Table of contents 目次

  1. About 400...001 400...001 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
    4. Algebraic factorization 代数的因数分解
    5. Related sequences 関連する数列
  2. Prime numbers of the form 400...001 400...001 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
    3. Range of search 捜索範囲
    4. Prime factors that appear periodically 周期的に現れる素因数
    5. Difficulty of search 捜索難易度
  3. Factor table of 400...001 400...001 の素因数分解表
    1. Last updated 最終更新日
    2. Range of factorization 分解範囲
    3. Terms that have not been factored yet まだ分解されていない項
    4. Factor table 素因数分解表
  4. Related links 関連リンク

1. About 400...001 400...001 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

40w1 = { 41, 401, 4001, 40001, 400001, 4000001, 40000001, 400000001, 4000000001, 40000000001, … }

1.3. General term 一般項

4×10n+1 (1≤n)

1.4. Algebraic factorization 代数的因数分解

  1. 4×104k+1 = (2×102k-2×10k+1)×(2×102k+2×10k+1)

1.5. Related sequences 関連する数列

2. Prime numbers of the form 400...001 400...001 の形の素数

2.1. Last updated 最終更新日

June 25, 2020 2020 年 6 月 25 日

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

  1. 4×101+1 = 41 is prime. は素数です。
  2. 4×102+1 = 401 is prime. は素数です。
  3. 4×103+1 = 4001 is prime. は素数です。
  4. 4×1013+1 = 4(0)121<14> is prime. は素数です。
  5. 4×10229+1 = 4(0)2281<230> is prime. は素数です。
  6. 4×10242+1 = 4(0)2411<243> is prime. は素数です。
  7. 4×10309+1 = 4(0)3081<310> is prime. は素数です。
  8. 4×10957+1 = 4(0)9561<958> is prime. は素数です。
  9. 4×101473+1 = 4(0)14721<1474> is prime. は素数です。
  10. 4×101494+1 = 4(0)14931<1495> is prime. は素数です。
  11. 4×103182+1 = 4(0)31811<3183> is prime. は素数です。
  12. 4×103727+1 = 4(0)37261<3728> is prime. は素数です。
  13. 4×104177+1 = 4(0)41761<4178> is prime. は素数です。
  14. 4×1023210+1 = 4(0)232091<23211> is prime. は素数です。 (Hugo Pfoertner)
  15. 4×1025719+1 = 4(0)257181<25720> is prime. は素数です。 (Hugo Pfoertner)
  16. 4×1032835+1 = 4(0)328341<32836> is prime. は素数です。 (Ray Chandler / srsieve, PFGW / August 30, 2010 2010 年 8 月 30 日)
  17. 4×1036990+1 = 4(0)369891<36991> is prime. は素数です。 (Peter Benson / NewPGen, PRP, OpenPFGW / August 23, 2003 2003 年 8 月 23 日)
  18. 4×10103958+1 = 4(0)1039571<103959> is prime. は素数です。 (Peter Benson / NewPGen, OpenPFGW, Proth.exe / December 31, 2004 2004 年 12 月 31 日)

2.3. Range of search 捜索範囲

  1. n≤50000 / Completed 終了 / Ray Chandler / September 7, 2010 2010 年 9 月 7 日
  2. n≤150000 / Completed 終了 / Ray Chandler / February 20, 2012 2012 年 2 月 20 日
  3. n≤200000 / Completed 終了 / Predrag Kurtovic / February 7, 2015 2015 年 2 月 7 日
  4. n≤250000 / Completed 終了 / Predrag Kurtovic / June 27, 2017 2017 年 6 月 27 日
  5. n≤300000 / Completed 終了 / Predrag Kurtovic / June 17, 2018 2018 年 6 月 17 日
  6. n≤400000 / Completed 終了 / Predrag Kurtovic / July 7, 2018 2018 年 7 月 7 日
  7. n≤500000 / Completed 終了 / Predrag Kurtovic / August 27, 2019 2019 年 8 月 27 日
  8. n≤600000 / Completed 終了 / Predrag Kurtovic / June 24, 2020 2020 年 6 月 24 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。

  1. 4×104k+1 = (2×102k-2×10k+1)×(2×102k+2×10k+1)
  2. 4×105k+1+1 = 41×(4×101+141+36×10×105-19×41×k-1Σm=0105m)
  3. 4×106k+4+1 = 13×(4×104+113+36×104×106-19×13×k-1Σm=0106m)
  4. 4×106k+5+1 = 7×(4×105+17+36×105×106-19×7×k-1Σm=0106m)
  5. 4×1013k+7+1 = 53×(4×107+153+36×107×1013-19×53×k-1Σm=01013m)
  6. 4×1016k+4+1 = 17×(4×104+117+36×104×1016-19×17×k-1Σm=01016m)
  7. 4×1018k+11+1 = 19×(4×1011+119+36×1011×1018-19×19×k-1Σm=01018m)
  8. 4×1022k+17+1 = 23×(4×1017+123+36×1017×1022-19×23×k-1Σm=01022m)
  9. 4×1028k+20+1 = 29×(4×1020+129+36×1020×1028-19×29×k-1Σm=01028m)
  10. 4×1032k+11+1 = 641×(4×1011+1641+36×1011×1032-19×641×k-1Σm=01032m)

Read more続きを読むHide more続きを隠す

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 14.86%. 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 14.86% です。

3. Factor table of 400...001 400...001 の素因数分解表

3.1. Last updated 最終更新日

January 4, 2021 2021 年 1 月 4 日

3.2. Range of factorization 分解範囲

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

n=211, 213, 215, 222, 225, 226, 231, 233, 237, 239, 243, 246, 247, 250, 251, 253, 254, 255, 257, 258, 261, 265, 266, 267, 269, 271, 274, 275, 278, 279, 282, 283, 285, 286, 287, 289, 290, 291, 293, 294, 295, 297, 299 (43/300)

3.4. Factor table 素因数分解表

4×101+1 = 41 = definitely prime number 素数
4×102+1 = 401 = definitely prime number 素数
4×103+1 = 4001 = definitely prime number 素数
4×104+1 = 40001 = 13 × 17 × 181
4×105+1 = 400001 = 7 × 57143
4×106+1 = 4000001 = 41 × 97561
4×107+1 = 40000001 = 53 × 754717
4×108+1 = 400000001 = 19801 × 20201
4×109+1 = 4000000001<10> = 47 × 127 × 670129
4×1010+1 = 40000000001<11> = 13 × 3076923077<10>
4×1011+1 = 400000000001<12> = 7 × 193 × 41 × 317 × 641
4×1012+1 = 4000000000001<13> = 277 × 7213 × 2002001
4×1013+1 = 40000000000001<14> = definitely prime number 素数
4×1014+1 = 400000000000001<15> = 7333 × 54547933997<11>
4×1015+1 = 4000000000000001<16> = 173 × 23121387283237<14>
4×1016+1 = 40000000000000001<17> = 13 × 41 × 457 × 569 × 821 × 351529
4×1017+1 = 400000000000000001<18> = 72 × 23 × 2687 × 132089534249<12>
4×1018+1 = 4000000000000000001<19> = 12056437 × 331772977373<12>
4×1019+1 = 40000000000000000001<20> = 922367 × 43366685928703<14>
4×1020+1 = 400000000000000000001<21> = 17 × 29 × 53 × 1129 × 5953 × 35933 × 63389
4×1021+1 = 4000000000000000000001<22> = 41 × 97560975609756097561<20>
4×1022+1 = 40000000000000000000001<23> = 13 × 273773 × 11238957373163449<17>
4×1023+1 = 400000000000000000000001<24> = 7 × 26249 × 2176953679868076607<19>
4×1024+1 = 4000000000000000000000001<25> = 1999998000001<13> × 2000002000001<13>
4×1025+1 = 40000000000000000000000001<26> = 733 × 1847 × 4219 × 2447761 × 2860952089<10>
4×1026+1 = 400000000000000000000000001<27> = 41 × 293 × 33297261300258053775077<23>
4×1027+1 = 4000000000000000000000000001<28> = 797 × 31557220333<11> × 159038740554601<15>
4×1028+1 = 40000000000000000000000000001<29> = 13 × 15384616923077<14> × 199999980000001<15>
4×1029+1 = 400000000000000000000000000001<30> = 7 × 19 × 131 × 35343237863<11> × 649577122635449<15>
4×1030+1 = 4000000000000000000000000000001<31> = 1199481995446957<16> × 3334772856269093<16>
4×1031+1 = 40000000000000000000000000000001<32> = 41 × 659 × 1613 × 752459 × 1474663 × 827143245899<12>
4×1032+1 = 400000000000000000000000000000001<33> = 593 × 877 × 3089 × 3121 × 3989 × 19999999800000001<17>
4×1033+1 = 4000000000000000000000000000000001<34> = 53 × 75471698113207547169811320754717<32>
4×1034+1 = 40000000000000000000000000000000001<35> = 13 × 78517 × 39187985747329583696230409681<29>
4×1035+1 = 400000000000000000000000000000000001<36> = 7 × 472477 × 1342739 × 277543751143<12> × 324532520167<12>
4×1036+1 = 4000000000000000000000000000000000001<37> = 17 × 41 × 881 × 267713 × 8479780817<10> × 2869440456241033<16>
4×1037+1 = 40000000000000000000000000000000000001<38> = 59 × 11161 × 60744207660148306983002252091499<32>
4×1038+1 = 400000000000000000000000000000000000001<39> = 89 × 21929 × 710777042881<12> × 288348545377013952641<21>
4×1039+1 = 4000000000000000000000000000000000000001<40> = 23 × 450493 × 26255689 × 14703498742403429328114331<26>
4×1040+1 = 40000000000000000000000000000000000000001<41> = 13 × 15384615383076923077<20> × 200000000020000000001<21>
4×1041+1 = 400000000000000000000000000000000000000001<42> = 7 × 41 × 18287 × 28607 × 8232503 × 323617065960441802399049<24>
4×1042+1 = 4000000000000000000000000000000000000000001<43> = 345997 × 405788401 × 244759045477<12> × 116399007761442929<18>
4×1043+1 = 40000000000000000000000000000000000000000001<44> = 379 × 641 × 18867364133062891<17> × 8726729622988730725849<22>
4×1044+1 = 400000000000000000000000000000000000000000001<45> = 541 × 42767521 × 467644594134881<15> × 36968576709426987061<20>
4×1045+1 = 4000000000000000000000000000000000000000000001<46> = 22013 × 64997 × 2795679912153810318713513708145726641<37>
4×1046+1 = 40000000000000000000000000000000000000000000001<47> = 13 × 41 × 53 × 5849 × 2494117169<10> × 888265814281<12> × 109273660408134809<18>
4×1047+1 = 400000000000000000000000000000000000000000000001<48> = 7 × 19 × 251 × 273641 × 49043851 × 892830248999542574297475458717<30>
4×1048+1 = 4000000000000000000000000000000000000000000000001<49> = 29 × 157 × 997 × 1093 × 196277 × 2346997 × 27736601 × 39336709 × 1604034898237<13>
4×1049+1 = 40000000000000000000000000000000000000000000000001<50> = 6047 × 9198701017619<13> × 719107005037030071155743700669957<33>
4×1050+1 = 400000000000000000000000000000000000000000000000001<51> = 20832397 × 19200862963585035365829481840231827379249733<44>
4×1051+1 = 4(0)501<52> = 41 × 127 × 2699 × 340957 × 834775929756340659346435744705824635801<39>
4×1052+1 = 4(0)511<53> = 13 × 172 × 15473 × 2717549 × 9730969 × 4596227727257<13> × 5661209930204358073<19>
4×1053+1 = 4(0)521<54> = 7 × 2887 × 19793161462714632094611311791775941412242070364689<50>
4×1054+1 = 4(0)531<55> = 397 × 5569 × 18513601 × 97724029689006262970120726321857649103557<41>
4×1055+1 = 4(0)541<56> = 47 × 311792317 × 3546491561<10> × 769658009527008787510356671896509059<36>
4×1056+1 = 4(0)551<57> = 41 × 61 × 941 × 622549 × 526655496128047225409<21> × 518389881029517119825821<24>
4×1057+1 = 4(0)561<58> = 2383 × 309519429257646847<18> × 5423105248953848825200534252128523601<37>
4×1058+1 = 4(0)571<59> = 13 × 173 × 10252493 × 1734766609991044971257473234202380382148194988893<49>
4×1059+1 = 4(0)581<60> = 72 × 53 × 1721 × 7172369 × 561815797 × 22210104408309019466753678280866226961<38>
4×1060+1 = 4(0)591<61> = 229 × 76597 × 69336888435401<14> × 28844674820724601<17> × 114020450593997974882777<24>
4×1061+1 = 4(0)601<62> = 23 × 41 × 231611 × 151054394039690896708813<24> × 1212427431602724544074830260849<31>
4×1062+1 = 4(0)611<63> = 5881 × 242593794022971299662713397<27> × 280368440058228030693613482669893<33>
4×1063+1 = 4(0)621<64> = 57463303 × 92412075452419139957<20> × 753252673202065154243392276401159931<36>
4×1064+1 = 4(0)631<65> = 13 × 113 × 3061 × 5233 × 697935976337<12> × 37277079488149<14> × 65338124795818366546880104541<29>
4×1065+1 = 4(0)641<66> = 7 × 19 × 2204550857157326593682271383927<31> × 1364231987313074370799674019902811<34>
4×1066+1 = 4(0)651<67> = 41 × 677 × 956647082893<12> × 15916078812572232654253<23> × 9464542666233135185372313917<28>
4×1067+1 = 4(0)661<68> = 164117 × 1742051 × 139908969084878224421852702990639345649008391006902174303<57>
4×1068+1 = 4(0)671<69> = 17 × 97 × 9929 × 91453 × 126085681 × 165300869 × 5685054840613<13> × 2254552250995694797203588661<28>
4×1069+1 = 4(0)681<70> = 1441373 × 2775131766725198820846512318463021022316915885062367617542440437<64>
4×1070+1 = 4(0)691<71> = 132 × 1493 × 214426983624269161<18> × 739322702995632778091948645116533136331014788973<48>
4×1071+1 = 4(0)701<72> = 7 × 41 × 54059 × 623599681 × 206158145486328458561<21> × 200541243562919356138928178827285917<36>
4×1072+1 = 4(0)711<73> = 53 × 2861 × 23173 × 41729 × 39024189068687294863375801<26> × 699056274030059420482348829080741<33>
4×1073+1 = 4(0)721<74> = 383 × 24733 × 4222643524750338840751339185002352540273726532526653589843444435659<67>
4×1074+1 = 4(0)731<75> = 1877 × 819374245465341477001<21> × 260083864515468281071095575684487609275500129561813<51>
4×1075+1 = 4(0)741<76> = 223 × 641 × 296554471805228957<18> × 700580501444791801<18> × 134689758945851757063416146149285251<36>
4×1076+1 = 4(0)751<77> = 13 × 29 × 41 × 7537 × 205929062893<12> × 3295105303424261<16> × 51048013082528437769<20> × 9912209782592943898697<22>
4×1077+1 = 4(0)761<78> = 7 × 167 × 27179 × 160481 × 905917 × 1631579 × 53075227971470436723416564853216129170625280592743997<53>
4×1078+1 = 4(0)771<79> = 661152529 × 1490111265532794649<19> × 32601096982344030022369<23> × 124539585518612667972527269049<30>
4×1079+1 = 4(0)781<80> = 10399301453<11> × 44286505549343<14> × 86852917252842856443203096773392846999695124656258528219<56>
4×1080+1 = 4(0)791<81> = 709 × 958682189 × 3901200066397<13> × 5347577827006842697<19> × 28208744710860366713399153737658674189<38>
4×1081+1 = 4(0)801<82> = 41 × 263 × 277 × 82613 × 6607585172530757<16> × 7457700591622276977648263<25> × 328961073500403971350916708317<30>
4×1082+1 = 4(0)811<83> = 13 × 89 × 8320453 × 127095503602181369<18> × 32692601016761314157119495004047542663458645548499540849<56>
4×1083+1 = 4(0)821<84> = 7 × 19 × 23 × 61331 × 2132065135506677737272745109390372272910797502215335604455310419649103760569<76>
4×1084+1 = 4(0)831<85> = 17 × 109 × 853425905273368333<18> × 21499961203232518024633<23> × 117647058823529411764823529411764705882353<42>
4×1085+1 = 4(0)841<86> = 53 × 971 × 2991889 × 3116849 × 829547000162864046944367046259459<33> × 100476073473841019014510202342341373<36>
4×1086+1 = 4(0)851<87> = 41 × 197 × 733 × 7986133 × 65307413 × 5076336961<10> × 1187792304317<13> × 576148187135201<15> × 37289088323622219708408124357<29>
4×1087+1 = 4(0)861<88> = 150893 × 409597 × 2164979 × 4035102268771272917<19> × 7408425138353516758928742273260814998297567120698567<52>
4×1088+1 = 4(0)871<89> = 13 × 309929 × 7230701 × 11817812485849<14> × 482836088598383929<18> × 7551796575516578981<19> × 31863018833731140278508013<26>
4×1089+1 = 4(0)881<90> = 7 × 186806046659<12> × 181062640643378909404647518804407631099<39> × 1689437662993745555909697934943056683623<40>
4×1090+1 = 4(0)891<91> = 317 × 773 × 845166009699652159666515021017148258333637<42> × 19314310664570004537506940810390365837495453<44>
4×1091+1 = 4(0)901<92> = 41 × 52562142481636817481601<23> × 18561072856541213939514050581011188369320296717040037332455429879961<68>
4×1092+1 = 4(0)911<93> = 2293 × 9076746840853577<16> × 2203432611999477182878829995513<31> × 8722197993894461404273789795028347143480157<43>
4×1093+1 = 4(0)921<94> = 127 × 2081291 × 176869847757581148834467117<27> × 85559780579232529861792445700437376029567083586972454614129<59>
4×1094+1 = 4(0)931<95> = 13 × 1361 × 225721 × 1939265163533<13> × 5164750569576816620964067538335815709623314583988191852709325014543362449<73>
4×1095+1 = 4(0)941<96> = 7 × 59 × 1607 × 26921 × 2181259 × 8726647 × 2050333674467557<16> × 573619207734231410765653214023473131490255218752669688731<57>
4×1096+1 = 4(0)951<97> = 41 × 653 × 21347052697<11> × 1948217037997<13> × 39654833524613<14> × 631411766525927033401<21> × 143475878369122834469397183454904461<36>
4×1097+1 = 4(0)961<98> = 251 × 691 × 53077 × 157211 × 2224367 × 543367039097502667247<21> × 22867526479928742063772216587242930120801823067098947687<56>
4×1098+1 = 4(0)971<99> = 53 × 7547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754717<97>
4×1099+1 = 4(0)981<100> = 5340514614533165278697161411<28> × 748991490279753729991982536795069576765844598816949515716785117147315691<72>
4×10100+1 = 4(0)991<101> = 13 × 17 × 3677 × 54829 × 267581 × 1729468241<10> × 530526767289696833<18> × 1976577034596636110381<22> × 1850013310736271697135674572900561429<37>
4×10101+1 = 4(0)1001<102> = 72 × 19 × 41 × 47 × 173 × 4517179 × 6579538699<10> × 43363042523148153702266204810980480699687116865954056179861696866240783475881<77>
4×10102+1 = 4(0)1011<103> = 463049479397<12> × 8638385697375033388477501655442812500798005297363031687909266430467188209717273606396266733<91>
4×10103+1 = 4(0)1021<104> = 75691460528272051<17> × 1023246397461943840048249<25> × 39556096425362661005215663<26> × 13056279985721006726424982182157633373<38>
4×10104+1 = 4(0)1031<105> = 29 × 1153 × 1229 × 4073 × 44773 × 136573 × 380321041 × 11586215577990829<17> × 3031758035603884709<19> × 29254915858051818526570428231358748733761<41>
4×10105+1 = 4(0)1041<106> = 232 × 3329 × 92623529 × 10065112367161<14> × 61374787300570333<17> × 1770038185341029783677361<25> × 22427348776522401264947020870679665813<38>
4×10106+1 = 4(0)1051<107> = 13 × 41 × 2237 × 236672805169<12> × 236806432528979638909578742022011126001<39> × 598583780294530529081821283615359397949289067281249<51> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 for P39 x P51 / 0.94 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 22, 2007 2007 年 3 月 22 日)
4×10107+1 = 4(0)1061<108> = 7 × 641 × 739 × 211511398519689785054417917<27> × 570329330270045351436503539535108189841256840826470291937286786510642047521<75>
4×10108+1 = 4(0)1071<109> = 14282353 × 449624801 × 4448153205854852299395290701502028576933415201<46> × 140032948352417840393666225586218181275872400017<48>
4×10109+1 = 4(0)1081<110> = 73637 × 85645489596205447<17> × 504566703184287260002689525090090859<36> × 12570160427975508498024126528760502161684857548395201<53>
4×10110+1 = 4(0)1091<111> = 2797 × 11813 × 12106185410285130629221105282016464351627060726230087557078015981435891044452369287927188316344672904641<104>
4×10111+1 = 4(0)1101<112> = 41 × 53 × 419 × 954263 × 4603818109825557387601129945008576400336570077856109340401190640622283958065767097101108400901358321<100>
4×10112+1 = 4(0)1111<113> = 13 × 409 × 5897 × 803237 × 882851476915327188602341<24> × 93926450809509114392492557<26> × 19153270310774260418014378549639674313960981532321<50>
4×10113+1 = 4(0)1121<114> = 7 × 503 × 1597 × 27693103 × 1921587721428489822984360074527<31> × 1336771611781129939139846137350975094986672392926838753978751165909733<70> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 for P31 x P70 / 1.48 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 22, 2007 2007 年 3 月 22 日)
4×10114+1 = 4(0)1131<115> = 1481 × 10284099811172636668173569<26> × 19239826379011231330142545758809249<35> × 13650152431907201963179891116352788668531001597230041<53> (Makoto Kamada / Msieve 1.17 for P35 x P53 / March 22, 2007 2007 年 3 月 22 日)
4×10115+1 = 4(0)1141<116> = 205327 × 194811203592318594242354877829023947167201585763197241473357132768705528254929941020908112425545593127060737263<111>
4×10116+1 = 4(0)1151<117> = 17 × 41 × 61 × 193 × 6197 × 53653 × 415721 × 8418828519021619133<19> × 1041409915758482772813621281597<31> × 40224367811668375803852835183908505200564069461<47>
4×10117+1 = 4(0)1161<118> = 4164125225093709812091452961256189013773247773370698915379<58> × 960585905509117746404238452290739780153822354353075575508219<60> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 for P58 x P60 / 1.55 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 23, 2007 2007 年 3 月 23 日)
4×10118+1 = 4(0)1171<119> = 13 × 2521 × 1917014041<10> × 32794004557<11> × 19414403288312435820668470666126269499692898656496134681162055945274405314730287544170314937001<95>
4×10119+1 = 4(0)1181<120> = 7 × 19 × 663127 × 1049565721<10> × 100814601578535670801<21> × 17915709037898119173692619891853<32> × 2392459322134858608657877987740046002908201967261647<52>
4×10120+1 = 4(0)1191<121> = 509 × 18797 × 471749 × 3696899840127421<16> × 1332399407553263054444728109<28> × 3181885712427202864515492961<28> × 56543929648956861705455421014649847997<38>
4×10121+1 = 4(0)1201<122> = 41 × 179 × 35407 × 1677282149548946503<19> × 91775729995559202309480860055465558152596719087388419932408692990597402155192941860585945575179<95>
4×10122+1 = 4(0)1211<123> = 1693 × 2081 × 34301081 × 250868621552100821173<21> × 237061104674256043241201<24> × 55656577748792728734500686238834161290097068307476037683753452569<65>
4×10123+1 = 4(0)1221<124> = 151007 × 488636333 × 537902543 × 100779815274977560127837755663970009211033146759104806586600787111420881878953212789248848361924885397<102>
4×10124+1 = 4(0)1231<125> = 13 × 53 × 10253 × 14281 × 90620549 × 41641602785482764604422844952478401980473629079093433<53> × 105069597079303499041538586981063998401693897581284689<54>
4×10125+1 = 4(0)1241<126> = 7 × 3465927964099<13> × 18646352828611<14> × 40406937613934921<17> × 21882280681486971925481937485784203208914088263175996664282980555648871573032498247<83>
4×10126+1 = 4(0)1251<127> = 41 × 89 × 157 × 2333 × 43969 × 37132169765645505210537037<26> × 1833052150971326717676530757844097982202256630343703419817263946327914048885728723324893<88>
4×10127+1 = 4(0)1261<128> = 23 × 2544761 × 16180327 × 35832931081<11> × 54093077531<11> × 21790833172315990738253233519382438490953607919672593208341683869485576176214437220110961811<92>
4×10128+1 = 4(0)1271<129> = 373 × 761 × 2633 × 5817901501<10> × 34078691320501<14> × 1513015890063439996908593<25> × 862917513178823378823631229<27> × 2067538466388206817464922662772364909800768017<46>
4×10129+1 = 4(0)1281<130> = 2571557 × 3993481 × 389504261589723049023540667029763241272203254578966125062684058985602519974144182176885796920166971006571953362133253<117>
4×10130+1 = 4(0)1291<131> = 13 × 24329 × 26293188445622053<17> × 10943887203994016693<20> × 439518862738820048374800235746739067905044179173052197766563183577009727868501488261896597<90>
4×10131+1 = 4(0)1301<132> = 7 × 41 × 39983 × 6117344564173<13> × 13540374519737783<17> × 914330696485126819<18> × 460262717377104473504549506528838721203624141138015878165033860155386374302161<78>
4×10132+1 = 4(0)1311<133> = 17 × 29 × 433 × 701 × 3373 × 4254113 × 30223181 × 88380821229433<14> × 378879178609013<15> × 35917654067934382596442843652221<32> × 51247760017521254232765394554789953067443953049<47>
4×10133+1 = 4(0)1321<134> = 18650253859<11> × 656859394409<12> × 3004948379353932636885592567<28> × 1215103598620682615274146445588556223<37> × 894236732175920580152377822028339767396828303931<48> (Makoto Kamada / Msieve 1.17 for P37 x P48 / March 23, 2007 2007 年 3 月 23 日)
4×10134+1 = 4(0)1331<135> = 2521769 × 6482122769<10> × 498771505631914848917<21> × 339732985011027186094197732510445277293910533<45> × 144410272621457596142773322790127495868916847945915681<54> (Shaopu Lin / Msieve v. 1.17 for P45 x P54 / March 24, 2007 2007 年 3 月 24 日)
4×10135+1 = 4(0)1341<136> = 127 × 214556798183205397<18> × 146795921913563321819395980538666834042505147352976071774890915399867927840476992392706923237735278878621927216090179<117>
4×10136+1 = 4(0)1351<137> = 13 × 41 × 149 × 4481 × 11122527809<11> × 16596601969<11> × 1637757436921<13> × 2972939782892017<16> × 82473787923605350135609<23> × 410588190710389639144589153<27> × 3693097747722714009348879879577<31>
4×10137+1 = 4(0)1361<138> = 7 × 19 × 53 × 1009 × 3823 × 218117 × 1603681 × 23055346723785830899288317321960983887657807<44> × 1824138707895749513832021600956777695371243638120294559951871173502726613<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P44 x P73 / 7.70 hours on Cygwin on AMD XP 2700+ / March 26, 2007 2007 年 3 月 26 日)
4×10138+1 = 4(0)1371<139> = 6961 × 9998845837<10> × 27181130477<11> × 92639850016760801<17> × 21243739982186736081596209<26> × 1074340998593730730892428867826432317325432888260258081212279529347431801<73>
4×10139+1 = 4(0)1381<140> = 641 × 27851 × 7102095496029555951338486428062736055043334947960741098720689<61> × 315482054875753501037036269251586513863489506091455405288439226913423699<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 for P61 x P72 / 8.58 hours on Core 2 Duo E6300@2.33GHz / March 24, 2007 2007 年 3 月 24 日)
4×10140+1 = 4(0)1391<141> = 63377 × 83561 × 500467433 × 679233377 × 4899244937<10> × 23696426502493<14> × 3839802081892921<16> × 66052631879764390352533<23> × 7546035908518137699673476947473361898516667544440801<52>
4×10141+1 = 4(0)1401<142> = 41 × 3167 × 1385099246529648770253437136267455844731<40> × 41102459480233672086378912659093765960173<41> × 541102285545511773447658741193840771596059733459284964441<57> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 for P40 x P41 x P57 / 7.40 hours on Core 2 Duo E6300@2.33GHz / March 25, 2007 2007 年 3 月 25 日)
4×10142+1 = 4(0)1411<143> = 13 × 3250517 × 70502989264785613<17> × 13426309871176552568186516301787835466311568281191496953878958627394634905531548898527727705393436465260263421649042037<119>
4×10143+1 = 4(0)1421<144> = 72 × 7874219 × 10763828209<11> × 96314054182771268977482219619348989633785487937642420968781693916432139510787929323379246182872041692533059858697565965894819<125>
4×10144+1 = 4(0)1431<145> = 173 × 8317 × 25621 × 33113 × 319133 × 503249 × 579112895164952297<18> × 67704575690756412277<20> × 127833457376629982084572450664243129<36> × 4070728657304927469734608391624183892984329021<46>
4×10145+1 = 4(0)1441<146> = 3527 × 3016133 × 9386330623739<13> × 75701171851442047<17> × 431900725161775951764678157<27> × 12252413917377543644136805930318944909387796884332369139786560301466153041715531<80>
4×10146+1 = 4(0)1451<147> = 41 × 2729 × 2184156109565083400994331504190413<34> × 185296227258331476479382730913150879294782961<45> × 8833287103024449941246276528945173645345205610821578498935895813<64> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 for P34 x P45 x P64 / 11.10 hours on Core 2 Duo E6300@2.33GHz / March 26, 2007 2007 年 3 月 26 日)
4×10147+1 = 4(0)1461<148> = 47 × 251 × 733 × 863 × 6442862514461602713781483216855754068454488467466706327<55> × 83194530963377483428159654973172315536690121265505564170886744203220844329565112601<83> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P55 x P83 / 12.48 hours on Cygwin on AMD XP 2700+ / March 27, 2007 2007 年 3 月 27 日)
4×10148+1 = 4(0)1471<149> = 132 × 17 × 138549833 × 1693109461<10> × 2976415801<10> × 796769450569<12> × 162214004147497<15> × 1070055437699459212912601513126490566842954733<46> × 144182457504055569482879143621295762376248991721<48>
4×10149+1 = 4(0)1481<150> = 7 × 23 × 13259 × 207877 × 2614971570401<13> × 344706864796710622005213145364745706122291413413780429853772014962334522600966629386228064440103850507036806595831441440265287<126>
4×10150+1 = 4(0)1491<151> = 53 × 277 × 61357 × 2304158963285019721<19> × 5047235270038343639185708957<28> × 381833693783494213482826202929761765045615299273179467013156591317268744276402346427879154651849<96>
4×10151+1 = 4(0)1501<152> = 41 × 1601 × 980423 × 670961329 × 479516387641<12> × 1931836501146231929868971910071660171111512618650385393945865617903542995026941985367517437264335727157861561970857469063<121>
4×10152+1 = 4(0)1511<153> = 543661 × 4675861 × 14926753 × 52223864333161118057243878862623357<35> × 382966681140453190759201610136931180705493<42> × 527077985383865837122630444188680560669184029075046608177<57>
4×10153+1 = 4(0)1521<154> = 59 × 397 × 13063 × 167318969 × 606641514185778295831468249<27> × 3183635597702264953513076409369407360357<40> × 40455156645999949292666657280615001667447267467607551015375410772491397<71> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P40 x P71 / 26.67 hours on Athlon XP 3000+ / March 29, 2007 2007 年 3 月 29 日)
4×10154+1 = 4(0)1531<155> = 13 × 25707428533<11> × 622744718528007083089<21> × 192197594968209977118057036742684208332916351564626023278876166757315566433401247957901720654599642233127888813956068110721<123>
4×10155+1 = 4(0)1541<156> = 7 × 19 × 90173 × 63329687397592132145980877526417873030946686466430656344663544587463<68> × 526652909060236900579923203193911048657743442112564846958614597680814721066334503<81> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P68 x P81 / 25.81 hours on Cygwin on AMD XP 2700+ / April 3, 2007 2007 年 4 月 3 日)
4×10156+1 = 4(0)1551<157> = 41 × 117647489 × 601895033 × 454356957312809<15> × 5341058207367813588605221<25> × 5288095175146719223160893179452720213<37> × 107361595370695238400797719157921129302056548074664130232322929<63>
4×10157+1 = 4(0)1561<158> = 1321757 × 46712194341161070054665870112933244096080435997557581817007450649<65> × 647855429982898406721265781990638069224565341233236221727068040304877394852504476748157<87> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P65 x P87 / 28.48 hours on Cygwin on AMD 64 3200+ / April 17, 2007 2007 年 4 月 17 日)
4×10158+1 = 4(0)1571<159> = 25263414276699562450578618285557<32> × 15833172651129734691753638260959425453361976485639459624681318174193891148379882892150660341586988134980814335626714549512537693<128> (Makoto Kamada / GMP-ECM 5.0.3 B1=85070, sigma=3599089489 for P32 x P128)
4×10159+1 = 4(0)1581<160> = 131 × 52009 × 17330918709002002575539<23> × 33875725650758540850207863307029935526293568365103392584123312512205435389144906177579530015230347839191982884839325363901546049921<131>
4×10160+1 = 4(0)1591<161> = 13 × 29 × 853 × 249517493 × 519168493069<12> × 1092173329376508437<19> × 160550853845011584389826077<27> × 82739149005614537671026137265110876506013<41> × 66182786292580938056857269476000328045369018340249<50>
4×10161+1 = 4(0)1601<162> = 7 × 41 × 24481 × 1793611 × 6778769 × 51739157 × 24543891373<11> × 7075521653495357<16> × 365498852272237776807460331845037<33> × 1425813087563283653143535013962362288561660254770001654328238688640363615813<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P33 x P76 / 20.75 hours on Cygwin on AMD XP 2700+ / March 28, 2007 2007 年 3 月 28 日)
4×10162+1 = 4(0)1611<163> = 2497329853<10> × 75396687085921<14> × 376268494658838666197<21> × 7033585355523255976857977544415093<34> × 8027072786280128866004929270459039253458495879153981797095597384581952824282996219837<85> (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=1124441233 for P34 x P85 / April 3, 2007 2007 年 4 月 3 日)
4×10163+1 = 4(0)1621<164> = 53 × 73978717 × 19915232337028022644423<23> × 512261774037057670967542856493977494372940799796521098095418261503423667203083915141568831529293379787730027819780685726100536178487<132>
4×10164+1 = 4(0)1631<165> = 17 × 97 × 937 × 262253 × 6891629 × 6639016981<10> × 4809423279366120261605554143564035809924606662417867200996041<61> × 4486013842492913780384052131069660841652414226854579805176904834375247431701<76>
4×10165+1 = 4(0)1641<166> = 23743 × 80900761 × 513790423 × 61142992571<11> × 7779120398579544883895822513251508700047607501669183213883240931<64> × 8521353913589854424771282379603548481995888227244581651836279018886769<70> (Kenji Ibusuki / GGNFS-0.77.1 snfs for P64 x P70 / 51.86 hours on Core 2 Quad Q6700 (2.66GHz), Windows XP and Cygwin / March 2, 2008 2008 年 3 月 2 日)
4×10166+1 = 4(0)1651<167> = 13 × 41 × 4517 × 152421337841<12> × 941160476969540120952877<24> × 338717486802811900673981008844119653096357974239957<51> × 341928753479598700237304527485927308118819144008567869244980664981674968409<75> (Serge Batalov / Msieve 1.36 snfs for P51 x P75 / 23.50 hours on Opteron-2.6GHz; Linux x86_64 / August 22, 2008 2008 年 8 月 22 日)
4×10167+1 = 4(0)1661<168> = 7 × 1171 × 321850576013<12> × 452834568437<12> × 334819846493942686654911244234336665685732640496966982512267869273961723073832542974680534405433160996863130567626286114687860700987297851293<141>
4×10168+1 = 4(0)1671<169> = 457 × 108533 × 409730312389<12> × 93411933000652685441898259747177<32> × 52255203297194322487918784669188516128517<41> × 40322921276290620277618877465920528643175473599262864740732386428828904824821<77>
4×10169+1 = 4(0)1681<170> = 317 × 769 × 145112173 × 741131087 × 1525722368634215200183830631475295084172954111987708688260657091635320684718502089815481557958855197157252102548295224312605614793133357560373856487<148>
4×10170+1 = 4(0)1691<171> = 89 × 809 × 12037 × 389533 × 50122020190096192578898087923762046470485403737718517<53> × 23639069626409130088066491289529080774163216816334627185245521359044363228829638540915634190946573122893<104> (Kenji Ibusuki / GGNFS-0.77.1 snfs for P53 x P104 / 78.39 hours on Core 2 Quad Q6700 (2.66GHz), Windows XP and Cygwin / March 20, 2008 2008 年 3 月 20 日)
4×10171+1 = 4(0)1701<172> = 23 × 41 × 641 × 55305917 × 571780967537331426467595011<27> × 983788565105385106532942023<27> × 3392183977152881040429986688657533088590419<43> × 62705813661270651499429351472678860702534232323580249870005333<62> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P43 x P62 / 10.75 hours on Cygwin on AMD XP 2700+ / March 26, 2007 2007 年 3 月 26 日)
4×10172+1 = 4(0)1711<173> = 13 × 293 × 6317 × 10821849037<11> × 1421625392482859915483832616008001758580123586608198873632381915389763080921<76> × 108056649779213250338622526245609523248658330816513865559158044196250326196011521<81>
4×10173+1 = 4(0)1721<174> = 7 × 19 × 19081 × 1380947158352491<16> × 1031387844700915926546275570854626898299232457527<49> × 4950984722498265333902822196208270860948138231881<49> × 22352008973784616122462526641600512964655392476154917761<56> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P49(1031...) x P49(4950...) x P56 / 92.56 hours on Core 2 Quad Q6700 / October 16, 2008 2008 年 10 月 16 日)
4×10174+1 = 4(0)1731<175> = 21669802129<11> × 90895849637269554525310385291775885388075787009<47> × 2030771183197325350577624750920707697746469994254856700264575730266390155389375430973873995208761043763694185654787441<118> (matsui / GGNFS-0.77.1-20060513-pentium-m snfs for P47 x P118 / 105.95 hours / July 14, 2008 2008 年 7 月 14 日)
4×10175+1 = 4(0)1741<176> = 16811 × 33374333358396914109100082498630504183786129383<47> × 105371111708302205780401868932937382113312422601077<51> × 676600448832315856534571187702619060715236193076202145589311912099919790801<75> (matsui / GGNFS-0.77.1-20060513-prescott snfs for P47 x P51 x P75 / February 8, 2008 2008 年 2 月 8 日)
4×10176+1 = 4(0)1751<177> = 41 × 53 × 61 × 113 × 1013 × 430121 × 11426141 × 80884901 × 6252736601<10> × 18689267390859149292717056482637255317654199244915941552355138149<65> × 567495530173653267529874247825892220316564875841726498015299495959356337<72>
4×10177+1 = 4(0)1761<178> = 127 × 6659 × 9739 × 69371 × 1058602893359918430986584487<28> × 6613355335599340569623394994644333734548049640883060507455398558497289708022568396139682510787269921256324528401245789362207525550004619<136>
4×10178+1 = 4(0)1771<179> = 13 × 566167021042476149422414249581680453<36> × 6061095723787709816177996585617442722607441719998843595973408858077<67> × 896645819043518706309661143084647289327440781070529452934200366627156144117<75> (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=531751960 for P36 / March 26, 2007 2007 年 3 月 26 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P67 x P75 / 59.57 hours on Core 2 Quad Q6700 / March 8, 2009 2009 年 3 月 8 日)
4×10179+1 = 4(0)1781<180> = 7 × 18457340200388066441<20> × 6004231495142581556980974994915411<34> × 515626709759236369230555350134883854087864590105169849025864162520888571350730707352467835084057429485986388639654825004337893<126> (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=2723994585 for P34 x P126 / March 26, 2007 2007 年 3 月 26 日)
4×10180+1 = 4(0)1791<181> = 17 × 233 × 11113 × 60107617 × 5525523109177<13> × 18966827428229747257<20> × 84774463712793346273<20> × 470115515406025639190126858917694761<36> × 361956680025158803047826849991830275331755207987544646460405310663321715919113<78>
4×10181+1 = 4(0)1801<182> = 41 × 1619 × 39293 × 30576859493<11> × 241401448929077<15> × 2077692861147390086533008886417768067467725384178251411463577449555727370531714620689079810440916876471502278084657087636963275443748788347824202503<148>
4×10182+1 = 4(0)1811<183> = 1160317 × 413745536263432081<18> × 30385872315370452048023578488339493475461704437<47> × 27420685405397558932205897020211411740511536898793314180500096877831147046352018738909437880962687052207823325649<113> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P47 x P113 / 87.22 hours on Core 2 Quad Q6700 / March 12, 2009 2009 年 3 月 12 日)
4×10183+1 = 4(0)1821<184> = 571331 × 17022010645669213<17> × 411302495331540351096624737709336167001799823065120271742613631066484339478569900893608595236556946204914561093603844242212191786134503556784400139088557339624167<162>
4×10184+1 = 4(0)1831<185> = 13 × 181 × 197 × 269 × 1945721 × 714653561 × 74953971409<11> × 404456814671197<15> × 6235763129526027221<19> × 2760112522862723807812664721033907942981<40> × 442140427088359732723919401655352200442156534928655623582787212323205365610813<78>
4×10185+1 = 4(0)1841<186> = 72 × 11387136743730658714583956573<29> × 716884805183080328390151232007836066382576126466769923060288875148399148124935727379700456665628633735390872417050473157442542103739431462713157977652619013<156>
4×10186+1 = 4(0)1851<187> = 41 × 1277 × 10302637 × 18930161 × 391726120432932548967124005640017420299524591508036017422310707844564674476058001102379920105794482705962546997707950441216394877921057009240485597529605804457857401649<168>
4×10187+1 = 4(0)1861<188> = 173 × 466357 × 17220341786228465534537012038573242088381604649445961<53> × 28790792619619581217940562985478392520067468106423516010341011616813295711690892727971687568687842629056533596007927442531799081<128> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P53 x P128 / 123.18 hours on Core 2 Quad Q6700 / March 17, 2009 2009 年 3 月 17 日)
4×10188+1 = 4(0)1871<189> = 29 × 3121 × 87442273 × 47981418968173<14> × 741548670319163677<18> × 469477203241985275180141<24> × 887855725323927778428067905829036736061102263034655095257<57> × 3407823789490258686400384521327420200673346836273759228105068009<64>
4×10189+1 = 4(0)1881<190> = 53 × 18077 × 2643247 × 96964568413<11> × 3643105412001703<16> × 13506270059310058545933600271041349759458769588496747569910410889<65> × 331054716915185039351115638053193982176316954185352183355312068630530447500029226468933<87> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P65 x P87 / 141.02 hours on Core 2 Quad Q6700 / March 23, 2009 2009 年 3 月 23 日)
4×10190+1 = 4(0)1891<191> = 13 × 3929 × 749212249 × 29090728066409<14> × 35931483680231802283901933540889672060081039517709758737692657346760870151470055777789795773004731558783470983290996179404117750527088920858749286063304888393298893<164>
4×10191+1 = 4(0)1901<192> = 7 × 19 × 41 × 647 × 46903543 × 4164599914798824246547757<25> × 765226605021062082766257793518013247<36> × 758492370060731172732749892408126693839219951872236949815340112500285954615089467270693873387494136665940937734088263<117> (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=3120847556 for P36 / April 14, 2007 2007 年 4 月 14 日)
4×10192+1 = 4(0)1911<193> = 109 × 6581 × 26096209 × 6867491821<10> × 59570268209<11> × 273203515315421<15> × 24631420088448566099321<23> × 26230629738266686917601<23> × 1649861139458928415606764241<28> × 1793513415513160594803114592713415561157304692799480329352881941524270449<73>
4×10193+1 = 4(0)1921<194> = 23 × 47 × 9641387878495279411<19> × 3837909611610355848177122629200006844797882368715559135086528572099369204241254419822350508391343985371943871062052253656604854487110794376292596221461942865984755780601811<172>
4×10194+1 = 4(0)1931<195> = 721324202162977116296517293557<30> × 230366834312643340988031253121778481<36> × 4539551603725680577678687090612374940158174209<46> × 530269411486144259272416902466941069870793165414892485082648513501276740375531374317<84> (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=2362285868 for P30 / March 26, 2007 2007 年 3 月 26 日) (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=2436293813 for P36 / April 21, 2007 2007 年 4 月 21 日) (Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, sigma=632711195 for P46 x P84 / July 27, 2007 2007 年 7 月 27 日)
4×10195+1 = 4(0)1941<196> = 161971 × 4235420235990630674411<22> × 1782770591401940738293939<25> × 3270625053699212080692362493772858750666560394798793476886954585597967393938023443092469894332061712616542478561422647444539097061183051509475339<145>
4×10196+1 = 4(0)1951<197> = 13 × 17 × 412 × 25889 × 118801 × 553769 × 33209893 × 1013068290246913<16> × 18806089121412281873<20> × 14213662795471783729249<23> × 142851133452691513013398945489<30> × 49208667527925948973221056694552522133283274195899584254244124598255278818709511593<83>
4×10197+1 = 4(0)1961<198> = 7 × 251 × 5093190443767<13> × 1918281337544801<16> × 23301614476086791174193268524783637900374553651086479598676942509371151606132217635609620426691548453826094285457806633452456767854973084897460444026604823399971309779<167>
4×10198+1 = 4(0)1971<199> = 601 × 929931633094791878075356891588302829966299262696914473414281<60> × 7157057364649085307661377430067986943422261055343880321564902746003515911775225750122658781467332419066410898034428685018858357725799521<136> (Wataru Sakai / Msieve for P60 x P136 / 598.43 hours / March 3, 2009 2009 年 3 月 3 日)
4×10199+1 = 4(0)1981<200> = 14092207 × 27329994207449<14> × 103858354572756598961544410066501676256846583840753041387052260431908902185135719697115097666505659907583087248314673208582579183479386989196198354232004355351786310608896508872807<180>
4×10200+1 = 4(0)1991<201> = 31541 × 51001 × 329257 × 1593797 × 18155779891740157<17> × 596998838337353504040649<24> × 173113057012428875682266741<27> × 3955770714637851776058805084888354384537087623653<49> × 63839354599755592537240016160672526653527833995247027347015572381<65>
4×10201+1 = 4(0)2001<202> = 41 × 5121931 × 103849329299<12> × 13503675809573<14> × 587861201947289<15> × 1860750042755447209<19> × 2795453108496978738236562037<28> × 1684776046154235009517333610464790582051<40> × 2636510377862930365366650606354695539107142487471106263373162893880619<70> (Robert Backstrom / GGNFS 0.77.1-20051202-athlon, Msieve-1.38 gnfs for P40 x P70 / 13.15 hours / November 4, 2008 2008 年 11 月 4 日)
4×10202+1 = 4(0)2011<203> = 13 × 53 × 401 × 57046808129<11> × 4352160109233622287476004876885802806219798409446401497170469759529369422418203133<82> × 583123015262945556349244647056353780728267122790222566698427071203798962005200699046348941121122402068437<105> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P82 x P105 / August 24, 2018 2018 年 8 月 24 日)
4×10203+1 = 4(0)2021<204> = 7 × 641 × 3996493212534098134156111341457064136963014957402517508990780184800320983<73> × 22306161491827264164393810143013170259394176192731199083359389215809287265225238597639960484443643575958988629141966737446379681<128> (Wataru Sakai / Msieve for P73 x P128 / 858.79 hours / May 8, 2009 2009 年 5 月 8 日)
4×10204+1 = 4(0)2031<205> = 157 × 977 × 1097 × 117757 × 119929 × 130729 × 14788601 × 112700188358977<15> × 1011168875778642564121<22> × 1145752847230341104854444689755408827131862665943263929<55> × 6668219558002128682158806103505276064352507360154596086811797813918493447153374881817<85>
4×10205+1 = 4(0)2041<206> = 49048739 × 1340576829415582072376659<25> × 608331683217417163805795747590704069377173907054777153930489027864772074508375822311131626385934663449597573367164604502335486269650432180157579535254123979829571693432017001<174>
4×10206+1 = 4(0)2051<207> = 41 × 8489980721<10> × 161526918197<12> × 8620981820393556165598209791935039169<37> × 9614845316674752971125223167274964585506988001<46> × 85827308286463291545643661160043563366431087143222524276657149458595022132599515717888654971338922437<101> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2709458539 for P37 / March 13, 2011 2011 年 3 月 13 日) (Jo Yeong Uk / GMP-ECM 6.3 B1=11000000, sigma=5407201763 for P46 / April 27, 2013 2013 年 4 月 27 日)
4×10207+1 = 4(0)2061<208> = 2137537151086140780378598137246884887064851<43> × 2812726946992196303955780250469663669810710081<46> × 4510386964277796118081223118223701478503227449062032837<55> × 147504388817832250629782059406052001349839987803889705588283463583<66> (Robert Backstrom / GMP-ECM 6.2.1 B1=3628000, sigma=3845259699 for P43, GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs for P46 x P55 x P66 / 101.97 hours, 17.25 hours / January 6, 2009 2009 年 1 月 6 日)
4×10208+1 = 4(0)2071<209> = 13 × 733 × 4513 × 46589 × 218233 × 8623123641424928553601<22> × 275759473220416681288561<24> × 36106110373082818812350759763661<32> × 1060615417762646572618195239987309218160726413<46> × 1004638515256209055038246038744545150819657528797448156508330342617613<70> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=696637667 for P32 / October 31, 2008 2008 年 10 月 31 日)
4×10209+1 = 4(0)2081<210> = 7 × 19 × 3868312352905881234614717303045694938316220300630823137841921435236696906862947702213074172986063797<100> × 777475685161057172420107889087596154100076593781412039785204592057085537200948941303744478811373723078515001<108> (Serge Batalov / Msieve-1.39 snfs for P100 x P108 / 1000.01 hours on Opteron-2.6GHz; Linux x86_64 / February 17, 2009 2009 年 2 月 17 日)
4×10210+1 = 4(0)2091<211> = 5717 × 3771013 × 233278222252612529180268961<27> × 911781382426316231653996553754721<33> × 872305985302314642837664533768067528978848533430533241529384958629887457539688700015453948305990321439785340542663401455101411284361180402201<141> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2914364967 for P33 x P141 / March 13, 2011 2011 年 3 月 13 日)
4×10211+1 = 4(0)2101<212> = 41 × 59 × 148721 × 1332356352410729241381459477648619855405009<43> × [83450977684793282694551706981476556088621921512009377560353348583288515960273808416054497177857020031325682869956011963367750061419815803842510520381026012953211<161>] (Serge Batalov / GMP-ECM 6.2.1 B1=43000000, sigma=1854358772 for P43 / February 17, 2009 2009 年 2 月 17 日) Free to factor
4×10212+1 = 4(0)2111<213> = 17 × 2857 × 2131693 × 70842509 × 663053414577744687381599917<27> × 139893211207942643736922745313159710321<39> × 23474613840481557853118432748582756807946049343049856395181<59> × 25046014308160060753652965557111998610872516551741092521547633774020201<71> (Makoto Kamada / Msieve-1.38 snfs for P39 x P59 / 1.62 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / November 2, 2008 2008 年 11 月 2 日)
4×10213+1 = 4(0)2121<214> = 1091 × 34361 × 4269047 × 2836927429276991352710729<25> × [8810291618252846318741362925342329396537080601641446794149478971401796137928306301441229305771806124478694771112148333660490759809147040407405323752228466732260965957031088877<175>] Free to factor
4×10214+1 = 4(0)2131<215> = 13 × 89 × 997 × 17503955120237<14> × 1485058612125103453932281<25> × 1333987279362861290496004852240598783809970645042807264538099579389277668813962496788930262902451506668191857384961859976223548132387811966426431129896290637992370007605877<172>
4×10215+1 = 4(0)2141<216> = 7 × 23 × 53 × 1297201 × 280709138925610745225627616235368407<36> × [128734342401119972983581009935100049656649334653400039391667634128613012584259319294236788779710630652264467617853270939946120791315424107847649862903165446035555727219771<171>] (Ignacio Santos / GMP-ECM 6.2.3 B1=1000000, sigma=2323201769 for P36 / June 22, 2010 2010 年 6 月 22 日) Free to factor
4×10216+1 = 4(0)2151<217> = 29 × 41 × 1373 × 688512200950880259397<21> × 50573650464010212230513357749<29> × 995113252657683337996926110413<30> × 41833433897402299416847516692008758830906126644136052429<56> × 1690346080592033636898907143447681168419065457194335326431482594037873908193<76> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=2673524017 for P30 / November 1, 2008 2008 年 11 月 1 日)
4×10217+1 = 4(0)2161<218> = 18686807 × 578022421484392833484314349887736849483921909178334750733<57> × 3703225908027418809075172754492065279505406206615636647652312656725745127646139680370212557167658670799266733808441570447351849092965953387204337084674371<154> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs for P57 x P154 / 174.05 hours, 56.83 hours / April 17, 2009 2009 年 4 月 17 日)
4×10218+1 = 4(0)2171<219> = 1049 × 3529 × 108052008673334736208579275462658441387593090182097348916954197563913438455331704809475945056634109696019985299524219992809138822789573305319049217960080725655679848381421429576698152121560670797675044929375856481<213>
4×10219+1 = 4(0)2181<220> = 127 × 277 × 491 × 5081 × 391976229133<12> × 33124455314005419719484291502626516313409725827657409<53> × 73254080393331932260764267211845352077103045721318111077525237<62> × 47918754047887215225543872174584546174623050261093695745230498173472499321834339201<83> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P53 x P62 x P83 / January 4, 2021 2021 年 1 月 4 日)
4×10220+1 = 4(0)2191<221> = 13 × 1181 × 6589057 × 124219769 × 1249376837<10> × 607021466763300821<18> × 444449141043266291533<21> × 42291256679033137134771637121479530755891442059584525827865339970574160993<74> × 223296850841264041346286705754966008069735102697303194855843986237022783354244973<81>
4×10221+1 = 4(0)2201<222> = 7 × 41 × 55493239095428870021395686757<29> × 25115279729838673041822990404411304580037176086385392155823273909673771694393791630240491096085374125051037065829934662353778187686075644790068872620199820114451706178407000835125992731217139<191>
4×10222+1 = 4(0)2211<223> = 6097015972179447612468707229921763686040066157<46> × [656058638890223304734304814532016364046521353594428916682596906758480771159191063541717990626390717402033424938857168466764328812593445093132882486910603381621639064614968488293<177>] (Serge Batalov / GMP-ECM 6.2.1 B1=11000000, sigma=2238052366 for P46 / November 7, 2008 2008 年 11 月 7 日) Free to factor
4×10223+1 = 4(0)2221<224> = 36796872653<11> × 1087048901606556863064837913903682960358560556067373250856900749347493740122437246841211878354460222448730825298921361571286572781237165318077336771872867018887307504469080947469940958626280897382760524021100973317<214>
4×10224+1 = 4(0)2231<225> = 257 × 459834665137<12> × 80139003431254841<17> × 1117554729596171621<19> × 14062325122689483593<20> × 2767593820315607196395314730016666048255527051377982687119041941<64> × 971075360824875755457217544245461262021767508202022480923000915283508183947227086253070744073<93>
4×10225+1 = 4(0)2241<226> = 31237 × 609641 × 3910997 × [53706768769429363793482678416871438245556988417973753812346805832702342873602425939717837859237868760949667888190502096723565700869017553283380850238323411769596938288424660294475642510961192383548068546243249<209>] Free to factor
4×10226+1 = 4(0)2251<227> = 132 × 41 × 797 × 7672476084343263227874361<25> × [944051236095625745605914377984667843452266499332174506062342859837045027395377946743564230504319254831003037392991414235483922896812610601139178907120628322515230507074953238453161918168433330957<195>] Free to factor
4×10227+1 = 4(0)2261<228> = 73 × 19 × 2274638262341070593950100717451021126508724154034353396727<58> × 26983602469312680130580985847029543470319676934990817496724014747605720259827010445557677689524276607304620925751442325052907279775178255048557619638932527039814094539<167> (RSALS + Jeff Gilchrist / ggnfs-lasieve4I14e on the RSALS grid + msieve 1.48 for P58 x P167 / February 24, 2011 2011 年 2 月 24 日)
4×10228+1 = 4(0)2271<229> = 17 × 53 × 2381 × 21089 × 240017 × 249089 × 11728313 × 34665109 × 636573841 × 725488909 × 886678473578749<15> × 16755502705377552397<20> × 1214464431029862275147439736082080827831090257987254979629<58> × 436523024418824031180581936516007205843771593262444864684074629830283990147587370053<84>
4×10229+1 = 4(0)2281<230> = definitely prime number 素数
4×10230+1 = 4(0)2291<231> = 173 × 9152489 × 252624037933692072393129117016709280794603547867019871028519367412710565127633681619505155525156406852192846468232931112518868386764752050324638404041274228144403616182496393190297506216062340695715876578977682142204499933<222>
4×10231+1 = 4(0)2301<232> = 41 × 209929 × 171045796291<12> × 151665385898395010920361713151614617130219<42> × [17914505220645022132194954402500979428459361638158467906590559309010783910561177699484997168919844042329407282181531626843571647207113173504748854176220229117272439835781521<173>] (Jo Yeong Uk / GMP-ECM 6.3 B1=3000000, sigma=6134707835 for P42 / June 22, 2011 2011 年 6 月 22 日) Free to factor
4×10232+1 = 4(0)2311<233> = 13 × 313 × 337 × 251621 × 469541870881<12> × 30014273848957<14> × 534695718389538267842639037229978253206456308162436414822347550938002366555153353<81> × 15384615384615384615384615384615384615384615384615384615383076923076923076923076923076923076923076923076923076923077<116>
4×10233+1 = 4(0)2321<234> = 7 × 12983 × 12618170294693<14> × [348811271163252370210612734963523254646594918249087302660630940511337621609010871181668602767014545497037982893129583986945293766246967995915927305014200045819794612475555563990563745183513376198670997494006657169197<216>] Free to factor
4×10234+1 = 4(0)2331<235> = 101844481261409<15> × 15083067110761453<17> × 166470474810555341081321<24> × 281722440676563078737805904561<30> × 59520510316289955705069974366831129<35> × 932840774605491827367365884272243625937825837089740051536226422913469229092335449597657018460854220557450573143028437<117> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=2491282100 for P30 / November 2, 2008 2008 年 11 月 2 日) (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3553856087 for P35 x P117 / November 21, 2008 2008 年 11 月 21 日)
4×10235+1 = 4(0)2341<236> = 641 × 44263 × 3599263 × 255771973 × 2525595417360720847349418399085176183355724297940127<52> × 606360356715044363553197719386419019822429801044602418979358571249578646327872607361512864562827095184920847571890230832148464068658949833446599287566868039930539<162> (Jo Yeong Uk / GMP-ECM 6.4.4 B1=11000000, sigma=4030962254 for P52 x P162 / October 10, 2013 2013 年 10 月 10 日)
4×10236+1 = 4(0)2351<237> = 41 × 61 × 117544433 × 128559502397<12> × 645204292022947594566560089<27> × 6699286506274141797109815307016926080793<40> × 619463214764350244902246724110519391574061961990845426302616569085969<69> × 3952744382511096329705320980593637243303419285421995417863091081509746384257377<79> (Makoto Kamada / Msieve-1.38 snfs for P40 x P69 / 1.62 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / November 2, 2008 2008 年 11 月 2 日)
4×10237+1 = 4(0)2361<238> = 23 × 727 × 1699 × 4241 × 77962531 × 123866097520553272509520813<27> × 5083970348510261759335252157<28> × [676230413605955129605354486014521738526895649311989696184845947638518215716542400947488253388711090435926834770951019457366341947049456598366448537219021549936677729<165>] Free to factor
4×10238+1 = 4(0)2371<239> = 13 × 11728776877<11> × 286265807209<12> × 44874068978343506281<20> × 11885822804057748455895493<26> × 422911528517671635279241199954086672512819330893<48> × 4749360430317354949216389905325606214784731753082957<52> × 855431189865208976114047930253021465132317651100002178476508620983478733<72> (rkillian / GMP-ECM B1=110000000, sigma=3131248890 for P48 / August 31, 2010 2010 年 8 月 31 日) (Erik Branger / GGNFS, Msieve gnfs for P52 x P72 / September 11, 2010 2010 年 9 月 11 日)
4×10239+1 = 4(0)2381<240> = 7 × 47 × 41893 × 1098613 × 520512077 × [50751290197039174977112551431903899323929494349499256480302322628695135287849225834912975184531171005394421043505550569260012632282440159555947336687305498898507812826687595415993327189298091583773830362544443830680533<218>] Free to factor
4×10240+1 = 4(0)2391<241> = 3797 × 24977 × 275729 × 2471393 × 1295852116961<13> × 59021635048978918237423695747967725983412277880123146182396163677350125724605798633485923954941<95> × 809260202646847344797043610627690537279987440281654920929209559143365705090206211638537456406164458667642094964257<114>
4×10241+1 = 4(0)2401<242> = 41 × 53 × 22911583 × 62061919957<11> × 12945533764740055863423747387655263309689836911130140356964096739723898369118609489119010096253343363419508321485034771592993003974361916798079643431814073169713170812165542478032908785099461498126223933439950573612980127<221>
4×10242+1 = 4(0)2411<243> = definitely prime number 素数
4×10243+1 = 4(0)2421<244> = 167 × 499 × 33461534459<11> × 38246818028611<14> × [37506091803232300246153964037751360052070199287344009701430144095005843908692475793239852205548785338336670134733234023324341872177909170724055033663717297751021566608537985327024606478204000425747591569480230901853<215>] Free to factor
4×10244+1 = 4(0)2431<245> = 13 × 17 × 29 × 494041 × 6360593 × 70110421 × 1063728224989<13> × 12148418471901262420361101<26> × 65410771359361952392693793<26> × 2008466708215711599048187312289<31> × 153439118336387104335313493107209665842195972706444429<54> × 108749211544556029830506369336331342119441820820121702905724110978018201289<75> (Makoto Kamada / Msieve 1.38 for P31 x P54 / 51 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / November 3, 2008 2008 年 11 月 3 日)
4×10245+1 = 4(0)2441<246> = 7 × 19 × 367885532726263369<18> × 947255853369650441723806278949229684129<39> × 252848348718738248054735889573081237056927<42> × 60020541527437240963374051468568365819621167111923661277994930871623<68> × 568680468126153435753728167358980072501665559484793347884252370988739251938957<78> (yoyo@home / ECM B1=43000000, sigma=1774910016 for P39 / January 30, 2010 2010 年 1 月 30 日) (Youcef Lemsafer / msieve 1.52 (SVN 942) GPU for polynomial selection, GGNFS (SVN 440), msieve 1.51 (SVN 845) gnfs for P42 x P68 x P78 / December 19, 2013 2013 年 12 月 19 日)
4×10246+1 = 4(0)2451<247> = 41 × 557 × 1597 × 37372533192409<14> × 8727020049799717<16> × [336277270197571194694599167999489364048869681650509232785741533248676206882399428414702744553461554191510107698912625436480348696350938968554576404701771244631046341141003347894755534981647251532984417755325653<210>] Free to factor
4×10247+1 = 4(0)2461<248> = 251 × 18797 × 85093 × 18313975459545581365621451<26> × [5440280160228364168388954886554154956082230667821654009825515137353304533015851832287889842237427177754937406635211474521081167104083163271414973599848661004051886455901155247175357847137327435058370081960353081<211>] Free to factor
4×10248+1 = 4(0)2471<249> = 317 × 4349 × 25633 × 1115580458177<13> × 234046722213975127327184686613228150778995773714719821<54> × 17613153769512112517578753541630628864236833323216296297<56> × 2461338222207399496484039883032285004259961128085456678539752052171509493196922687274302976705525864295840055350573941<118> (Sinkiti Sibata / Msieve snfs / 6.26 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 3, 2008 2008 年 11 月 3 日)
4×10249+1 = 4(0)2481<250> = 1746449 × 26733795833299<14> × 17677918550311046578053131<26> × 4846322688208438969819911619492873330875712349390199687135598584660142832537401299208570433227770123237467674481232936840180075956293104033604008336872481275509793405168852166511016795506306583658406071521<205>
4×10250+1 = 4(0)2491<251> = 13 × 3646063837616479765543282237<28> × 609367039316849421092272000364917<33> × [1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213<190>] (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=3159199225 for P33 / November 2, 2008 2008 年 11 月 2 日) (Wataru Sakai / GMP-ECM 6.2.1 B1=1000000, sigma=1542610798 for P28 / February 17, 2009 2009 年 2 月 17 日) Free to factor
4×10251+1 = 4(0)2501<252> = 7 × 41 × 19087 × 97609247263201<14> × [748082434748235860636239907642765083824788407055672659789624670604847770974862363513254565669203926168070605695617394268245916336696424334921604552572906070388233659037980699576334071346025098331432910350184701172971776967267525329<231>] Free to factor
4×10252+1 = 4(0)2511<253> = 397 × 7873 × 1440350573<10> × 2229047435261<13> × 36932628930437<14> × 107736255909559973<18> × 4123529909623015354083772655568051493609117858463711973469746114474124049290479911005579086149<94> × 24294080290431977484205856648128532855996752201593191404216725955719772300601271009843048129492066193<101>
4×10253+1 = 4(0)2521<254> = [40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<254>] Free to factor
4×10254+1 = 4(0)2531<255> = 53 × 387613 × 2607686673217004431453<22> × [7466728841485330116984362247807564055023379096637179913082368836295817176172476677041898711213023371963056286003054821025139078482163020837938497429137548907465615316057420651494358127038086352740157428245984413332304773796853<226>] Free to factor
4×10255+1 = 4(0)2541<256> = 6910973 × 815687281 × 48399152768807<14> × 713830174307666346787995247<27> × [20538297635356765652238220182543936034577038799560625017387112066600521600882087601795534974873462854867943848322502036209998347369601234466062167208720013993884935951189052517259867725801951568462813<200>] Free to factor
4×10256+1 = 4(0)2551<257> = 13 × 41 × 56197 × 567673 × 636553 × 7236234233<10> × 11534976517911799708073<23> × 4495452939128488386198992617835818205788246431269172596631251681228090482467453931182248215133<94> × 9848816726749033144940215248526050592330418607879728226701614448726504415289878465342152418428945565845544022157<112>
4×10257+1 = 4(0)2561<258> = 7 × 2557 × 160108014481<12> × 3848854942278832550475727<25> × [36264910333774066742885924834337095350499210417844182233379270797957539981698262682595152756504796676576346470134447930646971316977327675074019033861202447253032690208938150379348632163522220810399149402609962232119677<218>] Free to factor
4×10258+1 = 4(0)2571<259> = 89 × 152293 × 642345877 × 244145848153049<15> × [1881792610048936211778560849374308188440394585353865981060170928658490962932711290162010901371451294789909399077374198872533427266598503830447227210191574274708627532392161408569868918740101605690938045548988994147766449450025481<229>] Free to factor
4×10259+1 = 4(0)2581<260> = 23 × 3637 × 8097242180181481<16> × 81410585994660916003585960425437<32> × 725388798130252110871375368116262668325425260837498032426546343485831652844577394553417305385243340386900982885266262381044566518564567503629549190842682837940215938492339820511156124916258771582204891269583<207> (Serge Batalov / GMP-ECM B1=1000000, sigma=919186755 for P32 x P207 / November 27, 2013 2013 年 11 月 27 日)
4×10260+1 = 4(0)2591<261> = 17 × 97 × 4933 × 42841 × 488701 × 78124583041<11> × 21390872183292097<17> × 7415130526556777411200086328720558894888565818630568766776924866568141804792415130673422278868807200611629<106> × 189535422417303108316011451292600116581176240973405414634492639882722966871523215270608698695295930586005335501<111>
4×10261+1 = 4(0)2601<262> = 41 × 127 × 18383122529<11> × 1039937452221173925706321<25> × [40183328948972108128642045951367163089457837040801098562482396955496611432071442825034714169444597192873970262777510366317183675706791607969254805304710150153521812300145319159931912433629573383048445714461437097196506949527<224>] Free to factor
4×10262+1 = 4(0)2611<263> = 13 × 289853 × 128279634944813161<18> × 16771583128304592797678664819251569961<38> × 4934089976064961835172872410841383821855530477560066127435849435959653407843398088277016817346059409515839781777584342352023183696451906339105075076366279388564740838712830459651768164273507654869331929<202> (Erik Branger / GMP-ECM B1=3e6, sigma=3:1906561011 for P38 x P202 / March 6, 2019 2019 年 3 月 6 日)
4×10263+1 = 4(0)2621<264> = 7 × 19 × 5443384022330201<16> × 552509024653569108513998872114125160915674700625221569419224416709485627649444927083817427320125090868326867767277727613695510471142159982516771005639656244272964299780872580833919180074129270261054796539454301541299313770069044335930271246629397<246>
4×10264+1 = 4(0)2631<265> = 35048935969<11> × 2235989233064513<16> × 280589003276980409509108055820930763237<39> × 5569664199018945342012125025897799237592789<43> × 1279765320779697626573449003825710054785721776540857<52> × 25520280863145368368504594177961197432182783462011204471092682007131932251045685899925721913155021264662433<107>
4×10265+1 = 4(0)2641<266> = 37369 × 97068877 × 263340401 × 12331625189138490383<20> × 22669096879101237479561714908776488303<38> × 36286514649400413375353684983915170059<38> × [4128109672535034952586344929366336911092207999595657729039803975618608045667873033780843205420508762689611736294110869837975384821029902852304577673047<151>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:3172490337 for P38(2266...), B1=3e6, sigma=3:429851317 for P38(3628...) / March 6, 2019 2019 年 3 月 6 日) Free to factor
4×10266+1 = 4(0)2651<267> = 41 × 23117 × [422031299951360892680605657118560198017085937178530845740174320028444909616721724166672821289790957346351592165832979002887749169917186908167044208833748154931910525144097311977142784794634294052418397610458779675394625642410769394712158827259423695158351419133<261>] Free to factor
4×10267+1 = 4(0)2661<268> = 53 × 641 × [117740558678950931622170547199246460424454714037618108497924822653283489830159244105613281135018985665086980837724075000735878491743443322638565919995290377652841962735113178112030141583021811438495275660083007093868660406793630235775468754599240573396520766491037<264>] Free to factor
4×10268+1 = 4(0)2671<269> = 13 × 3061 × 14929 × 78536606591077<14> × 100850137683037<15> × 5266926956928268901<19> × 12767813141635680191944316804737<32> × 12371453300851625336100226233553526689108901804677286873855739571109<68> × 10218318371920206805579751893993221448173825615249815786989174291060065485602328710741503398367904444958891886430649<116>
4×10269+1 = 4(0)2681<270> = 72 × 59 × 733 × 7181388860306826803303<22> × 1585861878247104125347783<25> × [16574259028808339503068451099871401604563230231839929782385029261365562321881910022253382052755329137951863469510745887712484397688660811982712641330141031752083545824134455258302540738055502765760561678448729733819983<218>] Free to factor
4×10270+1 = 4(0)2691<271> = 52769 × 75802080767117057363224620515833159620231575356743542610244651215675870302639807462714851522674297409463889783774564611798593871401769978585912183289431294889044704277132407284579961719949212605886031571566639504254391783054444844510981826451136083685497166897231329<266>
4×10271+1 = 4(0)2701<272> = 41 × 367 × 13729 × 189381313715615047766317318174129<33> × 3655756502102286109090975386197287<34> × [279677017327787744394644704056047045735121471323422340148759796517143739396402030389817713433414433069137467277612893793134280386172641789401522248897574460413210846591946014472058873731698029732449<198>] (Serge Batalov / GMP-ECM B1=250000, sigma=759012371 for P33, B1=250000, sigma=2497093279 for P34 / November 27, 2013 2013 年 11 月 27 日) Free to factor
4×10272+1 = 4(0)2711<273> = 292 × 3433 × 74653 × 35708317 × 1698112589189<13> × 11850603968626079117<20> × 62183941073792717542202469302909<32> × 315599474712830161124206807761437<33> × 661475750626788107893439102829883013<36> × 6164854975815183097666014881068023584333<40> × 32271211666552094737122815939006017043088192288221182216646347142623059150865531937<83>
4×10273+1 = 4(0)2721<274> = 173 × 12451 × 1288307886175860392792933<25> × 1441418161678896893493857172377103306352283780431015946697487157534855826403524711056830021234133782100320162817694821241236796097238561715491571144359345081405642796747461586761799614245011969891117979236169526224795464461857500236767938692939<244>
4×10274+1 = 4(0)2731<275> = 13 × 532093 × 715603287401<12> × 5922749794417694932693<22> × 100274288355343656837519241<27> × [13606417465634688667549332261596475546978742902713155780329346404934902645990546406812687107259324943527716622610970572684449567201278860646559719550283852521557938579469839008246155610400020288919531230000853<209>] Free to factor
4×10275+1 = 4(0)2741<276> = 7 × 171571 × 492668023 × 27446064450241<14> × 10001505067626639916691720388310823<35> × [2462738249623729529748167328626922839102801659363945760480812120380760632389672140446215177796223813370146637311704472051633807172510779591705589996803280506932170652032930969419742054936783902516708521393449577997<214>] Free to factor
4×10276+1 = 4(0)2751<277> = 17 × 41 × 5501 × 12241 × 344017 × 16878015685697<14> × 9225143708641590768727961<25> × 12097303041886415984718313<26> × 620740454339818647293247359897<30> × 1801003494791934182340101632949<31> × 57869656388325167891975686425478902773366341<44> × 2032966258414901380215871246281700628420911131551246082920311811702353824931709633497484499133<94> (factordb.com / for P44 x P94 / November 4, 2018 2018 年 11 月 4 日)
4×10277+1 = 4(0)2761<278> = 56194022545928357<17> × 1233632769306687811<19> × 1090510378744645875651911413<28> × 2328166517499983251079549080367<31> × 227268963047031105173024020971687631847864491481060532547063283946459654482599072726342127222612481191722884798630860744663272758086399405993808116904588395019284838079679866652412616253<186> (Serge Batalov / GMP-ECM B1=1000000, sigma=362282003 for P31 x P186 / November 27, 2013 2013 年 11 月 27 日)
4×10278+1 = 4(0)2771<279> = 3490649 × 2484333961693<13> × 64474936410618841841<20> × 40274146453655187523428236604117435493<38> × [17763419274212574169838493142338316955144535174758435121926889697125158328538126254507187490217543416269077745788072798632472135676277734189368059913722934154198196182838884045155777049496534067820655561<203>] (Serge Batalov / GMP-ECM B1=1000000, sigma=154634166 for P38 / November 27, 2013 2013 年 11 月 27 日) Free to factor
4×10279+1 = 4(0)2781<280> = 2213 × 10979 × 1002272099<10> × [164259369535554655124966328110762456538337380334388604378014410089089345077296833936665725122874028348781558534292732492281437836702364831538793045692915277678852184096999759181237622941617837947029929313431651802149847771300146536121344202657752377545922402983237<264>] Free to factor
4×10280+1 = 4(0)2791<281> = 13 × 53 × 271849 × 8919598277<10> × 2309302597109<13> × 714128437261677325177<21> × 1504018110618546143321<22> × 30564237166768160426582113<26> × 1811031061904134150062610843708191514800845797<46> × 2162709952694504347158542345232572892025005576782353<52> × 80634288543440300713293881031152543052448889730728931852602606148669415329811293080717<86>
4×10281+1 = 4(0)2801<282> = 7 × 19 × 23 × 41 × 3863 × 2675927333<10> × 11669206405189547743<20> × 2465234757970043033291561339<28> × 10725018001300738202791306438049748373532600387310492243305742926875239988360630766558585289475227606175682357617110559054602790865430406305993417521525398156831914182259133441817423204870735187238775298416961880100413<218>
4×10282+1 = 4(0)2811<283> = 157 × 197 × 5197 × 208108037 × 21033953009<11> × 10112145472508235274502494889<29> × 216521744102273452990658880630790769<36> × 9620203854347185964736756802042689725737517<43> × [269899788054728606000872655481575029871760618690743422264687864265038524440282868429951990577681503059457743412818278047197564058645830865868101813677<150>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:915599978 for P36, B1=3e6, sigma=3:278019505 for P43 / March 6, 2019 2019 年 3 月 6 日) Free to factor
4×10283+1 = 4(0)2821<284> = 773 × [51746442432082794307891332470892626131953428201811125485122897800776196636481241914618369987063389391979301423027166882276843467011642949547218628719275549805950840879689521345407503234152652005174644243208279430789133247089262613195342820181112548512289780077619663648124191461837<281>] Free to factor
4×10284+1 = 4(0)2831<285> = 149 × 13829 × 41953 × 552886825287361670007498565355401<33> × 4132595417977996777449857169255008317144899432636201910123386508141<67> × 774208286515906125959068168479724621487305659143982683250058150798513<69> × 2615790617935131496085392114470830970913615481023665508135880079372565794706648319187165386818369138757669<106> (Serge Batalov / GMP-ECM B1=1000000, sigma=1822623960 for P33 / November 27, 2013 2013 年 11 月 27 日) (Erik Branger / Msieve v. 1.52 snfs for P67 x P69 / March 6, 2019 2019 年 3 月 6 日)
4×10285+1 = 4(0)2841<286> = 47 × 5167 × 256169 × 91252673417602728960491923091<29> × [704614379948494812027446383843039780948014414557892751098695471426612268652074620711407471026057218082430931345744692465286573876751870294678130116897853322618827616949896573798301616584098199881960344035605507134097664069602871941750044472168131<246>] Free to factor
4×10286+1 = 4(0)2851<287> = 13 × 41 × 52650548792889125968538921<26> × [1425377437382621879305881390086756267584009864371504172063418337715271471432367376756595541546445135577723564668218504397395230982700631791914133299267013106042483046184519626581979926754868805387027518335743066620835703194913852951295297296159865024537312757<259>] Free to factor
4×10287+1 = 4(0)2861<288> = 7 × 1637 × 26815239758938131779<20> × [1301761993056211582996867096099088523695235942689119275028543525723482807181421611605045798675333039288340382274545046258365559021396933887963309035894035920263158437022580007471516641032852456854443495500894696042403697194694545705069263880222429522876081138602041<265>] Free to factor
4×10288+1 = 4(0)2871<289> = 113 × 229 × 277 × 1657 × 14293 × 65213 × 5271517 × 15302761 × 1886906334739118018852657<25> × 10207457384959441989237717990428744617<38> × 9407401310817350002993634519379334667282511144625585322436433701410667609178583633<82> × 24719701314925605069747954139456168794795797910577570884844761091118247639761717429283834132512396508009485621237<113> (Erik Branger / Msieve v. 1.52 snfs for P38 x P82 / March 6, 2019 2019 年 3 月 6 日)
4×10289+1 = 4(0)2881<290> = 131 × 11610689 × [26298483358772393213642444225251114832321668920899243581259640009042233831730070731039895240412316063911991746741707819788083283949000300597581949524178220406207044570924034273948141385556463603468722354767199286847721700486574341865381628445863400737264437244254275961960897996139<281>] Free to factor
4×10290+1 = 4(0)2891<291> = 8792662477167137854990975723601<31> × [45492477510506455539754565259717139989257193597263860980416707653912565470148907541858180539760335453591566221728892352199856638664830790858574074624226113596782665550153140364805106121096602444427298876862593240165337011653729152221982499328774962273965236401<260>] Free to factor
4×10291+1 = 4(0)2901<292> = 41 × 4423 × 1080667649<10> × 55674882737557<14> × [366612892628810219783149043538657886788360105866128804663771988384986986299805157269985584632436691436396971709590063055738175508390657269556418407425935113107414348158332279497437057010638715964264478577387852136711386318193095172379474417957872690837379758188899<264>] Free to factor
4×10292+1 = 4(0)2911<293> = 13 × 17 × 2909 × 275729323690614099269934539131273<33> × 372111967394961909592835612503935795821<39> × 114663311787537402408686873721585791834042270457596128922919667261557719341<75> × 5288626808049290001851019382817251500647856783986038025226749874395113309358225136843218658275378797895126530396382579263294285638733902742153<142> (Serge Batalov / GMP-ECM B1=1000000, sigma=159599806 for P33 / November 27, 2013 2013 年 11 月 27 日) (factordb.com / for P39 x P75 / November 4, 2018 2018 年 11 月 4 日)
4×10293+1 = 4(0)2921<294> = 7 × 53 × 249971 × 15344237651<11> × [281093716696348505238023724718722466640598795377087970236962313417790593371243467181354449864550894581311254266586444130889236064647917418779959091378658051665500627917706140019154475617767355729413071690839318990001269841190120027627305387553158575962554014782093208226730211<276>] Free to factor
4×10294+1 = 4(0)2931<295> = 3519201209<10> × 689108590736380377835026441378001<33> × [1649408503008445059736945534726388599840251956186358805152902050048600066984901299056970106704782038236283617077735287829377270118390244493120488742982162579391234550102842435980261250113589514802948363337564759003618144443289066633304536818982756421689<253>] (Serge Batalov / GMP-ECM B1=1000000, sigma=2114117975 for P33 / November 27, 2013 2013 年 11 月 27 日) Free to factor
4×10295+1 = 4(0)2941<296> = 18371 × 7755544660931<13> × 1936547144327633503265767<25> × [144972896794635063476587324438000561472413049324255211909049170559537467408378462401566128538063833151652194485466528237194192093803401046529206817021615969499989960780450865822910891095505283090127794731988461728685192138264679238736194607128583824727903<255>] Free to factor
4×10296+1 = 4(0)2951<297> = 41 × 61 × 90793 × 17541905910541<14> × 1695502704314699670140875957239256050263283775495561<52> × 1938182199627468010237847883805414752917615172119009<52> × 106212692004607024538255608482366521391196698270737751314649713434169857095073<78> × 287705160721607300148523107064786015650118069448204602830522292834862744860460363438654328682001<96> (Erik Branger / Msieve v. 1.52 snfs for P52(1938...) x P78, Msieve v. 1.52 snfs for P52(1695...) x P96 / March 6, 2019 2019 年 3 月 6 日)
4×10297+1 = 4(0)2961<298> = 223 × 251 × 1051 × [67995268141294779155023822737151898862206280202754410117845489014573986781685875698224284873791347986302285237668025444441295885778012822309682646874921327349908392525055788842598654717019587889859156811418336586538606191856502514133538932892121104400223684033604417434986281869658408601687<290>] Free to factor
4×10298+1 = 4(0)2971<299> = 13 × 36958243081<11> × 230397432662477<15> × 2327857246449601083411853<25> × 25737694866504896208683249<26> × 6031171723243168960225265172087413591533155200793998355527599764365401988347155576176202692864731363396999097814628688075513459770352909686482533638687827352001327371502087781943501327144304461521425662528278973440224870693<223>
4×10299+1 = 4(0)2981<300> = 7 × 19 × 179 × 641 × 87877 × 338161 × 113277997909627531<18> × 8041825126081566720192211<25> × [968274197454224509976186833586434206705553758604611371080659121145842739685506803350889153564264928339855058793395096193675077025512908201717498909233237741011238368159142021039273036303189781058779808196209956812989201250100637772973814899<240>] Free to factor
4×10300+1 = 4(0)2991<301> = 29 × 109 × 569 × 27809 × 754373 × 4837213 × 1394518166441<13> × 55664430167317<14> × 8096547123326928430753<22> × 565816508635546421110971650045577892613<39> × 2010472718584962847333672313792242435240818902443265532497926289<64> × 30653559987029968722483384463576994151309325841460559042449393971528915456614014825719351580905808702942026001315693262450310017<128>
plain text versionプレーンテキスト版

4. Related links 関連リンク