 = 3(4)₁₁₄8_<116> = 2⁵ × 23 × 197 × 745383908587_<12> × 318709589511276894306277602220758711592332523570749194631626395780577404305808414454414541691935337_<99>

31×10¹¹⁶+329 = 3(4)₁₁₅8_<117> = 2⁵ × 3 × 139 × 39516450002278503905283622305931923829382209_<44> × 653213615729539380028885417797141299942438832256405169160377269396313_<69> (Dmitry Domanov / Msieve 1.54 snfs for P44 x P69 / July 27, 2022 2022 年 7 月 27 日)

31×10¹¹⁷+329 = 3(4)₁₁₆8_<118> = 2⁵ × 2145631 × 5907234558276644914257836919427301178285434105537_<49> × 8492390486519875079978443207715532980087865388363874695963687_<61> (Dmitry Domanov / Msieve 1.54 snfs for P49 x P61 / July 27, 2022 2022 年 7 月 27 日)

31×10¹¹⁸+329 = 3(4)₁₁₇8_<119> = 2⁵ × 1076388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889_<118>

31×10¹¹⁹+329 = 3(4)₁₁₈8_<120> = 2⁵ × 3 × 13 × 17 × 3673605617229781595584781177_<28> × 4419398329831299336029537493025677707103747496654540338342453054661252618573899131675239_<88>

31×10¹²⁰+329 = 3(4)₁₁₉8_<121> = 2⁵ × 7 × 28051 × 23036502199_<11> × 23796127117433045981215243487919426553923887450181493721014688644305093797184245350122853164912409896323_<104>

31×10¹²¹+329 = 3(4)₁₂₀8_<122> = 2⁵ × 71 × 109 × 487 × 6116491 × 46693137527730400654694697244129451086832587025072030688261050485783010321472305636818915548128843786478503_<107>

31×10¹²²+329 = 3(4)₁₂₁8_<123> = 2⁵ × 3² × 47 × 6211 × 306443689 × 367774638724980913_<18> × 95635376380237260713295474436003797905281_<41> × 380116112244586956871370574536361241597661192189_<48> (Dmitry Domanov / for P41 x P48 / July 27, 2022 2022 年 7 月 27 日)

31×10¹²³+329 = 3(4)₁₂₂8_<124> = 2⁵ × 1913 × 189887 × 145378883798348581_<18> × 1831337887601553179951_<22> × 9127223181551187098579_<22> × 121941216207607713227320863439567738637062512057626831_<54>

31×10¹²⁴+329 = 3(4)₁₂₃8_<125> = 2⁵ × 1076388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889_<124>

31×10¹²⁵+329 = 3(4)₁₂₄8_<126> = 2⁵ × 3 × 13 × 45955863017_<11> × 3367127212522394662265018658325781_<34> × 888740319037078195183334557251426259411_<39> × 2006916322324979909833420112013875690633_<40> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1102401863 for P34 / June 24, 2022 2022 年 6 月 24 日) (Dmitry Domanov / for P39 x P40 / July 27, 2022 2022 年 7 月 27 日)

31×10¹²⁶+329 = 3(4)₁₂₅8_<127> = 2⁵ × 7 × 72763 × 164921846590987_<15> × 904522007831423_<15> × 30130413337801464973570511810221351219151_<41> × 47017350574918225813856321810822630113822760794679_<50> (Ignacio Santos / Yafu for P41 x P50 / July 28, 2022 2022 年 7 月 28 日)

31×10¹²⁷+329 = 3(4)₁₂₆8_<128> = 2⁵ × 19 × 811 × 222768559424149_<15> × 2210760486559616077_<19> × 11314941624897874998422293_<26> × 12535649569350122352850175202624862601497665924638936004217360789_<65>

31×10¹²⁸+329 = 3(4)₁₂₇8_<129> = 2⁵ × 3 × 479 × 2767 × 12923 × 124301 × 2650379 × 14464294130314497404959_<23> × 62475336680371851165724064875261_<32> × 703641556033824900786481270525602750351642710142877_<51> (Dmitry Domanov / for P32 x P51 / July 27, 2022 2022 年 7 月 27 日)

31×10¹²⁹+329 = 3(4)₁₂₈8_<130> = 2⁵ × 126395237 × 2446966837987601_<16> × 26501362888286149_<17> × 13132342617797889281965587251037637810155391082585357065091434454572473391703704630602353_<89>

31×10¹³⁰+329 = 3(4)₁₂₉8_<131> = 2⁵ × 1663 × 541817354436144186159587_<24> × 64376255907365393089604527192918183401324361_<44> × 18556596769823650466853266062759220519894475586372197261029_<59> (Bob Backstrom / for P44 x P59 / July 28, 2022 2022 年 7 月 28 日)

31×10¹³¹+329 = 3(4)₁₃₀8_<132> = 2⁵ × 3³ × 13² × 255133 × 726157 × 110453162221837_<15> × 273893689788911_<15> × 420883007939722070123786030475273304914891114312955748965330562714676720332410244871209_<87>

31×10¹³²+329 = 3(4)₁₃₁8_<133> = 2⁵ × 7 × 61 × 137940601973_<12> × 8362591611682973981_<19> × 15359425538565421485090211681_<29> × 14227655890389073043016793761662064191261296448589949216561218773827019_<71>

31×10¹³³+329 = 3(4)₁₃₂8_<134> = 2⁵ × 3001 × 13537 × 17431 × 7694753268797193749377_<22> × 27242350809638411863541483591027_<32> × 502973266230011455955954919009697_<33> × 14416980019671090046925637624589949_<35> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1946135654 for P32, B1=1000000, sigma=1:2184411932 for P33 x P35 / June 24, 2022 2022 年 6 月 24 日)

31×10¹³⁴+329 = 3(4)₁₃₃8_<135> = 2⁵ × 3 × 43 × 616153 × 137484802159963862706621863601679176237189870591893_<51> × 985000011013645819818637859601846084300522939582982171102724218498546956829_<75> (Bob Backstrom / Msieve 1.54 snfs for P51 x P75 / July 28, 2022 2022 年 7 月 28 日)

31×10¹³⁵+329 = 3(4)₁₃₄8_<136> = 2⁵ × 17² × 83 × 2473 × 8761 × 5409517 × 49435103 × 2394464899721957663_<19> × 10760728317164179999_<20> × 59824962230203227521_<20> × 502445505920924816312628962742521240680354605402737_<51>

31×10¹³⁶+329 = 3(4)₁₃₅8_<137> = 2⁵ × 174680553099917158575254416776929_<33> × 6162041908999424625819852609038268732958889561789959777160492843846806458338365183254690349408333681241_<103> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:100589155 for P33 x P103 / June 24, 2022 2022 年 6 月 24 日)

31×10¹³⁷+329 = 3(4)₁₃₆8_<138> = 2⁵ × 3 × 13 × 23 × 23251 × 7758558798181_<13> × 860381542027153_<15> × 3013018037592394735165791141690555319047596497_<46> × 25660271946428352160208353120796740641868130228292012647_<56> (Bob Backstrom / for P46 x P56 / July 27, 2022 2022 年 7 月 27 日)

31×10¹³⁸+329 = 3(4)₁₃₇8_<139> = 2⁵ × 7 × 3370865226335931073304831_<25> × 23807178508860789933181888382468201_<35> × 191611622688007627278116066176600573037763034432756419515286314407726099662617_<78> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:888945888 for P35 x P78 / June 24, 2022 2022 年 6 月 24 日)

31×10¹³⁹+329 = 3(4)₁₃₈8_<140> = 2⁵ × 24917 × 1248947068949225862989_<22> × 34588316214825096124520581311433060667593399474704758206495271986401007288493078543726202307748022446456088192553_<113>

31×10¹⁴⁰+329 = 3(4)₁₃₉8_<141> = 2⁵ × 3² × 1195987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654320987654321_<139>

31×10¹⁴¹+329 = 3(4)₁₄₀8_<142> = 2⁵ × 12143 × 19276986077_<11> × 26726103571_<11> × 17205544859930948949372685323613085389144526502675746910048760527859477292290559411656423296864430709682886994391569_<116>

31×10¹⁴²+329 = 3(4)₁₄₁8_<143> = 2⁵ × 29² × 813931 × 1576186303_<10> × 37843170168647_<14> × 1842238306256611389102782858323355345658899_<43> × 14310168656990621456690022029919656765422009685827528691567736160201_<68> (Bob Backstrom / for P43 x P68 / July 28, 2022 2022 年 7 月 28 日)

31×10¹⁴³+329 = 3(4)₁₄₂8_<144> = 2⁵ × 3 × 13 × 695853718887749_<15> × 1433114115119229447433_<22> × 9001168100519939359577_<22> × 11532914668119836563919696681_<29> × 2666047739536179457805360976146280390156889449005831419_<55>

31×10¹⁴⁴+329 = 3(4)₁₄₃8_<145> = 2⁵ × 7 × 1794619 × 4535437 × 31037115365829149701_<20> × 13452881251666101775559_<23> × 4524630375318683055591949747482224919189299761436400043257802784533533485990746389232651_<88>

31×10¹⁴⁵+329 = 3(4)₁₄₄8_<146> = 2⁵ × 19 × 191 × 118026611 × 25965853097_<11> × 96783139334100123217832517143163590995127805394389527411686568686826900384495960948137614049749123018474082920287193266423_<122>

31×10¹⁴⁶+329 = 3(4)₁₄₅8_<147> = 2⁵ × 3 × 54958084369_<11> × 10299579495850845638927339_<26> × 94722910988977763074147459467917_<32> × 66917827760010923661386803068971248362480960209052763217024093917340232974029_<77> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1010097733 for P32 x P77 / June 24, 2022 2022 年 6 月 24 日)

31×10¹⁴⁷+329 = 3(4)₁₄₆8_<148> = 2⁵ × 59 × 13461683 × 135524506651159680517405686725783965948601116483019964307921783538858174740866402747242672492555966906393060136999100019208554583630591737_<138>

31×10¹⁴⁸+329 = 3(4)₁₄₇8_<149> = 2⁵ × 1747 × 413411 × 6310008072407918005671541_<25> × 236191551048214701232201610358434001627386789290491452682662705393260113114746442103731923407288675956984131987837_<114>

31×10¹⁴⁹+329 = 3(4)₁₄₈8_<150> = 2⁵ × 3² × 13 × 24726816968840423_<17> × 2534510665661797129_<19> × 1467982935033253243928486175229541153060582049175632800901049256197919986054079784742495484805621828101851345451_<112>

31×10¹⁵⁰+329 = 3(4)₁₄₉8_<151> = 2⁵ × 7² × 632987 × 48174203326222529_<17> × 1922309274614159855017469_<25> × 27946595569187721716503076833_<29> × 1340947029693859842015773375166576265685444725542154561863801572992063591_<73>

31×10¹⁵¹+329 = 3(4)₁₅₀8_<152> = 2⁵ × 17 × 5399 × 550117 × 5314694436811_<13> × 33176732066553792572652177057816261907_<38> × 8163420354539190018987353266211618545541_<40> × 14810435380784526662439596581490151924513774755207_<50> (Bob Backstrom / GMP-ECM 7.0.4 B1=10760000, sigma=1:1934259975 for P38 x P40 x P50 / August 5, 2022 2022 年 8 月 5 日)

31×10¹⁵²+329 = 3(4)₁₅₁8_<153> = 2⁵ × 3 × 1534513896028918964498904856409085690729103_<43> × 2338175608737104160796527186311271113306134990241851749040743962367434361449697253044424371484147016425730621_<109> (Bob Backstrom / GMP-ECM 7.0.4 B1=23080000, sigma=1:3782671387 for P43 x P109 / July 31, 2022 2022 年 7 月 31 日)

31×10¹⁵³+329 = 3(4)₁₅₂8_<154> = 2⁵ × 131 × 2104005672142307_<16> × 1054054076245676813_<19> × 702359707821143855375845745437_<30> × 370425538528158286887027664486571191_<36> × 1424057749793852401668106000778288309788256084588527_<52> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3631557856 for P30 / June 24, 2022 2022 年 6 月 24 日) (Dmitry Domanov / for P36 x P52 / July 27, 2022 2022 年 7 月 27 日)

31×10¹⁵⁴+329 = 3(4)₁₅₃8_<155> = 2⁵ × 1031 × 144056729 × 12866670799571_<14> × 563262452784708579922373341964691381692775124616053488350288123365694914172022954337649780036998350775223025345759128517142071341_<129>

31×10¹⁵⁵+329 = 3(4)₁₅₄8_<156> = 2⁵ × 3 × 13 × 43 × 4441 × 16070459347_<11> × 3293448700426252042746246101800411506959_<40> × 27307137467711277167185349299462616288420704383703800944789712348141378551116142633900655433833449_<98> (Bob Backstrom / GMP-ECM 7.0.4 B1=13070000, sigma=1:2470358705 for P40 x P98 / August 1, 2022 2022 年 8 月 1 日)

31×10¹⁵⁶+329 = 3(4)₁₅₅8_<157> = 2⁵ × 7 × 71 × 37312067153_<11> × 37945440074923_<14> × 786343318492031093_<18> × 194532295728939834179085519997074444533091115142378944262971721271715158160093295256597365981436408499595244511_<111>

31×10¹⁵⁷+329 = 3(4)₁₅₆8_<158> = 2⁵ × 1561519 × 689321672607818981958521727170075348996002539123051905797424744040187079945161659184991594011272926483052008261755949744376398166713878530385406062231_<150>

31×10¹⁵⁸+329 = 3(4)₁₅₇8_<159> = 2⁵ × 3⁵ × 6818815025609154579657471757252206084742526147_<46> × 6496119763120913750677168881013277562051239711259982222671570147673405772305084788926851485603673612122277409_<109> (Bob Backstrom / Msieve 1.54 snfs for P46 x P109 / July 29, 2022 2022 年 7 月 29 日)

31×10¹⁵⁹+329 = 3(4)₁₅₈8_<160> = 2⁵ × 23 × 1662589 × 6782081 × 7685767 × 7405195209959476987032973_<25> × 405143853529205156317393919920679089947318696605166103_<54> × 17999503035145277315762264739626221520715936348739414842599_<59> (Bob Backstrom / for P54 x P59 / August 3, 2022 2022 年 8 月 3 日)

31×10¹⁶⁰+329 = 3(4)₁₅₉8_<161> = 2⁵ × 729907 × 10081273578420395107714971565216810618489693_<44> × 146280446378822597226335123057732816246618404447424919168511504323623878220909320793681056077679402657333125439_<111> (Bob Backstrom / Msieve 1.54 snfs for P44 x P111 / July 31, 2022 2022 年 7 月 31 日)

31×10¹⁶¹+329 = 3(4)₁₆₀8_<162> = 2⁵ × 3 × 13 × 347 × 2454658747544698656730642165376783_<34> × 324029089340460613057585889025751807164916198041183151249856769156414314102295821802334093196591141294918123637332604988451_<123> (Eric Jeancolas / ECM for P34 x P123 / June 24, 2022 2022 年 6 月 24 日)

31×10¹⁶²+329 = 3(4)₁₆₁8_<163> = 2⁵ × 7 × 139 × 10739 × 2032394676691_<13> × 126152429331862750832569_<24> × 1472343892962267767909436160726720253_<37> × 27288495807302892773073206599496916503851154718222130461797692031337074229724165601_<83> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3078236891 for P37 x P83 / June 24, 2022 2022 年 6 月 24 日)

31×10¹⁶³+329 = 3(4)₁₆₂8_<164> = 2⁵ × 19 × 149 × 850453 × 1963921 × 12997651 × 4509092101918224437935867_<25> × 634834046972732339388095194455793588302495099407747_<51> × 6118441570091739474104140900149933139388646450748281137432056537_<64> (Bob Backstrom / for P51 x P64 / August 5, 2022 2022 年 8 月 5 日)

31×10¹⁶⁴+329 = 3(4)₁₆₃8_<165> = 2⁵ × 3 × 97 × 15371694128658728207231364680721541969218450931_<47> × 2406326107384816191550787745028679757945780192410202866075045458011787859062635475490126953586751867810686196388609_<115> (Bob Backstrom / GMP-ECM 7.0.4 B1=14550000, sigma=1:228273830 for P47 x P115 / July 29, 2022 2022 年 7 月 29 日)

31×10¹⁶⁵+329 = 3(4)₁₆₄8_<166> = 2⁵ × 23202391 × 4639129169441584226767357247315110278457461081872505677922973062943766825103882133909772009655767325397149323485191198135092581143421334848158057886744900079_<157>

31×10¹⁶⁶+329 = 3(4)₁₆₅8_<167> = 2⁵ × 14568297523349_<14> × 381439046633863_<15> × 193702513187882372989169782646693505445797968298189886858878549482102446015982636260898951120329144688717096206440661954956179580849225347_<138>

31×10¹⁶⁷+329 = 3(4)₁₆₆8_<168> = 2⁵ × 3² × 13 × 17 × 257353 × 6593369 × 24046003124821892894196043814627243_<35> × 132634011998234892342992114161561218780141823148676376244205852517027688130479552397581590948242275993023191325467151_<117> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2541945033 for P35 x P117 / June 24, 2022 2022 年 6 月 24 日)

31×10¹⁶⁸+329 = 3(4)₁₆₇8_<169> = 2⁵ × 7 × 47 × 327169875042215467747382640999662276258020938872002701789935832489023978385680513340087808172914555893279297534616683552853765619723066531577169875042215467747382641_<165>

31×10¹⁶⁹+329 = 3(4)₁₆₈8_<170> = 2⁵ × 12437 × 3973757 × 209740994627_<12> × 103841019328891754602829331880640699931186755488294524800660275582992489141256270653612465251473995853955050200962511848189746334895137386265375123_<147>

31×10¹⁷⁰+329 = 3(4)₁₆₉8_<171> = 2⁵ × 3 × 29 × 827 × 6203 × 153953 × 240659140577_<12> × 9962567806074781_<16> × 65340259483818260423823075733652045597097618046652218831399486632291611615563244100546618796208155273897249385548113458704570867_<128>

31×10¹⁷¹+329 = 3(4)₁₇₀8_<172> = 2⁵ × 15356272206697_<14> × 1669510742009404586274424560662591_<34> × 117857850452529266721705298510034542914694872616191047_<54> × 35623424860754475935439888900323968443993073611288445456970347896528281_<71> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1305994605 for P34 / June 24, 2022 2022 年 6 月 24 日) (Eric Jeancolas / cado-nfs-3.0.0 for P54 x P71 / August 13, 2022 2022 年 8 月 13 日)

31×10¹⁷²+329 = 3(4)₁₇₁8_<173> = 2⁵ × 31357666630413212529823_<23> × 159967321833851780572620053531733458162092836832021_<51> × 214582446969910783039254969313297070911779446782785698635181483852375184714465873288865063910871883_<99> (Bob Backstrom / Msieve 1.54 snfs for P51 x P99 / August 1, 2022 2022 年 8 月 1 日)

31×10¹⁷³+329 = 3(4)₁₇₂8_<174> = 2⁵ × 3 × 13 × 1699 × 68997255085913660180032801127380397489421119135396918207_<56> × 2354395432752068198393398129274628355646429342787411020028756225096516158107245403970221975650407346217213344107_<112> (Bob Backstrom / Msieve 1.54 snfs for P56 x P112 / July 30, 2022 2022 年 7 月 30 日)

31×10¹⁷⁴+329 = 3(4)₁₇₃8_<175> = 2⁵ × 7 × 113 × 11505316587778779740090587014826486778859968371785799_<53> × 11827532472516138902471774259337279996894442957583134700982580515360007220797797088666712227620938696859451533556431321_<119> (Bob Backstrom / Msieve 1.54 snfs for P53 x P119 / July 30, 2022 2022 年 7 月 30 日)

31×10¹⁷⁵+329 = 3(4)₁₇₄8_<176> = 2⁵ × 132616906600590436837993928224517484935987_<42> × 8116528401093745550571145532681139998966332481294495444929992628142780759646287436517093144731453447881935325423093347068637406392547_<133> (ebina / Msieve 1.53 snfs for P42 x P133 / July 28, 2022 2022 年 7 月 28 日)

31×10¹⁷⁶+329 = 3(4)₁₇₅8_<177> = 2⁵ × 3² × 43 × 83 × 10759037 × 4973261437605719_<16> × 6262755507193093851798066781356755331125161416731689476061123241730262854386930104846683026122333521273119439196649526629661748301220603577579382003_<148>

31×10¹⁷⁷+329 = 3(4)₁₇₆8_<178> = 2⁵ × 359 × 10169 × 5715487 × 130841226698840054911039_<24> × 652899415852904316266693_<24> × 1260211837749785929609421_<25> × 148237000497679454837106884059453650967723_<42> × 323260178317636722479202438204460336158295520832677_<51> (Dmitry Domanov / for P42 x P51 / July 27, 2022 2022 年 7 月 27 日)

31×10¹⁷⁸+329 = 3(4)₁₇₇8_<179> = 2⁵ × 3169 × 4219163057533591_<16> × 4482935748283129826574460240612910664413025591977322402440369423_<64> × 17958007254516714116509288341551187802218584303563099203481512539880765427723593333999142326017_<95> (Bob Backstrom / Msieve 1.54 snfs for P64 x P95 / July 31, 2022 2022 年 7 月 31 日)

31×10¹⁷⁹+329 = 3(4)₁₇₈8_<180> = 2⁵ × 3 × 13 × 275997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997151_<177>

31×10¹⁸⁰+329 = 3(4)₁₇₉8_<181> = 2⁵ × 7 × 3533 × 596904701 × 164428524103690909207367793049317878131964759985294501342378515789340718097_<75> × 44345072652597214762989438945362287942331393552773577787621839394617574177995447326471516327_<92> (Bob Backstrom / Msieve 1.54 snfs for P75 x P92 / August 5, 2022 2022 年 8 月 5 日)

31×10¹⁸¹+329 = 3(4)₁₈₀8_<182> = 2⁵ × 19 × 23 × 421 × 11103831621553063_<17> × 2873787271400821366961_<22> × 183348849389639446948821017454612223807699969092664433256228724044919903035062565045597083457862254729519939607204283257677239693805001399_<138>

31×10¹⁸²+329 = 3(4)₁₈₁8_<183> = 2⁵ × 3 × 32563 × 464351 × 381277997923961_<15> × 622351029688897748662192978202395654978088626062165985317391706910185670539291746277623243108327482734701576643563711698393515081186935175520163579619473591_<156>

31×10¹⁸³+329 = 3(4)₁₈₂8_<184> = 2⁵ × 17 × 3433 × 10424753 × 227851873 × 947741009 × 1304494367978353_<16> × 628052896811550649256915814924394892850249054417507975347371749270647521883880614155101960339122718179425072175589599700218130647943637873_<138>

31×10¹⁸⁴+329 = 3(4)₁₈₃8_<185> = 2⁵ × 29303 × 489052746499_<12> × 536673911464656527437_<21> × 139955810832923956979075410703920198137790111320796690506404007339225455738088741707909915955263107908300449092999541694165426643361934413204714201_<147>

31×10¹⁸⁵+329 = 3(4)₁₈₄8_<186> = 2⁵ × 3³ × 13 × 659 × 256914425795444470994048371724487446600018681_<45> × 181129081296818323441517559526766727456134928799330693699716255458374169117331936445485759439775671994424850106764666398386695211492741_<135> (Bob Backstrom / Msieve 1.54 snfs for P45 x P135 / August 3, 2022 2022 年 8 月 3 日)

31×10¹⁸⁶+329 = 3(4)₁₈₅8_<187> = 2⁵ × 7 × 389 × 35093670709568901523354987759127_<32> × 13081763645721827456776721420995655337182310220165583028186553_<62> × 86104623039881836566573037410908329393815666602616799787857316439992737658989676753345453_<89> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2968888583 for P32 / June 24, 2022 2022 年 6 月 24 日) (Bob Backstrom / Msieve 1.54 snfs for P62 x P89 / October 13, 2022 2022 年 10 月 13 日)

31×10¹⁸⁷+329 = 3(4)₁₈₆8_<188> = 2⁵ × 152090929350326043768258329258051853017512554639124251533_<57> × 2214490203462391676421045780105156239209974141992250809385473461_<64> × 3195892253375316811900124829507865038364778777684272695321858239753_<67> (Bob Backstrom / Msieve 1.54 snfs for P57 x P64 x P67 / August 3, 2022 2022 年 8 月 3 日)

31×10¹⁸⁸+329 = 3(4)₁₈₇8_<189> = 2⁵ × 3 × 181 × 7747484628277_<13> × 676718509108508335603_<21> × 12076298618769294706429154629643004851162206611643553743199_<59> × 313088239472539215427516478885923050839503397889811381174503036517460257185573932681425672567_<93> (Eric Jeancolas / cado-nfs-3.0.0 for P59 x P93 / February 9, 2023 2023 年 2 月 9 日)

31×10¹⁸⁹+329 = 3(4)₁₈₈8_<190> = 2⁵ × 967 × 474647 × 196162318931969556108698160813599_<33> × 1195518785937720130514776849443217146170869154860211736357427848313257069924330082847633416907752732508018985175214008889046915514800419802449621639_<148> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:57302133 for P33 x P148 / June 24, 2022 2022 年 6 月 24 日)

31×10¹⁹⁰+329 = 3(4)₁₈₉8_<191> = 2⁵ × 5003 × 6432619 × 694993759 × 5476564978249_<13> × 70507663732361_<14> × 759328080240302402110783647155593857030727866052725954562117918217233_<69> × 164133012025744672379429521684382771403612252517152281850618688344187490719_<75> (Eric Jeancolas / cado-nfs-3.0.0 for P69 x P75 / February 22, 2023 2023 年 2 月 22 日)

31×10¹⁹¹+329 = 3(4)₁₉₀8_<192> = 2⁵ × 3 × 13 × 71 × 691 × 1844813 × 3049410227903239578885091850823205959988407886740476271022168693138601016898290710311815425867139176829032113730267239981258350383626942123255788076909004852744086246607997171007_<178>

31×10¹⁹²+329 = 3(4)₁₉₁8_<193> = 2⁵ × 7² × 61 × 36011672428534255232147503810267276309430876175606854763763428868815285677112375004646667410133452288019032749711906620571725958142819969517861789524552990595145161889892569049477714583101_<188>

31×10¹⁹³+329 = 3(4)₁₉₂8_<194> = 2⁵ × 4153 × 9059 × 157433 × 167981404564060686880050432217_<30> × 11533065334778031203150530293080584857986038187230963573696977210397_<68> × 93804847858730950865054907865906600370682651231440014847719571895941535917578197271_<83> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3129991359 for P30 / June 24, 2022 2022 年 6 月 24 日) (Eric Jeancolas / cado-nfs-3.0.0 for P68 x P83 / February 12, 2023 2023 年 2 月 12 日)

31×10¹⁹⁴+329 = 3(4)₁₉₃8_<195> = 2⁵ × 3² × 503 × 9787 × 191119 × 148033849 × 18624837582563_<14> × 22025066484312891557491_<23> × 147661430096310217085629286201856367_<36> × 1491095827185823708441802897353967629807_<40> × 95074024990386085069838433833247793645218423858009884582940203_<62> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2371822272 for P36 / June 24, 2022 2022 年 6 月 24 日) (Dmitry Domanov / Msieve 1.54 gnfs for P40 x P62 / July 28, 2022 2022 年 7 月 28 日)

31×10¹⁹⁵+329 = 3(4)₁₉₄8_<196> = 2⁵ × 167 × 2063 × 11971 × 52767488950733659_<17> × 85325675102395691246747945483_<29> × 481362840754879806598973665359080771782387654269103_<51> × 12042158903182377344804675822824289786179069447507643501431131080344800375618674699669869_<89> (Eric Jeancolas / cado-nfs-3.0.0 for P51 x P89 / February 14, 2023 2023 年 2 月 14 日)

31×10¹⁹⁶+329 = 3(4)₁₉₅8_<197> = 2⁵ × 1103 × 312367145448985314071_<21> × 3124124587162785164510350723049536637443576803704254936562870454546315731727014050638086298236203047642153637089932992539041495290625362552185089415415764046241722440037153_<172>

31×10¹⁹⁷+329 = 3(4)₁₉₆8_<198> = 2⁵ × 3 × 13 × 43 × 27517586876786306098973_<23> × 95830976735099175643481033542967803_<35> × 8261811427365105123141516782404191643_<37> × 294608046541604261064498179676510303821698578908741329232877432830292261067240761626005285469360521_<99> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:112715447 for P35, B1=1000000, sigma=1:1789433184 for P37 x P99 / June 24, 2022 2022 年 6 月 24 日)

31×10¹⁹⁸+329 = 3(4)₁₉₇8_<199> = 2⁵ × 7 × 29 × 233 × 2086519 × 124025766052781_<15> × 1169046457739013486943273_<25> × 48094738124345740918031073388365736603197625379_<47> × 230338963341470284610794963129711081990019890883_<48> × 679025747982576668616417872513778255867737887996948009_<54> (Bob Backstrom / GMP-ECM 7.0.4 B1=27420000, sigma=1:2063683394, Msieve 1.54 gnfs for P47 x P48 x P54 / October 4, 2022 2022 年 10 月 4 日)

31×10¹⁹⁹+329 = 3(4)₁₉₈8_<200> = 2⁵ × 17 × 19 × 186587 × 492647 × 51304223 × 2283626987_<10> × 10755959823907_<14> × 17811709935419_<14> × 3736171702954050452938029271851900027261057433_<46> × 432304310292768057111711294397220240342854852568034534925775080901059341517320611019963207845083_<96> (Eric Jeancolas / cado-nfs-3.0.0 for P46 x P96 / February 14, 2023 2023 年 2 月 14 日)

31×10²⁰⁰+329 = 3(4)₁₉₉8_<201> = 2⁵ × 3 × 179 × 4783 × 7283 × 499067 × 9558877 × 11089957 × 48527851 × 132933083 × 383330889881_<12> × 61202339635519_<14> × 48980158912710709_<17> × 177875871909147102671_<21> × 19522417211773698036435569633216380741_<38> × 422524445164413373258350334046196602148707894152432567_<54> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1811578580 for P38 x P54 / June 24, 2022 2022 年 6 月 24 日)

31×10²⁰¹+329 = 3(4)₂₀₀8_<202> = 2⁵ × 5979519941_<10> × 70960110000140087_<17> × 8841997476593589252949407187_<28> × 28690506865492764118196628994728264779279690113543501863054587266463459582288393474591574488821493781886254590496387747188710848437024763406607441_<146>

31×10²⁰²+329 = 3(4)₂₀₁8_<203> = 2⁵ × 7995186916455169125282847715723_<31> × 267987100779115896076510766050045735207190024738887955456190283_<63> × 502373467469900708744229271980967994651166144289761407180302726586331458982789062482692468198990252508481921_<108> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3645474252 for P31 / June 24, 2022 2022 年 6 月 24 日) (Bob Backstrom / Msieve 1.44 snfs for P63 x P108 / August 18, 2023 2023 年 8 月 18 日)

31×10²⁰³+329 = 3(4)₂₀₂8_<204> = 2⁵ × 3² × 13 × 23² × 677 × 6823 × 2058864553331156626483_<22> × 11964004191402090269329_<23> × 270993455160679080191432540649591527338278943_<45> × 5640277828867548269953456919948588165931983106511318100284792640682396219185763522555823297329735995363_<103> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1:2361311252 for P45 x P103 / November 9, 2022 2022 年 11 月 9 日)

31×10²⁰⁴+329 = 3(4)₂₀₃8_<205> = 2⁵ × 7 × 4903 × 1916150089747020447205901_<25> × 1636740198918585246546091731653165444706832929232802734852629227875869050493582029222447020631715530283667250148462208005784092109953368101835527861808319983432798712410416909_<175>

31×10²⁰⁵+329 = 3(4)₂₀₄8_<206> = 2⁵ × 59 × 8439587311381_<13> × 49459470261121633846619_<23> × 1066466475520948762904555619852322439326256300228995218683131321_<64> × 40982581904294750465820993463820920117047290894328760549337793806201196996119147306041916668249254401509_<104> (Bob Backstrom / Msieve 1.44 snfs for P64 x P104 / February 28, 2024 2024 年 2 月 28 日)

31×10²⁰⁶+329 = 3(4)₂₀₅8_<207> = 2⁵ × 3 × 848251 × 31358611 × 10981225571_<11> × 149354236300690163_<18> × 82242896084740987631588507876085490247909557777823713203176447007283546363345278613086137209443594928969420442045823499615656220026882554348397606870983878663167371_<164>

31×10²⁰⁷+329 = 3(4)₂₀₆8_<208> = 2⁵ × 19306093 × [5575384356062559570643780121067938960456105173060592264260246176628740413137390816924423232027779462622959958231263512969138234695590085932399107830304603261203024811332302651234969648643507979003773_<199>] Free to factor

31×10²⁰⁸+329 = 3(4)₂₀₇8_<209> = 2⁵ × 139 × 94903418989_<11> × 81596691020507232344659485473185517509446735919264348007477212326072768107820107708222852532245328563084227058447982972108482768365294657058267270472901633161518764367926412648768848714089403159_<194>

31×10²⁰⁹+329 = 3(4)₂₀₈8_<210> = 2⁵ × 3 × 13² × 1619 × 13113372499508290832470050410849574625884788853382952304413795362624174331305989024428707043806582933299329935430092222034066477455083907309877756972354777267591445384004893673730087470763101494322095833_<203>

31×10²¹⁰+329 = 3(4)₂₀₉8_<211> = 2⁵ × 7 × 257 × 210439043353577_<15> × 33819287546072681_<17> × [8407120448615020472222492718653587129608611056789921482654553372725810838045525557332856032789855653349362009485503175250468750552992469434733147983470594007567786129669940303_<175>] Free to factor

31×10²¹¹+329 = 3(4)₂₁₀8_<212> = 2⁵ × 221158039 × 627862451 × 4534879267_<10> × 1709370620592683327149592128755420345979845646065799369038522377360416837516623319761620473837602673969265021504177684582022753936207758929370101697960754102832111734969125163846169703_<184>

31×10²¹²+329 = 3(4)₂₁₁8_<213> = 2⁵ × 3³ × 11714159725571_<14> × 1385704150565699_<16> × 25261667898088782675439344223278359_<35> × [972213755078706676154338957772612658244889692728868643427941349745471972921585489204794006926716568540639191339267565455511983714883569227573967637_<147>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:728670735 for P35 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²¹³+329 = 3(4)₂₁₂8_<214> = 2⁵ × 197 × 769 × 155387 × 121784251 × [37546618387728452977952569611239422948687880509351234178758153416410577973732710431441599460831585884401600194862061303234384734347130444340940187440779290102532026837202461685953756169912069229_<194>] Free to factor

31×10²¹⁴+329 = 3(4)₂₁₃8_<215> = 2⁵ × 47 × 5076833 × [4511058617243285871785970676990233741795616621827069971633005906286789123652016115914418806390523169174473697957598339102303265319267869794102325456235232228894821805242827435541304140010157735205295954039_<205>] Free to factor

31×10²¹⁵+329 = 3(4)₂₁₄8_<216> = 2⁵ × 3 × 13 × 17 × 439 × 2922297139_<10> × [12655135062529582242216152649754929333376680670209797939730165984384427385752898825222140316759472102996494315614379810567932453131952047503887172155044292088829800750755679720934184512991863083975443_<200>] Free to factor

31×10²¹⁶+329 = 3(4)₂₁₅8_<217> = 2⁵ × 7 × 6121 × 17249837639_<11> × [145634334259928818677228681377878375910272888679161489171052448793910268773111873783084722931839274509203988138647498635638417641801722329255319336296493408120348940142059160858157003060482212048318433_<201>] Free to factor

31×10²¹⁷+329 = 3(4)₂₁₆8_<218> = 2⁵ × 19 × 83 × 3743428154648160807593_<22> × 152628082945137527591711_<24> × 869902948081594916819760263_<27> × 34448481158960111833030620330980966540399_<41> × 39865083655290197047019675463513900053634949815003847076663135599240557433760012644934211859034447807_<101> (Ignacio Santos / GMP-ECM B1=3000000, sigma=1:3873504258 for P41 x P101 / July 28, 2022 2022 年 7 月 28 日)

31×10²¹⁸+329 = 3(4)₂₁₇8_<219> = 2⁵ × 3 × 43 × 431 × [193598605890193868394915176332108291316190738842225379753033128093830624451678787188418656610530565098093291046401713859761666376893269463279715262664596285704579019206980141529324068578371713320183616411965842711_<213>] Free to factor

31×10²¹⁹+329 = 3(4)₂₁₈8_<220> = 2⁵ × 4829311005437_<13> × 2566382556914447_<16> × 8684856292000958619717429094041319769602527240954407371791771664009510918426036079190271703849574817400260930051281186969667348341457522559254201146419618796450315004127432350258300646992451_<190>

31×10²²⁰+329 = 3(4)₂₁₉8_<221> = 2⁵ × 5077 × 269209 × 39019171 × 162765451 × 3146698876184087160913699817358652351_<37> × 39407330730684966879949191502863764756621483115560682258570251634608271827878188795504677533111587870455353520252216252398230956166628213868521487819781264163_<158> (Dmitry Domanov / GMP-ECM 7.0.5 B1=3000000, sigma=3:1219804430 for P37 x P158 / September 7, 2022 2022 年 9 月 7 日)

31×10²²¹+329 = 3(4)₂₂₀8_<222> = 2⁵ × 3² × 13 × 7481 × 1248995220598647156559_<22> × [9846069864919909419548926762294515405121663327987010283124106313970299646982540266612369733226018178835016749502476850042628759033464581029143819085878521989025312870390555298800089331264085523_<193>] Free to factor

31×10²²²+329 = 3(4)₂₂₁8_<223> = 2⁵ × 7 × 5569 × 41878217 × 9932184859_<10> × 30059401462637_<14> × 56149967048771349473679149_<26> × 3933065115779483818238239806288129235170233318693839258807124353774939222023392261314332721318806347813627086395005975059027176349225114288326730566917709471997_<160>

31×10²²³+329 = 3(4)₂₂₂8_<224> = 2⁵ × 151902469 × 583607831 × 2942212791487_<13> × 2661064405753316741761207649_<28> × [1550792875955819680717152726324109851843883280027394925478417312464916870702705687434165517778042942307911033436473288222253570650399117115935378812524871216251574077_<166>] Free to factor

31×10²²⁴+329 = 3(4)₂₂₃8_<225> = 2⁵ × 3 × 389261866818466516131636779149_<30> × 9217350243650299978465932028570968914259765241681875906093362291549313616829817615521016971775199696352878878208202269784452893025359287607278504578248119686039017004244031844103002131069773087_<193> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2399090632 for P30 x P193 / June 24, 2022 2022 年 6 月 24 日)

31×10²²⁵+329 = 3(4)₂₂₄8_<226> = 2⁵ × 23 × 1562287001173_<13> × 5887237902632548601_<19> × 508825613392227057255202389658298936368822667044271599685299879466438358809432277147018177357852037465760700182449000320205015439507618353288825164528351575691258005557041079513729003747039691_<192>

31×10²²⁶+329 = 3(4)₂₂₅8_<227> = 2⁵ × 29 × 71² × 941 × 37332941 × 356309563 × 157319560551150457976540259620633_<33> × [3739060395627450211467225162882645950250766605934689628251268654773109329591429920300460235741315210479745113998013102741365521261495001894658230520107784792209667247399_<169>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2240655136 for P33 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²²⁷+329 = 3(4)₂₂₆8_<228> = 2⁵ × 3 × 13 × [275997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997151_<225>] Free to factor

31×10²²⁸+329 = 3(4)₂₂₇8_<229> = 2⁵ × 7 × 8741 × [1759179055827036607267702108109384164755403744077808830125498698888471225732408663423421460259350660906546960774165899437607480165539884107553710573959973342195055957783334513685732081796605306501199419629805169217135811347_<223>] Free to factor

31×10²²⁹+329 = 3(4)₂₂₈8_<230> = 2⁵ × 109 × 15748112242108327769_<20> × 627067376024551185831631388797115446070056864782438577410898422736066546975339107376273496192886622593117257697004801022630787516270766506796769704298326427066322784618397871367264999193880462693165848397509_<207>

31×10²³⁰+329 = 3(4)₂₂₉8_<231> = 2⁵ × 3² × 291770029 × 348568201833077_<15> × 72078911804902529_<17> × 163151109189278749074827931728118842688644941834727498000000288668926173558806100339011466977458920700656834144130311891137360625759619326999812788338960092637485788482183678363207151205153_<189>

31×10²³¹+329 = 3(4)₂₃₀8_<232> = 2⁵ × 17 × 12538968611148008557465401797_<29> × [504961735112400792992201379664885665012297529576869367317599123365430799267105428899156556816425718350475223741775007093288050860714887900113849605200405733441028095629347766645645505590959906218304661_<201>] Free to factor

31×10²³²+329 = 3(4)₂₃₁8_<233> = 2⁵ × 537149623921381_<15> × 269910741482425284640620118464522795367849_<42> × 7424270072274685512458446851046967804230046156377365580421164008165150914846168436624019759286032465330238395792143432869299686917300215899850982776276127068018511560494645181_<175> (Dmitry Domanov / GMP-ECM 7.0.5 B1=11000000, sigma=3:3234150254 for P42 x P175 / November 10, 2022 2022 年 11 月 10 日)

31×10²³³+329 = 3(4)₂₃₂8_<234> = 2⁵ × 3 × 13 × [275997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997150997151_<231>] Free to factor

31×10²³⁴+329 = 3(4)₂₃₃8_<235> = 2⁵ × 7² × 5483 × 26431 × 3418144343440658178438991_<25> × 4434563591501735610941596105067153545506340114786619846868240539506660961608675363333972907008722529866001497153611345169462608485509517633095863639246656064562392873617370443124496978600365541276427_<199>

31×10²³⁵+329 = 3(4)₂₃₄8_<236> = 2⁵ × 19 × 552502145677_<12> × 11793680397293_<14> × 18019619965366952853450737629_<29> × [482488153115015803038147212955532067696752342694678911831677316199695162896850530601109370668273463848577438899860521526258863792056830663674212710898424231217488544405320186316199_<180>] Free to factor

31×10²³⁶+329 = 3(4)₂₃₅8_<237> = 2⁵ × 3 × 509 × 91835932477_<11> × 1284338865331_<13> × 438345935754718763131_<21> × 6883753849326388791047_<22> × 17225333918507321710942999_<26> × 5327046135192311634213102925441019_<34> × 24425189313793278923607425298502191833_<38> × 8836973269497785575240428780697939770398095885494120111281429652899401_<70> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1295066008 for P34, B1=1000000, sigma=1:2482533960 for P38 x P70 / June 24, 2022 2022 年 6 月 24 日)

31×10²³⁷+329 = 3(4)₂₃₆8_<238> = 2⁵ × 12547 × 157793 × 10289012882081_<14> × [5284061503897680424630466164397068745562886954769410387193350931940002013806559484607670033905772244730152466408203301186077480638173930367435050126448959024445523015282484136999101868518060153730775855119831608339_<214>] Free to factor

31×10²³⁸+329 = 3(4)₂₃₇8_<239> = 2⁵ × 25643 × 1193997877_<10> × 9000612565297_<13> × 1206761736322178016272619505183_<31> × [3236705756080864862366757689640845664088960249881508517177052494771082704833105382289335125218636020103001761208769950164602721906177325950789371451509775511916531117092511137477649_<181>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:514480477 for P31 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²³⁹+329 = 3(4)₂₃₈8_<240> = 2⁵ × 3⁴ × 13 × 43 × 12379 × 372677 × 5653993 × 2410735759_<10> × 1235360607845677984538755304033_<31> × 3060240795569358936423543867426193662782291792648295112666419203195686463641681529117082073204994125286192426717994083045929053467793832002645313460336511602792151936851757737687_<178> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3102494322 for P31 x P178 / June 24, 2022 2022 年 6 月 24 日)

31×10²⁴⁰+329 = 3(4)₂₃₉8_<241> = 2⁵ × 7 × 191 × 55318141013_<11> × 201271435307_<12> × 3002516647290151070886786949105656427_<37> × [2408256017386627725656875802918013530661908136457194019922094182712114779832091138723330296374362765907320295480518596501193740314862005537146670298205666168237124879506334909221_<178>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2148855940 for P37 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁴¹+329 = 3(4)₂₄₀8_<242> = 2⁵ × 383 × 48889 × 1131617 × 5645137 × 8998815107487648500821507528561685737125695764921754988724399342839022799865607788689681484522599588816817435193515066765477835688860528587712664096716188961327843133359408026783167525217026434523509313558404069375157743_<220>

31×10²⁴²+329 = 3(4)₂₄₁8_<243> = 2⁵ × 3 × 2243 × 1059881093_<10> × 10379450664656337317141504068456044934223_<41> × [145407619267224042947424270903271688969552103237082117954662286001024536781640287561821930307817896933355596459772634014139239208406972942712572648449548243177929046235286480268569583852019_<189>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1:479461701 for P41 / October 28, 2022 2022 年 10 月 28 日) Free to factor

31×10²⁴³+329 = 3(4)₂₄₂8_<244> = 2⁵ × 337 × 1437379 × 2461140947825051275493_<22> × [90288309882456178540012971719477355201763835346149915314617292992490976232008510577402874647102331531385539169503917635828869051258860742462193494965907629167675564342363167258438688116296633736364394805298192551_<212>] Free to factor

31×10²⁴⁴+329 = 3(4)₂₄₃8_<245> = 2⁵ × 2203290092219_<13> × 3543994970271204403338913_<25> × 22699284450506241103552982830786452689123_<41> × [6072845894838209491780038723985870395582461912293480154596856255526626177336797974268180002912095450162973392913164542710106900555978097842354259521408563302445789769_<166>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1:1879046696 for P41 / November 17, 2022 2022 年 11 月 17 日) Free to factor

31×10²⁴⁵+329 = 3(4)₂₄₄8_<246> = 2⁵ × 3 × 13 × 263 × 1559 × 535523 × 9386621 × 4293280507902986808427_<22> × [31190767388747773199548905899397309090895885717544252744850186974929754997349623959314512778780355269801808874605986564707304182299190770767577947960701423906530381111100698317209868306609534232715227083_<203>] Free to factor

31×10²⁴⁶+329 = 3(4)₂₄₅8_<247> = 2⁵ × 7 × 3019 × 122789 × 317330336958130337_<18> × 143263721079471844289280536550453015343_<39> × 912432551414448753127021670471808387744055001859016605421943179329181819058055234500202895438739093360214742930260059777196183291367204796949636108565601173825740921480070125980567_<180> (Dmitry Domanov / GMP-ECM 7.0.5 B1=3000000, sigma=3:661280153 for P39 x P180 / September 3, 2022 2022 年 9 月 3 日)

31×10²⁴⁷+329 = 3(4)₂₄₆8_<248> = 2⁵ × 17 × 23 × 18671 × 175236470683_<12> × 54074276322007237_<17> × 892688464408073197_<18> × 223800134540681650281971299466902561_<36> × 77884204780265682938343500661279524735747541505402607170161024835031651960782164811628251054618697972875042413054314609520546786793659107065635277622982454307_<158> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2470821798 for P36 x P158 / June 24, 2022 2022 年 6 月 24 日)

31×10²⁴⁸+329 = 3(4)₂₄₇8_<249> = 2⁵ × 3² × 75521 × 3817279 × [4148633419735858072827474506396325000334502560036422724773455987237634531026254671072332692137451380987112121783039871553363076474496374782433256598064992885600637022498335924368104745762354303490275175190413514671888494531471837045519_<235>] Free to factor

31×10²⁴⁹+329 = 3(4)₂₄₈8_<250> = 2⁵ × 2495909583938139419_<19> × 43126117060319239331273087126139860011922419428669927604906419826366730466458216843248595496813570845183212385972625624779664198017377745348303820733517809435193124669854714347766026569346564656859021928783239778005981135179875131_<230>

31×10²⁵⁰+329 = 3(4)₂₄₉8_<251> = 2⁵ × 571 × 2789 × 3169 × [213285997489552497718716143343344704168751377121223121145346249493273118147828693683444061963789514524473469351458773390906559773080047331791842257242772887522631827006217119544548566212255139005012601586332029180068080608145608350452405599_<240>] Free to factor

31×10²⁵¹+329 = 3(4)₂₅₀8_<252> = 2⁵ × 3 × 13 × 293316051681931457192094271_<27> × 627748755509536183770051817_<27> × 1498935372202677592944844824022683808493055496950492491585898077940946655821080938162150651540323992067180255806771363605313684958106613162953992218829515551811831188188114439363074303279563839993_<196>

31×10²⁵²+329 = 3(4)₂₅₁8_<253> = 2⁵ × 7 × 61 × [252081706999739786625032526671870934166016133229247983346344002081706999739786625032526671870934166016133229247983346344002081706999739786625032526671870934166016133229247983346344002081706999739786625032526671870934166016133229247983346344002081707_<249>] Free to factor

31×10²⁵³+329 = 3(4)₂₅₂8_<254> = 2⁵ × 19 × 1459020489994490470503616226073043_<34> × [38828821919998984753003786829532333492561961848021593692577677687287979434390311412388427634324795583255935903541706484608425106252520045431824904904631217748232710841374923980673308087194400451954240469261946928288017_<218>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1378468824 for P34 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁵⁴+329 = 3(4)₂₅₃8_<255> = 2⁵ × 3 × 29 × 139 × 12823 × 115619251169_<12> × 57489485209897022743_<20> × 5952584701458514658153_<22> × 44529200049245607350717311_<26> × 35836664466793723898269380679897_<32> × 14616729942375989831994624904073587_<35> × 32851091275328454469885966546479343711_<38> × 2289543279067985158050420465323131733612402870266177431351066479_<64> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3699209029 for P32, B1=1000000, sigma=1:578462849 for P38 / June 24, 2022 2022 年 6 月 24 日) (Ignacio Santos / Yafu for P35 x P64 / July 28, 2022 2022 年 7 月 28 日)

31×10²⁵⁵+329 = 3(4)₂₅₄8_<256> = 2⁵ × 557 × 982722720514739_<15> × 14138187155728539512695925470879157_<35> × 76726931705730552668901914876023568842313101_<44> × 181276478640353931309273664979079602884750728317532884382995094437906165462963229399170037434439432413893237302770464372815416675188288534110050078683631292799_<159> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2602401357 for P35 / June 24, 2022 2022 年 6 月 24 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1:3472030741 for P44 x P159 / November 15, 2022 2022 年 11 月 15 日)

31×10²⁵⁶+329 = 3(4)₂₅₅8_<257> = 2⁵ × 8628419123_<10> × 35318170910709094912937_<23> × [3532155132333386750904157201062444176874214341728463280795840550706834036687665460606696003853667339668009366241401301329139221375184248476765515901451242868680715691696331875956144964956840091870650813880050127131125588139_<223>] Free to factor

31×10²⁵⁷+329 = 3(4)₂₅₆8_<258> = 2⁵ × 3² × 13 × 1031 × 1268341 × 151899574415881_<15> × 343034804584732086514269767473_<30> × [1350186944396552978440248041265398569708229945809121715140217441674494085238944929240523617710725242542151050659303977229491516882091908680101122532601348302906963753808939888486062254469387061743116079_<202>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3431638643 for P30 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁵⁸+329 = 3(4)₂₅₇8_<259> = 2⁵ × 7 × 83 × 821 × 2273 × 5653103 × 1274498185374905401_<19> × 13779211331916904433336968184716243777313440439686991651773533778767223085846931017315098637342007140195147521349487170097486804945593938476333109216277120025954920742259274610591183924631595961924787574838640729211691549431_<224>

31×10²⁵⁹+329 = 3(4)₂₅₈8_<260> = 2⁵ × 2496802315757_<13> × 8788649579551_<13> × [49052697942203111731566044418982806109478086134762121202558947708916010935491449594351469445921044257413726155980995483686516213984786217197886535685241740412658716665198685024272846597051158772040042326002755571379344698432364413027_<233>] Free to factor

31×10²⁶⁰+329 = 3(4)₂₅₉8_<261> = 2⁵ × 3 × 43 × 47² × 97 × 1109 × 270060932051_<12> × 506247283549577_<15> × [2568360791864071991515958795434520772723468334908040200406049546590064488106927756686673298937408361507641957985975109366821133492932492892291379065291541356080967141366075606248388042541890086299964794384765940016735437119_<223>] Free to factor

31×10²⁶¹+329 = 3(4)₂₆₀8_<262> = 2⁵ × 71 × 3449 × 731737 × 1247528355900297694081_<22> × 246057003237564105433624752066641_<33> × [1956935408262856850185084547177322388476909555719739424938016968799993731066647717025510635472509991780076237618173215383703789421586346082285774970178757883441003946495364713012944164526613689183_<196>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1908309945 for P33 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁶²+329 = 3(4)₂₆₁8_<263> = 2⁵ × 509644915371692403675059387615359949_<36> × [2112036942630656485667038732546765672270516213293103262931476234664695029226451083704995018335641059783679640160864282649512276977895061395189639681347172360719702456642654515019383378939951843168832097746028645530836394668061_<226>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:902303052 for P36 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁶³+329 = 3(4)₂₆₂8_<264> = 2⁵ × 3 × 13 × 17 × 59 × 6904910603_<10> × 2334916464314033_<16> × 114769736893715208573950408011_<30> × [148712293745796031221306946166791598659295954445015871900643177824875125931026011035593229582942736707726759372375859372043683099758997080834333682630635098523530574319048016170523435284178625181667362453_<204>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1852468768 for P30 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁶⁴+329 = 3(4)₂₆₃8_<265> = 2⁵ × 7 × 413477 × 2945292393695027327577097852167583_<34> × [12626744528781929056335452993001604524241377936846861697838067992525001414746522363870392080592799767484826157115925491235204044852584846665428440622124895255937272607956954725081362561067684755798687702367091908675892656397_<224>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2832994938 for P34 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁶⁵+329 = 3(4)₂₆₄8_<266> = 2⁵ × 1097549 × 35795189 × 206533304413_<12> × 1089688980733249654981166750513999_<34> × [121738508067252821797748889793554809227439542716373862917150018839729795557871745512598838942918805820615295156550920195014551295676633979334115161611426756734329728960642608324409947209690748294164832281427_<207>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2354355675 for P34 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁶⁶+329 = 3(4)₂₆₅8_<267> = 2⁵ × 3³ × 229 × 311 × 231821 × 195380995651_<12> × 2975487887389_<13> × 126781747184739209739679_<24> × 624414093220845696393803977423_<30> × [524670759786459298669021699309318864052793428135722042170698819655809194131703160783109040297496993719128127672860011036637740280834187103296692170573393240338432396431638139611_<177>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:191592123 for P30 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁶⁷+329 = 3(4)₂₆₆8_<268> = 2⁵ × 5978857 × 9317163253091_<13> × 9181541615296952371_<19> × [210451355652378379664922797129181266412272770313618367194581233889983475285452736576165110276611934818071451709360303416792201900736844013215977896323079962879593637974452661828721144675274534984644465547666929420662412994058457_<228>] Free to factor

31×10²⁶⁸+329 = 3(4)₂₆₇8_<269> = 2⁵ × 149909 × 13554553 × [529732110210535204459748936853929151018623306794106109478050854582267560818173464688756991069884006459234106656931679914348924666734353826473068718224863432887287719568577317630001045450880478516739703759444644581676135766285619534047385269687848101848957_<255>] Free to factor

31×10²⁶⁹+329 = 3(4)₂₆₈8_<270> = 2⁵ × 3 × 13 × 23 × 673 × 14270452339946711_<17> × 5079966238064637436781268826710617_<34> × [245959234899743763015302313127528332272997180792169967643796525163142829306052364286484701964173762211387072149222274829440026386031756291973981384793375995968003206419374229195159300708049359047103112115726363687_<213>] (Dmitry Domanov / for P34 / September 4, 2022 2022 年 9 月 4 日) Free to factor

31×10²⁷⁰+329 = 3(4)₂₆₉8_<271> = 2⁵ × 7 × 16333309 × 16153234555837_<14> × 573696904427531546439058597028138538846619_<42> × [101590940726895505634585192236150080789089586055785263088961886290855948877241045995281850419784879649078948922377786366302086681203653479372319989821620714002215912917405940230878072065359251436736965512901_<207>] (Dmitry Domanov / GMP-ECM 7.0.5 B1=3000000, sigma=3:146071013 for P42 / September 5, 2022 2022 年 9 月 5 日) Free to factor

31×10²⁷¹+329 = 3(4)₂₇₀8_<272> = 2⁵ × 19² × 2939 × 37674415049_<11> × 1642305896419_<13> × 4017386506812571_<16> × 31656728963568559_<17> × [128929468840786139108684261517131464034451263125162407073778563924944217698419747787630756596810862523591408107091704720566719294138433502309662446076986389444605709429966850657084843774877914997558466879063349_<210>] Free to factor

31×10²⁷²+329 = 3(4)₂₇₁8_<273> = 2⁵ × 3 × 593 × 20347 × 17696033810003_<14> × 35485884708993222925721255693_<29> × [473545044586389572132640653213024362497078235763614383958075942185164799335451570282377559389376783010090342169644670885416092203607233641638387528202347294439194776759617279512391166233342511188282491794813850081111891407_<222>] Free to factor

31×10²⁷³+329 = 3(4)₂₇₂8_<274> = 2⁵ × 5372670987877_<13> × 6756390795020473_<16> × 2965269690691537068739707254405046330506981485282849686282504299527455812699398706112576323338391324876433602357920360675496818083559400958323577653519524614179230102086053449563321623618885552751799565917260688486457006649830706570131026806509_<244>

31×10²⁷⁴+329 = 3(4)₂₇₃8_<275> = 2⁵ × 6429916490071_<13> × 10390110206856429666721218155497_<32> × [16111787285370006439495543600722906660791231193528511654617419691381870021370013093222304318670603096644638265370587562373032958711304778661632324007773863825761703113365796842551440913753787279577386438361311215381068356700244247_<230>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:2394107898 for P32 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁷⁵+329 = 3(4)₂₇₄8_<276> = 2⁵ × 3² × 13 × 309816319 × 24076052113_<11> × 5836350993845528260553261233_<28> × 2793412846445372452538029871121296435894057_<43> × [756514491706736785883208527817185849880816546754087839656619437051166556944699829709434200587294595030554477489878887733814877373376512676221111094642036821257800742098447311834182931_<183>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1:3178136727 for P43 / October 28, 2022 2022 年 10 月 28 日) Free to factor

31×10²⁷⁶+329 = 3(4)₂₇₅8_<277> = 2⁵ × 7³ × 577 × 1069 × 1579 × 98912009111_<11> × 329430194189998081_<18> × 65046397353489249707263_<23> × [152021062718280751790572505847327331086896525282409256132572226539249779082681018305298698193180463712625095978352902593282877007948441608235077586482158538701890264974745475681140052232977419873454469626734800953_<213>] Free to factor

31×10²⁷⁷+329 = 3(4)₂₇₆8_<278> = 2⁵ × 1061 × 9829 × 532619 × 2843349635609101787471351_<25> × [68154975460490512139973182527099551584111162191569299032726035747623458786922962986337403637953612063499106558313770970016968271501636761278311685278662213302120488513953977699375280202158504386843918146592250882760607169467556622550948949_<239>] Free to factor

31×10²⁷⁸+329 = 3(4)₂₇₇8_<279> = 2⁵ × 3 × 6323 × 43541 × 274854871 × 132982311218236034671_<21> × 356557072800828835381860238565287207119321068366256307703700408250279881501219106979342881548990381023547840411861130845914321546609484735546224716165759080584272036792835590822110816418822882839307933677312772522173941524068386484300348101_<240>

31×10²⁷⁹+329 = 3(4)₂₇₈8_<280> = 2⁵ × 17 × 1013 × 1719681443193586625753941_<25> × [3634651990114740271527318816173869451042319737996353917817046762684484688656230695193406027427209019177766656481160446028988789366289983513203208457669727997759044889450031355600785664623805797743160626418720589277218457701966393363582157168985840849_<250>] Free to factor

31×10²⁸⁰+329 = 3(4)₂₇₉8_<281> = 2⁵ × 11464820359_<11> × 17389459743369869_<17> × 535810574680245913_<18> × 10076381034321664463292560834270009344537262942652775517633449448178030489063148633024447175572749685187525050939561421348218671002052054686507785700229516107637014374328596885940862217489023672681587509721555829545561312573953742609843_<236>

31×10²⁸¹+329 = 3(4)₂₈₀8_<282> = 2⁵ × 3 × 13 × 43 × 1842312101807_<13> × [3483958222381033496577713120169930226069495771118702647705474771920136127252507221054531417315092437508672348415755837750031513446734378221981122333092808692862308445257037164232822671880829740471918087650314323525541851824089524704759431798903034143896485204854451_<265>] Free to factor

31×10²⁸²+329 = 3(4)₂₈₁8_<283> = 2⁵ × 7 × 29 × 8221 × 69420264418597_<14> × 20399947204434607_<17> × [45544214158010255902822670616307487564459466601552288209005305632987712109351864108150880443791630210754626968932611015925040050153971890036783972532677655603461415365830129110502796780574097767222235442785437088831196150773206031275914865901557_<245>] Free to factor

31×10²⁸³+329 = 3(4)₂₈₂8_<284> = 2⁵ × 131 × 13723 × 19853 × 635711471 × 26067708160707371_<17> × [1819951464784011369552056887849683733479705432197493487651017881603422050051634732359792826543818701463046978859149652031204993260747679317521079074144152942433523743494230615581708317631670440750227708497956108177209720815879627001773045426513161_<247>] Free to factor

31×10²⁸⁴+329 = 3(4)₂₈₃8_<285> = 2⁵ × 3² × 34243133 × 3604596367_<10> × 1470339623139229_<16> × [6589901185409041351329889593977959890109445610069223606182067139835029445319996586305924024350562004366130768151481873493426101856223065213457141471223298832336354626518640695943149276083295280236757613070129146487825494304206219613627086284300413159_<250>] Free to factor

31×10²⁸⁵+329 = 3(4)₂₈₄8_<286> = 2⁵ × 32173 × 17924561 × 1502847143958410357_<19> × [124197916078382544939670504800557623840970679236632433215511125836480595229605062496190943431405713089907796234095198046871283590869196988706914537357344386102296960230452475534047204018432563084043572846054598106406522530066717308043090613247810404523609_<255>] Free to factor

31×10²⁸⁶+329 = 3(4)₂₈₅8_<287> = 2⁵ × 113 × [9525565388397246804326450344149459193706981317600786627335299901671583087512291052114060963618485742379547689282202556538839724680432645034414945919370698131760078662733529990167158308751229105211406096361848574237954768928220255653883972468043264503441494591937069813176007866273353_<283>] Free to factor

31×10²⁸⁷+329 = 3(4)₂₈₆8_<288> = 2⁵ × 3 × 13² × 12791 × 417646127 × [3974186917986859401510897461139899542377127358962208686950328490451033111651569200091143280977090122908361508248645164155138792950243586834463529554541177283603258910215324673046396392976757400191624791182419202820730493199011318857946522355042137205853606699269255289811_<271>] Free to factor

31×10²⁸⁸+329 = 3(4)₂₈₇8_<289> = 2⁵ × 7 × 1162807 × 13224020948432652180565634819006186739611117001345990335564701732088065331673256290153161259028354771672450358595178844798945125138551906708617151536741804086255917041249430889328137968712027863718557015036998387631811751205597303875006021621926066945747769822616293268774720984761_<281>

31×10²⁸⁹+329 = 3(4)₂₈₈8_<290> = 2⁵ × 19 × 223 × 406838051617228318988557_<24> × 172653377355078667418914989531257_<33> × 3616713423808338756570486927513315290515714812660819211773174827246001162093357492997815832101999389886033238650153230222853859448146070920521974777673566645876047373536850876661765522256719865536662328090669605353717905556424153_<229> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:4067081619 for P33 x P229 / June 24, 2022 2022 年 6 月 24 日)

31×10²⁹⁰+329 = 3(4)₂₈₉8_<291> = 2⁵ × 3 × 1283 × 5573 × [501801842862929756242198664807728466312841849106147564405625520070667374384676335584000714244671057379697844895891540728389811046574343726197272391140247785114004172909016843256627294996231966724511016183411160921451252057886120149630653383087419868979551778214017753026605836732157_<282>] Free to factor

31×10²⁹¹+329 = 3(4)₂₉₀8_<292> = 2⁵ × 23 × 23609212051_<11> × 357141488999_<12> × 555033980147528833430812452664631436684093501657107748996312715793059785297441711447283246935123857624117846980040179366560875451574755296948199446489451171328863927109736462006389316208269212448986787814618855008197894032904953044353050624651974630956514764443226307_<267>

31×10²⁹²+329 = 3(4)₂₉₁8_<293> = 2⁵ × 787 × 15780117072677_<14> × [86673084579463082690854742632241945085922046775969997667557221135094911467071890275870583156782353669763533942412570642389666216122152624038607163098797777490541137960991645735037857786609571768651666520473173806048582129508606230317443643247538988448953988584816234522395911_<275>] Free to factor

31×10²⁹³+329 = 3(4)₂₉₂8_<294> = 2⁵ × 3³ × 13 × 6257 × 101101480856614597_<18> × 48477299385076406435777451872463707815959982763772282869927308719878558826706087166137974158303425380145544214524800191520235059872584118084584722397936304648628829688391675200497446800956526516861274972501309759836157650781679941267934626675519786934451851998148630891_<269>

31×10²⁹⁴+329 = 3(4)₂₉₃8_<295> = 2⁵ × 7 × 21851 × 87641 × 62905710959563_<14> × 94686636238870094323_<20> × 1348074088657184601943742675101463658285804488238802899191802511165104510426053363721015821797766005871896672834696996377255578400430468954894689619627612652931632139183828672571424220412564889879128999018700630613995239806208976286393298284338144453_<250>

31×10²⁹⁵+329 = 3(4)₂₉₄8_<296> = 2⁵ × 17 × 367 × 100609 × 1870597 × 18283385949502981_<17> × 69907445412835102630789175480177_<32> × [717227768118057047013488682867023002983994127753499519250452564839305559807833394745215950475573526404909433403048338396754829795366100457494980581210016222371625844915786355671091115806880823598885481841229166413225354222077274351_<231>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3905276741 for P32 / June 24, 2022 2022 年 6 月 24 日) Free to factor

31×10²⁹⁶+329 = 3(4)₂₉₅8_<297> = 2⁵ × 3 × 71 × 193 × 8783 × 5981831660107_<13> × 8792829557849287_<16> × 1542197427190881135885114740821855088633_<40> × [367524753367847112610901159758373878433860856895799352977925093224242672621892390513609199610826241686677358576944504408611659916128858463806881914630220848470653477820154427811833363077694803871152860199258221490967871_<219>] (Dmitry Domanov / GMP-ECM 7.0.5 B1=11000000, sigma=3:44307937 for P40 / November 1, 2022 2022 年 11 月 1 日) Free to factor

31×10²⁹⁷+329 = 3(4)₂₉₆8_<298> = 2⁵ × 15251064050213_<14> × 7057795346901423476744161053362200166258087431838955280363352182903690242775578853278613736668461776145940881454091295429263340020033277446279022137660713396162489851683907822187673293704573647589514562556198974658716911446357881288342937630930206681120112066266635672464708814245253_<283>

31×10²⁹⁸+329 = 3(4)₂₉₇8_<299> = 2⁵ × 773 × 2713 × 169306987 × 12145917493_<11> × 153869604805459_<15> × 164136598175189_<15> × 49937860136841462869_<20> × 197900328681684267519087652794435004221166906127279471378784311096012526592922769369842592980652919236640410466189731647572515300100587729810613315986602839752425275601346118925463294759312457297426504531892622090543096036209_<225>

31×10²⁹⁹+329 = 3(4)₂₉₈8_<300> = 2⁵ × 3 × 13 × 83 × 280354549125149_<15> × 11860934270053035203875377089140992750691929582496825012654848401751637402994970307741878513842829058728729121715282295251259475970587446467579197022262196851378717978053464916310283778877790632401021433740518982826432910852453769134630764534110423065000789937548578056343333190153_<281>

31×10³⁰⁰+329 = 3(4)₂₉₉8_<301> = 2⁵ × 7 × 139 × 5114801 × 1207754793247669_<16> × 106027798041807401_<18> × 168899791110472667911409629197198133409928951714120461192437935939210670711923660932394762905858345196217685586701966107750863492749799417827119147240372128879154305627016446624704624780206352219678111704431602170850369895252958724363312442102409035982579697_<258>

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