Table of contents 目次

  1. About 399...997 399...997 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 399...997 399...997 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 399...997 399...997 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 399...997 399...997 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

39w7 = { 37, 397, 3997, 39997, 399997, 3999997, 39999997, 399999997, 3999999997, 39999999997, … }

1.3. General term 一般項

4×10n-3 (1≤n)

2. Prime numbers of the form 399...997 399...997 の形の素数

2.1. Last updated 最終更新日

October 15, 2015 2015 年 10 月 15 日

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

  1. 4×101-3 = 37 is prime. は素数です。 (Makoto Kamada / December 1, 2004 2004 年 12 月 1 日)
  2. 4×102-3 = 397 is prime. は素数です。 (Makoto Kamada / December 1, 2004 2004 年 12 月 1 日)
  3. 4×1014-3 = 3(9)137<15> is prime. は素数です。 (Makoto Kamada / December 1, 2004 2004 年 12 月 1 日)
  4. 4×1020-3 = 3(9)197<21> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 1, 2004 2004 年 12 月 1 日)
  5. 4×1030-3 = 3(9)297<31> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 1, 2004 2004 年 12 月 1 日)
  6. 4×1044-3 = 3(9)437<45> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 1, 2004 2004 年 12 月 1 日)
  7. 4×1066-3 = 3(9)657<67> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 1, 2004 2004 年 12 月 1 日)
  8. 4×10260-3 = 3(9)2597<261> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Makoto Kamada / PFGW / January 1, 2005 2005 年 1 月 1 日)
  9. 4×10872-3 = 3(9)8717<873> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Makoto Kamada / PFGW / January 1, 2005 2005 年 1 月 1 日)
  10. 4×108846-3 = 3(9)88457<8847> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 31, 2004 2004 年 12 月 31 日)
  11. 4×1026744-3 = 3(9)267437<26745> is PRP. はおそらく素数です。 (Erik Branger / PFGW / June 10, 2010 2010 年 6 月 10 日)
  12. 4×1057506-3 = 3(9)575057<57507> is PRP. はおそらく素数です。 (Serge Batalov / October 12, 2010 2010 年 10 月 12 日)
  13. 4×1098472-3 = 3(9)984717<98473> is PRP. はおそらく素数です。 (Erik Branger / srsieve, PFGW / November 22, 2013 2013 年 11 月 22 日)
  14. 4×10106892-3 = 3(9)1068917<106893> is PRP. はおそらく素数です。 (Bob Price / October 15, 2015 2015 年 10 月 15 日)

2.3. Range of search 捜索範囲

  1. n≤60000 / Completed 終了 / Serge Batalov / October 12, 2010 2010 年 10 月 12 日
  2. n≤100000 / Completed 終了 / Erik Branger / November 22, 2013 2013 年 11 月 22 日
  3. n≤200000 / Completed 終了 / Bob Price / October 15, 2015 2015 年 10 月 15 日

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

  1. 4×103k+1-3 = 37×(4×101-337+36×10×103-19×37×k-1Σm=0103m)
  2. 4×106k+3-3 = 7×(4×103-37+36×103×106-19×7×k-1Σm=0106m)
  3. 4×106k+5-3 = 13×(4×105-313+36×105×106-19×13×k-1Σm=0106m)
  4. 4×1016k+7-3 = 17×(4×107-317+36×107×1016-19×17×k-1Σm=01016m)
  5. 4×1018k+7-3 = 19×(4×107-319+36×107×1018-19×19×k-1Σm=01018m)
  6. 4×1022k+4-3 = 23×(4×104-323+36×104×1022-19×23×k-1Σm=01022m)
  7. 4×1028k+5-3 = 29×(4×105-329+36×105×1028-19×29×k-1Σm=01028m)
  8. 4×1035k+21-3 = 71×(4×1021-371+36×1021×1035-19×71×k-1Σm=01035m)
  9. 4×1041k+23-3 = 83×(4×1023-383+36×1023×1041-19×83×k-1Σm=01041m)
  10. 4×1046k+4-3 = 47×(4×104-347+36×104×1046-19×47×k-1Σm=01046m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 13.11%. 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 13.11% です。

3. Factor table of 399...997 399...997 の素因数分解表

3.1. Last updated 最終更新日

May 20, 2017 2017 年 5 月 20 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=191, 193, 199, 202, 203, 209, 211, 213, 214, 217, 219, 226, 227, 228, 229, 230, 233, 234, 236, 238, 239, 241, 242, 244, 245, 247, 249, 250 (28/250)

3.4. Factor table 素因数分解表

4×101-3 = 37 = definitely prime number 素数
4×102-3 = 397 = definitely prime number 素数
4×103-3 = 3997 = 7 × 571
4×104-3 = 39997 = 23 × 37 × 47
4×105-3 = 399997 = 13 × 29 × 1061
4×106-3 = 3999997 = 877 × 4561
4×107-3 = 39999997 = 17 × 19 × 37 × 3347
4×108-3 = 399999997 = 61 × 587 × 11171
4×109-3 = 3999999997<10> = 72 × 81632653
4×1010-3 = 39999999997<11> = 37 × 9923 × 108947
4×1011-3 = 399999999997<12> = 13 × 30769230769<11>
4×1012-3 = 3999999999997<13> = 3877 × 1031725561<10>
4×1013-3 = 39999999999997<14> = 37 × 1081081081081<13>
4×1014-3 = 399999999999997<15> = definitely prime number 素数
4×1015-3 = 3999999999999997<16> = 7 × 571428571428571<15>
4×1016-3 = 39999999999999997<17> = 37 × 1081081081081081<16>
4×1017-3 = 399999999999999997<18> = 13 × 3259 × 320011 × 29503081
4×1018-3 = 3999999999999999997<19> = 421 × 9501187648456057<16>
4×1019-3 = 39999999999999999997<20> = 37 × 1081081081081081081<19>
4×1020-3 = 399999999999999999997<21> = definitely prime number 素数
4×1021-3 = 3999999999999999999997<22> = 7 × 71 × 461 × 719 × 116159 × 209035921
4×1022-3 = 39999999999999999999997<23> = 37 × 97 × 11145165784341042073<20>
4×1023-3 = 399999999999999999999997<24> = 13 × 17 × 83 × 1301 × 7229 × 2318644165051<13>
4×1024-3 = 3999999999999999999999997<25> = 18743 × 213413007522808515179<21>
4×1025-3 = 39999999999999999999999997<26> = 19 × 37 × 72302177 × 786961148727587<15>
4×1026-3 = 399999999999999999999999997<27> = 23 × 2574207258361<13> × 6755984504099<13>
4×1027-3 = 3999999999999999999999999997<28> = 7 × 379 × 251429 × 68610847 × 87400635923<11>
4×1028-3 = 39999999999999999999999999997<29> = 37 × 734625688717<12> × 1471608055211293<16>
4×1029-3 = 399999999999999999999999999997<30> = 13 × 139 × 149 × 59126773 × 25126465043217323<17>
4×1030-3 = 3999999999999999999999999999997<31> = definitely prime number 素数
4×1031-3 = 39999999999999999999999999999997<32> = 37 × 6007 × 14322235957<11> × 12565790388439219<17>
4×1032-3 = 399999999999999999999999999999997<33> = 7691 × 128660797 × 404232234804635319011<21>
4×1033-3 = 3999999999999999999999999999999997<34> = 7 × 29 × 10067 × 1957329243820099911871250797<28>
4×1034-3 = 39999999999999999999999999999999997<35> = 37 × 8001239557<10> × 135114199916096960460133<24>
4×1035-3 = 399999999999999999999999999999999997<36> = 13 × 7457520359<10> × 4125933190661339665645991<25>
4×1036-3 = 3999999999999999999999999999999999997<37> = 43768477 × 75951361 × 1203269742197959442401<22>
4×1037-3 = 39999999999999999999999999999999999997<38> = 37 × 56995623551<11> × 18967791099148581733201031<26>
4×1038-3 = 399999999999999999999999999999999999997<39> = 6705317705327<13> × 59654145795690242290288211<26>
4×1039-3 = 3999999999999999999999999999999999999997<40> = 7 × 17 × 14197 × 16249 × 145710151224443707745495715671<30>
4×1040-3 = 39999999999999999999999999999999999999997<41> = 37 × 59 × 112967 × 3548593 × 45708657774110282863780189<26>
4×1041-3 = 399999999999999999999999999999999999999997<42> = 13 × 76649773 × 738937005361<12> × 543248267276036334373<21>
4×1042-3 = 3999999999999999999999999999999999999999997<43> = 337 × 383 × 83089 × 124477846643<12> × 2996371913431622738641<22>
4×1043-3 = 39999999999999999999999999999999999999999997<44> = 19 × 37 × 1181 × 1641217933<10> × 29355434641183427376160862363<29>
4×1044-3 = 399999999999999999999999999999999999999999997<45> = definitely prime number 素数
4×1045-3 = 3999999999999999999999999999999999999999999997<46> = 7 × 177019 × 3228063492780839506332250049026214296609<40>
4×1046-3 = 39999999999999999999999999999999999999999999997<47> = 37 × 313763 × 269797056541<12> × 12770836099780604453369576207<29>
4×1047-3 = 399999999999999999999999999999999999999999999997<48> = 13 × 2039 × 236471 × 23122795810801<14> × 2759822691958645263754801<25>
4×1048-3 = 3999999999999999999999999999999999999999999999997<49> = 23 × 224221 × 775632271188964769424886122639484375178759<42>
4×1049-3 = 39999999999999999999999999999999999999999999999997<50> = 37 × 599 × 19937 × 507803 × 961447 × 1196809 × 883509323 × 175353743605801<15>
4×1050-3 = 399999999999999999999999999999999999999999999999997<51> = 47 × 107 × 3158894269<10> × 695062569516198683<18> × 36225915040902452759<20>
4×1051-3 = 3(9)507<52> = 73 × 1712231 × 365583782023<12> × 1223144565046787<16> × 15231364254750409<17>
4×1052-3 = 3(9)517<53> = 37 × 349 × 63611 × 48696821736066944192856711185905749982289879<44>
4×1053-3 = 3(9)527<54> = 13 × 563 × 4508792797<10> × 669472970417<12> × 18105683287427638416198479287<29>
4×1054-3 = 3(9)537<55> = 863 × 25467289 × 157554227 × 3055001722088447<16> × 378115917576621876359<21>
4×1055-3 = 3(9)547<56> = 17 × 37 × 420593 × 151198438322738033468583234383090356749955851001<48>
4×1056-3 = 3(9)557<57> = 71 × 5633802816901408450704225352112676056338028169014084507<55>
4×1057-3 = 3(9)567<58> = 7 × 409 × 2753 × 1146529 × 12376910245691721880459<23> × 35763099107325055511993<23>
4×1058-3 = 3(9)577<59> = 37 × 109 × 281243 × 331739 × 287299967 × 101187915779<12> × 3656699644528751425137769<25>
4×1059-3 = 3(9)587<60> = 133 × 61129 × 2978397393312558167635716801555926711856053637005569<52>
4×1060-3 = 3(9)597<61> = 263 × 15209125475285171102661596958174904942965779467680608365019<59>
4×1061-3 = 3(9)607<62> = 19 × 29 × 37 × 23679727 × 82857147378059634428915391994675765821494951425553<50>
4×1062-3 = 3(9)617<63> = 31019 × 1928020865944930366655737<25> × 6688372750335340542004886694101999<34>
4×1063-3 = 3(9)627<64> = 7 × 63617 × 13485847 × 666055682666603755472599972034617812070244224180829<51>
4×1064-3 = 3(9)637<65> = 372 × 83 × 57589102432614935641957<23> × 6112771207054354650743708302111740923<37>
4×1065-3 = 3(9)647<66> = 13 × 99923 × 230648900888767<15> × 1335056929185551706854703176046879744751604309<46>
4×1066-3 = 3(9)657<67> = definitely prime number 素数
4×1067-3 = 3(9)667<68> = 37 × 191 × 1415618041<10> × 10940708399419<14> × 58875874683341<14> × 6207203675131402027653811969<28>
4×1068-3 = 3(9)677<69> = 61 × 569579 × 88515543443042011728726261263<29> × 130063862618281028427596700228301<33>
4×1069-3 = 3(9)687<70> = 7 × 2273 × 7433 × 1332905843<10> × 3367765494651823697<19> × 7534545642533328603766948389242689<34>
4×1070-3 = 3(9)697<71> = 23 × 37 × 157 × 768086840734739302416981743<27> × 389780810398725679736203279568532210997<39>
4×1071-3 = 3(9)707<72> = 13 × 17 × 164503 × 41114887589<11> × 4238704531469<13> × 39726560840077<14> × 1589207750248369442795488067<28>
4×1072-3 = 3(9)717<73> = 1871 × 352249 × 7937923381<10> × 764591617363845499559430105617469241549817083707736703<54>
4×1073-3 = 3(9)727<74> = 37 × 191642603 × 5641131273306077360476475479103574277171976635493106306227123627<64>
4×1074-3 = 3(9)737<75> = 887 × 5818166017<10> × 77508665968084189450350108656196230399506673811394627688166443<62>
4×1075-3 = 3(9)747<76> = 7 × 139 × 7726686743381<13> × 9036423408841<13> × 58878572728877462066045607624530463840165751109<47>
4×1076-3 = 3(9)757<77> = 37 × 743 × 5399 × 42061 × 137339 × 25577923321<11> × 977748778821013<15> × 1865477812668383714076620421802499<34>
4×1077-3 = 3(9)767<78> = 13 × 769 × 1348433033<10> × 1126224201967<13> × 92953364318788711024865861<26> × 283446401156340646460449531<27>
4×1078-3 = 3(9)777<79> = 50437103867<11> × 1521127036549<13> × 13090461671569<14> × 3982808278910696696660173074075777388939211<43>
4×1079-3 = 3(9)787<80> = 19 × 37 × 227 × 52511 × 531911 × 8974071977520504950755520570729598098378818487395511043825409097<64>
4×1080-3 = 3(9)797<81> = 5197 × 76967481239176447950740812006927073311525880315566673080623436598037329228401<77>
4×1081-3 = 3(9)807<82> = 7 × 429905104616648636805590262383317<33> × 1329196990899005274632571941765421472685842778863<49> (Makoto Kamada / GGNFS-0.70.1 / 0.10 hours)
4×1082-3 = 3(9)817<83> = 37 × 633467 × 5241938701<10> × 1003652010395997243385322927<28> × 324383813275946232168533221548185192809<39>
4×1083-3 = 3(9)827<84> = 13 × 1217 × 373207 × 183976723015651<15> × 8846057746959262692797989609<28> × 41625899446727682833390747912789<32>
4×1084-3 = 3(9)837<85> = 179 × 158227151710674945961<21> × 792416934593347412708017<24> × 178226468532273799274347390024249500839<39>
4×1085-3 = 3(9)847<86> = 37 × 29533183 × 440937489718490753<18> × 174841541251458548887919<24> × 474817108846565879364016232851645801<36>
4×1086-3 = 3(9)857<87> = 560339210063<12> × 2910108578133699757<19> × 3642526031595563862021289247<28> × 67343722759316479132676732161<29>
4×1087-3 = 3(9)867<88> = 7 × 17 × 113 × 1280657711<10> × 55962298748000034563<20> × 78104884470835008608189<23> × 53140762018860756693674449807763<32>
4×1088-3 = 3(9)877<89> = 37 × 461207 × 6728331699190450053997565437<28> × 348381418796454801769166303174587285261448294500404059<54>
4×1089-3 = 3(9)887<90> = 13 × 29 × 1710869 × 324955316673864286283<21> × 1908438797586984042356044773489236108979558272581057658434643<61>
4×1090-3 = 3(9)897<91> = 131 × 431 × 2426113 × 10924821030849421<17> × 2672920669806563436754652416058026090451436381625756575519466549<64>
4×1091-3 = 3(9)907<92> = 37 × 71 × 3665437631<10> × 17180051279<11> × 249015549073968083492209<24> × 971008792185667352545631164503912057426826271<45>
4×1092-3 = 3(9)917<93> = 23 × 1810187576877208871526409130255399557519619771<46> × 9607459784818641358549254154895258208490637809<46> (Makoto Kamada / GGNFS-0.70.5 / 0.22 hours)
4×1093-3 = 3(9)927<94> = 72 × 35831 × 2767423 × 823245634274008525366411254013971628940977727133219629071348351396185404307343781<81>
4×1094-3 = 3(9)937<95> = 37 × 4283399 × 9314954709392626979<19> × 6090576055816710482744217264577<31> × 4448674370532002675127154685511443893<37>
4×1095-3 = 3(9)947<96> = 13 × 634927 × 48461052639485750693810833007937556964452969820516010865452612299100163059326868709679647<89>
4×1096-3 = 3(9)957<97> = 47 × 325471808524526296145231<24> × 261486189432317965368156135630370874289986748336642007592130012248401021<72>
4×1097-3 = 3(9)967<98> = 19 × 37 × 5983617123308793233<19> × 595871316786455532727601469262781909<36> × 15958364833406470135721364290319763834567<41> (Makoto Kamada / msieve 0.83 / 12 minutes)
4×1098-3 = 3(9)977<99> = 59 × 2590501 × 3364369 × 16756266397495660265170067<26> × 46424083259976942362809777033804858449092735815461688746121<59>
4×1099-3 = 3(9)987<100> = 7 × 1597447 × 25846643 × 1306416613<10> × 299658652285829899<18> × 1133484455260961893<19> × 31189417511064443746809006129595178833061<41>
4×10100-3 = 3(9)997<101> = 37 × 827 × 3769 × 92233 × 3456611 × 1087902006402207194906055708531158876863165243383064495263818799081710623053199849<82>
4×10101-3 = 3(9)1007<102> = 13 × 223 × 397 × 8782349371891586188243722599<28> × 39574055578551176751373128076620200416753217239059355820193165742301<68>
4×10102-3 = 3(9)1017<103> = 217201 × 1417975819757831<16> × 12987613199132289488277229136087854074083822807875194590338278066575267405404421387<83>
4×10103-3 = 3(9)1027<104> = 17 × 37 × 107 × 3593 × 10567 × 966786214431481<15> × 16191466829554211639763153570257760239392703196870411484335957780141678016109<77>
4×10104-3 = 3(9)1037<105> = 14090624960303<14> × 47607131645687<14> × 596290265867746677988016500938867082451129542464344034079396853397313875140677<78>
4×10105-3 = 3(9)1047<106> = 7 × 83 × 428951 × 18876277319<11> × 60750133667<11> × 13996278880711426606256184042732512609555173423486222610929596464057336858419<77>
4×10106-3 = 3(9)1057<107> = 37 × 11510214387337<14> × 528234148935661033<18> × 177806806014649132740771072924877971299261563470006887400661192666408610761<75>
4×10107-3 = 3(9)1067<108> = 13 × 8300337583<10> × 8310187046893<13> × 10064470783946299681<20> × 44321978685090096285472252255974060798347593821022719864584868571<65>
4×10108-3 = 3(9)1077<109> = 1451 × 71387 × 818413 × 24591853126212844607<20> × 1918711470674901064999228540779604522458895995305276063888690767282817484791<76>
4×10109-3 = 3(9)1087<110> = 37 × 64586021 × 10240969722404715986028947<26> × 13469978624759433421839413963<29> × 121342167711360086672587831031985296236321366901<48>
4×10110-3 = 3(9)1097<111> = 3259711372391<13> × 126252937550816459<18> × 682261303898568048131<21> × 1424585803251198030404157853850025083427127661333815296092123<61>
4×10111-3 = 3(9)1107<112> = 7 × 2367063518507<13> × 103364899667525491<18> × 212988862752096997<18> × 6942084979915410161633<22> × 1579545466847789568882560155587217747603183<43>
4×10112-3 = 3(9)1117<113> = 37 × 1549 × 636263 × 85777789 × 15808405367<11> × 144863315461<12> × 5584044216766086695383811562860379057389048141720853158376146400329651341<73>
4×10113-3 = 3(9)1127<114> = 13 × 1702356884234854309940250225619<31> × 18074488994744710410784707596626357056720051107053667811146452741104552488586191851<83> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.68 hours on Core 2 Quad Q6600 / May 25, 2007 2007 年 5 月 25 日)
4×10114-3 = 3(9)1137<115> = 23 × 38182410646251288694086173701<29> × 8557162049392397246492851856633465448997<40> × 532278659879147137767915163188661873881865187<45> (Makoto Kamada / Msieve 1.21 for P40 x P45 / 36 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 25, 2007 2007 年 5 月 25 日)
4×10115-3 = 3(9)1147<116> = 19 × 37 × 27103 × 20834139481<11> × 884472363134547601<18> × 116731625313722328586044311173<30> × 975975541656353729902862269487977762741754646329041<51> (Makoto Kamada / Msieve 1.21 for P30 x P51 / 13 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 25, 2007 2007 年 5 月 25 日)
4×10116-3 = 3(9)1157<117> = 111873575327<12> × 3575464526192383678943758943838085315186773122553071079789358272575805724164187371310076839696996126378211<106>
4×10117-3 = 3(9)1167<118> = 7 × 292 × 327473 × 295852289419<12> × 12245569796731<14> × 7003861575883418397672756862558232089933<40> × 81770936304432745184614995093835628187932231<44> (Makoto Kamada / Msieve 1.21 for P40 x P44 / 34 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 25, 2007 2007 年 5 月 25 日)
4×10118-3 = 3(9)1177<119> = 37 × 97 × 30637 × 215570744989<12> × 472659461707936417<18> × 3570278690405841544129438303157233228105517957509863168727460668830442110144894433<82>
4×10119-3 = 3(9)1187<120> = 13 × 17 × 85819 × 2138429 × 25985319399001881232057951389966634997820353<44> × 379543338404314085166151446656730517304702047891649789900943119<63> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.95 hours on Core 2 Quad Q6600 / May 26, 2007 2007 年 5 月 26 日)
4×10120-3 = 3(9)1197<121> = 311 × 2251511 × 9660397 × 14957350687977701210646823592952109<35> × 39534466142745973691646463023061454844518637076105956734312901955956709<71> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 1.00 hours on Core 2 Quad Q6600 / May 26, 2007 2007 年 5 月 26 日)
4×10121-3 = 3(9)1207<122> = 37 × 139 × 31362003203<11> × 62470575164971<14> × 3969759234714744894037704003196593256092887749087437628623883208567141824555677045269570566283<94>
4×10122-3 = 3(9)1217<123> = 31391 × 2684288903<10> × 58006487029<11> × 344007467969662880678387556467819763326309749859<48> × 237892718439068787805376755582318249071248333701499<51> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 1.16 hours on Core 2 Quad Q6600 / May 26, 2007 2007 年 5 月 26 日)
4×10123-3 = 3(9)1227<124> = 7 × 256302150148215013<18> × 25102647305913097143361<23> × 88815788851720338548694957276606303287526272926397190756664442878723237554607010047<83>
4×10124-3 = 3(9)1237<125> = 37 × 9522196359001<13> × 38834291343805742113919<23> × 149155523791012197735610705008582596711<39> × 19600466520430135174656418654211910689406068497609<50> (Makoto Kamada / Msieve 1.21 for P39 x P50 / 1.3 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 25, 2007 2007 年 5 月 25 日)
4×10125-3 = 3(9)1247<126> = 13 × 347 × 1919134447<10> × 3973122502709<13> × 14176781570225689422590837043552305747546179<44> × 820298957620154295413668754748555247326186604713123112531<57> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 1.38 hours on Core 2 Quad Q6600 / May 26, 2007 2007 年 5 月 26 日)
4×10126-3 = 3(9)1257<127> = 71 × 7369 × 32042891 × 5553699251<10> × 2209879287587<13> × 1128517775297302919401<22> × 17226699595060402910131872066306081718003218552471155835746784855520009<71>
4×10127-3 = 3(9)1267<128> = 37 × 1663 × 18719 × 5365901 × 705022162775505898789224106446296802990040895033<48> × 9179899962009583566770141001685302094407984058465806768333958181<64> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 1.86 hours on Core 2 Quad Q6600 / May 27, 2007 2007 年 5 月 27 日)
4×10128-3 = 3(9)1277<129> = 61 × 4583 × 777828011 × 311290259457901<15> × 5909234011381331281049315973877864837863949811699218699136624546844926413738390369648150984383004729<100>
4×10129-3 = 3(9)1287<130> = 7 × 9052129 × 63126428205847644081456259784695006950456469569597542033639663269112871521321511373575368686353074666586327765703357898299<122>
4×10130-3 = 3(9)1297<131> = 37 × 14197 × 48230137 × 1572173919829<13> × 73727974647851<14> × 81394898625280885447385281<26> × 167345142764802807479902562381994592404839041928895822897011310971<66>
4×10131-3 = 3(9)1307<132> = 13 × 23399 × 543911 × 623726897 × 828786419196952444280361223<27> × 1462209895974975072704200124249596450319<40> × 3198487680222820760741533146630326383989131689<46> (Makoto Kamada / Msieve 1.21 for P40 x P46 / 43 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 25, 2007 2007 年 5 月 25 日)
4×10132-3 = 3(9)1317<133> = 313 × 413629 × 104026555909<12> × 37278261157741<14> × 1122976311419056133302023936827<31> × 7094702873415094273433133083811785863375798683701832839125940378144747<70> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2632651371 for P31 / May 19, 2007 2007 年 5 月 19 日)
4×10133-3 = 3(9)1327<134> = 19 × 37 × 607 × 275521 × 267823455452010358133437<24> × 19092348197612899949161309484911390214209<41> × 66535483009793897303525410667693774065268754524280636711649<59> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 2.94 hours on Core 2 Quad Q6600 / May 27, 2007 2007 年 5 月 27 日)
4×10134-3 = 3(9)1337<135> = 997 × 2029 × 194471 × 49789423417<11> × 436416642661<12> × 46793931784346247511412986641715951269795983953224486549855726082641286372761749332917201168151703447<101>
4×10135-3 = 3(9)1347<136> = 72 × 17 × 2371 × 114503287 × 712325890606810303<18> × 1682813458647058605235871613932873<34> × 14755392808750968815255246320358396466276190218604598023857668682200143<71> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2613109661 for P34 / May 19, 2007 2007 年 5 月 19 日)
4×10136-3 = 3(9)1357<137> = 23 × 37 × 2293 × 15081196794111057038592942294865571<35> × 1359222545014331678259321655350929515123649897436325733988274979310778665003786733637386489826449<97> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 3.84 hours on Core 2 Quad Q6600 / May 27, 2007 2007 年 5 月 27 日)
4×10137-3 = 3(9)1367<138> = 132 × 136193 × 17378748579776080907111588119140184676140720419512563466646727449129470243172573971231306494781574546772012585515933988040032121141<131>
4×10138-3 = 3(9)1377<139> = 167 × 61953817 × 234806247524789276541047560136279747605593670548390630143<57> × 1646515424474759157709862360552930904493428048558253258347121490936014861<73> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 4.94 hours on Core 2 Quad Q6600 / May 28, 2007 2007 年 5 月 28 日)
4×10139-3 = 3(9)1387<140> = 37 × 269 × 2011 × 6581 × 11196139 × 1745959717<10> × 3342091643039<13> × 42030792677242120321<20> × 110589422404399185908671437799806939415652612346241644280736544779968389917673587<81>
4×10140-3 = 3(9)1397<141> = 53542861 × 226403410206772427<18> × 750128536862459932873<21> × 43988562125386492396251399653770406904535392867942790220293629408832929896758536370011246277787<95>
4×10141-3 = 3(9)1407<142> = 7 × 52313 × 72534046490829353664593295091274835834185520668502881701648559<62> × 150594953495731883967116548567354812204313653884473343476632001562146074013<75> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 7.74 hours on Cygwin on AMD 64 3200+ / May 29, 2007 2007 年 5 月 29 日)
4×10142-3 = 3(9)1417<143> = 37 × 47 × 114791881 × 57131442695423<14> × 3507309130804130719373196811109108629739237469303089177330722922734068683815524352362226076177082987764895991845354721<118>
4×10143-3 = 3(9)1427<144> = 13 × 51907289797361376129791761<26> × 592772824190001801139841467068809474211084120743811730013344994580116709596724048090927534832587085140605754115117729<117>
4×10144-3 = 3(9)1437<145> = 359 × 9311 × 8600737381<10> × 1127069158597835253730690599540227387<37> × 25704964961697827080699390888797399431064217<44> × 4802484227003858903586540234824184542371863661547<49> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 10.39 hours on Cygwin on AMD 64 3200+ / May 29, 2007 2007 年 5 月 29 日)
4×10145-3 = 3(9)1447<146> = 29 × 37 × 636458547278605123477<21> × 22032652827179182252311595341228758697101383067<47> × 2658418526818926672086758087119698387445371990728081899202841400303836244571<76> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 9.31 hours on Core 2 Quad Q6600 / May 29, 2007 2007 年 5 月 29 日)
4×10146-3 = 3(9)1457<147> = 83 × 42777895789<11> × 15924396733100297500381<23> × 396348820700316782956965255363264113551018768822430003<54> × 17849330111541476189358027901066221476707550990700167833117<59> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 9.64 hours on Cygwin on AMD 64 3200+ / May 30, 2007 2007 年 5 月 30 日)
4×10147-3 = 3(9)1467<148> = 7 × 2971 × 22817 × 5376997 × 240199957029223<15> × 273199160813688267149<21> × 23889588913594574475929876312351944481893313094962135579909079561530512866545114896458278647676887<98>
4×10148-3 = 3(9)1477<149> = 37 × 157 × 373 × 2389 × 2917 × 201743 × 343164397202925323<18> × 64183606304071153348418983401419<32> × 6908604692602464799988145292045693<34> × 86294287414556460254625701135729827536592888259<47> (suberi / GMP-ECM 6.1.2 B1=3000000, sigma=3953659318 for P34, Msieve v. 1.21 for P32 x P47 / May 27, 2007 2007 年 5 月 27 日)
4×10149-3 = 3(9)1487<150> = 13 × 911 × 8293 × 545089 × 692711021 × 2688167459147<13> × 226142307192019<15> × 15326187926061329027<20> × 1157696703547254603848585872652004888990661141450769341724267842304423923546987717<82>
4×10150-3 = 3(9)1497<151> = 605809 × 668303 × 17421041925411688220041828729141<32> × 567122311859518978548006909404846623637198342715283109964847436402409068996195290258639929154813994828674871<108> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1490425036 for P32 / May 20, 2007 2007 年 5 月 20 日)
4×10151-3 = 3(9)1507<152> = 172 × 19 × 37 × 813601 × 94455601 × 97616772977<11> × 196347596050337<15> × 5853974215361273<16> × 1910611134746116246492096414368671609087657<43> × 11950731510953569288974090598473301504132412787619<50> (Jo Yeong Uk / Msieve v. 1.21 / 01:20:16 on Core 2 Quad Q6600 / May 27, 2007 2007 年 5 月 27 日)
4×10152-3 = 3(9)1517<153> = 21200771 × 25893612998221<14> × 14503289669621063451952205056921<32> × 230079279032884613931774793453258451457362123<45> × 218359280476393118332391848988420792397153683310217125049<57> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3405885018 for P32 / May 20, 2007 2007 年 5 月 20 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P45 x P57 / 4.32 hours on Core 2 Quad Q6600 / May 29, 2007 2007 年 5 月 29 日)
4×10153-3 = 3(9)1527<154> = 7 × 36598463075809<14> × 701099996975822570854039960283603801308933<42> × 22269944676906901137452796561787706700352178347453639664548712306567745747002959525951900206522943<98> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 19.25 hours on Cygwin on AMD 64 3400+ / May 31, 2007 2007 年 5 月 31 日)
4×10154-3 = 3(9)1537<155> = 37 × 853 × 13650357197160249109048459378477<32> × 92846432266895293000127005136899584386269985976279393784014840396257054232599914470996487908411988310488572830000344201<119> (suberi / GMP-ECM 6.1.2 B1=1000000, sigma=1519448081 for P32 / May 26, 2007 2007 年 5 月 26 日)
4×10155-3 = 3(9)1547<156> = 13 × 74021 × 717586043 × 10620083077<11> × 427997120828569<15> × 10662789829826507524988610737<29> × 668404157299327687829641084245529<33> × 17881706191141523544777563470541642887933189900446591227<56> (Makoto Kamada / Msieve 1.21 for P33 x P56 / 1.2 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 25, 2007 2007 年 5 月 25 日)
4×10156-3 = 3(9)1557<157> = 59 × 107 × 1194517 × 1712017 × 268088377 × 131763604859<12> × 2702234461760532104363775230161432847793282975403282127651<58> × 3245841528993986751667674942064439467735740830325023575616058697<64> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 23.94 hours on Cygwin on AMD 64 3400+ / June 1, 2007 2007 年 6 月 1 日)
4×10157-3 = 3(9)1567<158> = 37 × 233 × 654148025247903819445200473<27> × 62340393015907132203772014784207<32> × 113777601846523036079732053245822156937012105295007861651633387620863333730618728133717777250487<96> (Robert Backstrom / GMP-ECM 5.0 B1=560000, sigma=3591233526 for P32 / June 1, 2007 2007 年 6 月 1 日)
4×10158-3 = 3(9)1577<159> = 23 × 421 × 9719 × 84246010477<11> × 8014081898888363<16> × 11050093067758527443<20> × 569717318416326810720929025608283300614917244291184928750325669738466209246793461655441639351362116072477<105>
4×10159-3 = 3(9)1587<160> = 7 × 80177 × 6869025736566408403013738614059587089<37> × 1037569042972137310167842357523279974289448792553913560988035736213951007069294488349444811458102522621741991129070107<118> (Robert Backstrom / GMP-ECM 5.0 B1=1175000, sigma=1004187034 for P37 / June 3, 2007 2007 年 6 月 3 日)
4×10160-3 = 3(9)1597<161> = 37 × 8831 × 692401 × 130186804290707<15> × 1358074921776997541093613480752815421230715180216326847396861549763805381645783363747260889823314152798592670894158292366642503232978893<136>
4×10161-3 = 3(9)1607<162> = 13 × 71 × 738953 × 17948851 × 743599950371757358081470341<27> × 2846805213519635781879812334100609838888539<43> × 15435038486874269067278126927452408807037060575563649377214970000125309743587<77> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.28 / November 5, 2007 2007 年 11 月 5 日)
4×10162-3 = 3(9)1617<163> = 181 × 191 × 13967 × 44196517 × 187437667353133641579896219893084533271654501457295514149873246674988096493801677952503433632788842512148666727010903119940315609353248734828598213<147>
4×10163-3 = 3(9)1627<164> = 37 × 2731 × 2143105582125249973892797<25> × 184711102115652912559829651648340141708639942766746628988646716603251538362889943145259932091349376184382672397162783324799414700778183<135>
4×10164-3 = 3(9)1637<165> = 21347 × 59377 × 1751822150967709<16> × 3934065255006277<16> × 618354792441051937903025593120469857<36> × 74051794299396180801895939838809464335023542105428143074269478481756813823421500448195263<89> (Robert Backstrom / GMP-ECM 6.0.1 B1=1904000, sigma=1737887603 for P36 / January 27, 2008 2008 年 1 月 27 日)
4×10165-3 = 3(9)1647<166> = 7 × 27378378473<11> × 1137877654421<13> × 1743800503693<13> × 26423295905393<14> × 398084137530776700080306074969894910879972018982367787181873869209329782843778612347295824688609090437057044494476963<117>
4×10166-3 = 3(9)1657<167> = 37 × 109 × 467 × 21467 × 10558902718487179894422921589845289<35> × 93696796766281288719136025075673968299994681684211285870697078809182558148593470010534568057803410687480015936158750023029<122> (suberi / GMP-ECM 6.1.2 B1=11000000, sigma=2108914274 for P35 / June 17, 2007 2007 年 6 月 17 日)
4×10167-3 = 3(9)1667<168> = 13 × 17 × 139 × 4421 × 7873915303<10> × 618273762409165239603405636857538455481103354894431607<54> × 605007623043639365025444446465689291883809981765758204992885675613074765084447457982884602953543<96> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.34 / May 3, 2008 2008 年 5 月 3 日)
4×10168-3 = 3(9)1677<169> = 349 × 241074611 × 21544306803353103509843977179159206218824143080472857184693633917823174539019<77> × 2206736938256127773273970339311752643567289428173222443185875220281755576364296817<82> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve / 57.18 hours on AMD 64 X2 6000+ / July 2, 2008 2008 年 7 月 2 日)
4×10169-3 = 3(9)1687<170> = 19 × 37 × 59575883658323<14> × 30692857989778185165053603047<29> × 31116937215133474980374533761582448867535560741357354286987308023403975327343232952345796160429870240150136693005402842524679<125>
4×10170-3 = 3(9)1697<171> = 229 × 73679 × 1360033104762423088299063931973963977671913<43> × 3590519653945782877764230523114444807700131409621<49> × 4854829677573519382682020652046055052653649124445093405710647102555118179<73> (matsui / GGNFS-0.77.1-20060513-prescott snfs / March 29, 2008 2008 年 3 月 29 日)
4×10171-3 = 3(9)1707<172> = 7 × 992551249 × 11060804449<11> × 19009303771<11> × 1249207319055289192086424463607428111<37> × 2191904185664257747583477319317672323649397459016399392947765286350833997120102120957046738111957790744991<106> (suberi / GMP-ECM 6.2.1 Using B1=3000000, sigma=3148089844 for P37 / June 20, 2008 2008 年 6 月 20 日)
4×10172-3 = 3(9)1717<173> = 37 × 814943 × 27165623 × 48832770475637058688289728087471320936929235388394460371688450816622186572844678792645300936249874056281179579281939823074319813813592925895028739080175018129<158>
4×10173-3 = 3(9)1727<174> = 13 × 29 × 821 × 244871189 × 1470687859<10> × 295787873856326456210132161<27> × 12132126252958485317086257119095778549334463812140850594232880584559016984347205105566975235163058997056741777849838457705631<125>
4×10174-3 = 3(9)1737<175> = 60245455742914874964935791279271<32> × 607774847420791048914654367551267917766139342948849<51> × 109242838055647323468269962770165507744473968570265336406291259296580147900196558487369582443<93> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=314052089 for P32 / May 25, 2007 2007 年 5 月 25 日) (Warut Roonguthai / Msieve 1.47 snfs / September 23, 2011 2011 年 9 月 23 日)
4×10175-3 = 3(9)1747<176> = 372 × 1849333 × 52010557 × 303773523732781446111930850585230844141486761976048963557399688731622229122587275559123645226746156393682315465345557255618709325197992366195258595418382428773<159>
4×10176-3 = 3(9)1757<177> = 193 × 13113882797873453847959<23> × 140786620504536695020707731<27> × 1122561130255879507927802289317641759178868599963118388187172909479316565250143224878647226352077744450004274987499424113476201<127>
4×10177-3 = 3(9)1767<178> = 72 × 149 × 104527872343<12> × 744257197546368646250747557136527<33> × 63224187335558142488978610210973178703114619175033664316325471293<65> × 111388212165214594894961563138072669090100915626062887665542359189<66> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2266155566 for P33 / May 22, 2007 2007 年 5 月 22 日) (Warut Roonguthai / Msieve 1.48 snfs / December 7, 2011 2011 年 12 月 7 日)
4×10178-3 = 3(9)1777<179> = 37 × 2221 × 20241131 × 1207256893<10> × 579423690281255535601<21> × 5667272324211519330341603<25> × 3576972140873047796254427399<28> × 1695857482714828712186708311463192154412337336611818174538353402695440640401759136711<85>
4×10179-3 = 3(9)1787<180> = 13 × 751609465955754276518902944827<30> × 5440737829768967253704195829959<31> × 7524308589497537700550163236387070963072198888286762101154838011070880004644191216696466958842086243668442125836776933<118> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=927040615 for P30 / May 23, 2007 2007 年 5 月 23 日) (suberi / GMP-ECM 6.1.2 B1=11000000, sigma=3294625248 for P31 / June 13, 2007 2007 年 6 月 13 日)
4×10180-3 = 3(9)1797<181> = 23 × 2610247689748216883<19> × 4455431106591385317241127<25> × 14954114534311527479908333837569690356550148128083157624630490652393719070521316215760056259648131751868798013172319524364812384061793679<137>
4×10181-3 = 3(9)1807<182> = 37 × 6552361387299529<16> × 8291913204617709848350999199<28> × 1610703356861443104917170340729425061243949975177989668523<58> × 12353502674892318391055956643949191085736809403224331052816482028936976548742157<80> (Dmitry Domanov / Msieve 1.50 snfs / May 22, 2013 2013 年 5 月 22 日)
4×10182-3 = 3(9)1817<183> = 3313 × 11483 × 176053 × 39387975579353615896504296945339241<35> × 1516268457802174096132783680473005131671559431263031934817627015235299434290293219117245850021882172515022423742506186276722478373533891<136> (suberi / GMP-ECM 6.2.1 Using B1=3000000, sigma=2421712102 for P35 / June 20, 2008 2008 年 6 月 20 日)
4×10183-3 = 3(9)1827<184> = 7 × 17 × 257 × 261895240531<12> × 499404326677392851160118316001731919717314042704772510699181966654965057638113906373604439672083475557583263804048916838703040440535668283186875588603888051095992326089<168>
4×10184-3 = 3(9)1837<185> = 37 × 157259 × 148694525615558387<18> × 34534145325744924551610736069746683871669092538005717108954621175789535293680147<80> × 1338748710788831131175479530384595489834198458367075025613019266634148662315537331<82> (Dmitry Domanov / Msieve 1.50 snfs / June 13, 2013 2013 年 6 月 13 日)
4×10185-3 = 3(9)1847<186> = 13 × 2710082539<10> × 24544359207043689314883852987401263868524717<44> × 1711254231106590390191469193234817699792475403912781328971783723<64> × 270313594614181001025713349777904935988854107792014326687398953865981<69> (Robert Backstrom / Msieve 1.44 snfs / February 3, 2012 2012 年 2 月 3 日)
4×10186-3 = 3(9)1857<187> = 541 × 18181 × 293399 × 4847068969936404860710521156459235585519080320343476286401234398015921<70> × 285961213052931476822620205722956711645466417142175363075429539354193601891794737064219841656408375838283<105> (Robert Backstrom / Msieve 1.44 snfs / February 21, 2012 2012 年 2 月 21 日)
4×10187-3 = 3(9)1867<188> = 192 × 37 × 83 × 367 × 81233 × 113418820344084397<18> × 1491680926343259894290342089<28> × 7153413893207441460384612540575357075060779175356713007446539232782416744598244977081671777650334633749799506018933512445451568449<130>
4×10188-3 = 3(9)1877<189> = 47 × 61 × 2833 × 10321 × 42535499 × 84752832613<11> × 3589458682616526115303944010645313849880359656503121<52> × 368747625995792928886003610636829284961689064502743227973824854743419752177358550714772256180281142630317081<108> (Daniel Morel / GGNFS-0.77.1 for P52 x P108 / December 17, 2014 2014 年 12 月 17 日)
4×10189-3 = 3(9)1887<190> = 7 × 63857 × 360223 × 582137 × 1427514587<10> × 455065102771685432854413941<27> × 42951207869419459061300421901875659455265174321275046370207861095761<68> × 1529421985430320101703540035314141898971020909779238676210675105896219<70> (jafarism / ggnfs+msieve for P68 x P70 / May 20, 2017 2017 年 5 月 20 日)
4×10190-3 = 3(9)1897<191> = 37 × 3635999 × 87669989277938702330798029761042050099<38> × 1716323154172044902113264015543934465977<40> × 1975988884873260107276431644586768793669743214417979395740447602843978441558180122551894143256764261249253<106> (Wataru Sakai / GMP-ECM 6.2.3 B1=3000000, sigma=2212708475 for P40 / June 20, 2010 2010 年 6 月 20 日) (Wataru Sakai / GMP-ECM 6.2.3 B1=3000000, sigma=1719767535 for P38 / June 21, 2010 2010 年 6 月 21 日)
4×10191-3 = 3(9)1907<192> = 13 × 177127 × 331079288971<12> × 1473051576539791802518135543<28> × [356190149584275523195576561147499332086015646525597867121960594664691220473516464510001055670663735998707729228821428958114201172144961290600778899<147>] Free to factor
4×10192-3 = 3(9)1917<193> = 227 × 22555714451591<14> × 16957967335361069900199472268490978355464810229996017075468063815639<68> × 46068466062721657161827993298568302396403742512448314772822505916915071152871619883154383609653122872421411839<110> (matsui / Msieve 1.50 snfs / November 8, 2011 2011 年 11 月 8 日)
4×10193-3 = 3(9)1927<194> = 37 × 235266609366383526000551177317<30> × [4595131812341038524673377425547981526256392877400040967588225812152509612718673550314089210300607006960890832290659727712513631897072820523735853258609334800261893<163>] (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2241430052 for P30 / May 25, 2007 2007 年 5 月 25 日) Free to factor
4×10194-3 = 3(9)1937<195> = 502571964899<12> × 1925168799160814333812958029<28> × 413421366578363171432059253600288935368523036838341165155215332021502664189018105666593248581229852058266787902584327949523152495244420824849082527651076507<156>
4×10195-3 = 3(9)1947<196> = 7 × 101197 × 3771194733060677910727165656242155763<37> × 1497322513815848534027864445072580097326790638319429568818602330439582708603315019200778229678277949703995368212735241456117614079298626340503579378845661<154> (suberi / GMP-ECM 6.1.2 B1=11000000, sigma=623019224 for P37 / July 2, 2007 2007 年 7 月 2 日)
4×10196-3 = 3(9)1957<197> = 37 × 71 × 165877 × 663125854879949029<18> × 138426036845615656961011396327543838035903055332231512635031524827079330162710730925790055521594845830045140311764685242362450595921706270377656813672024949972992893312167<171>
4×10197-3 = 3(9)1967<198> = 13 × 479 × 18637 × 547945051 × 6290252972320835500301583137386179068730753834386757638534448663592729205181241395146096616285503212073204229043413531108653966160156017609835738557450047181599906128165511611095153<181>
4×10198-3 = 3(9)1977<199> = 4168943 × 33219052837<11> × 28883298505783667127465062432837137980505713805801748003225291601780899794002629751362561687679195460597080827273611634395066768992600093950856036323211882147261936771117127695068567<182>
4×10199-3 = 3(9)1987<200> = 17 × 37 × 113 × 2351 × 6599 × 1762649657<10> × [20579468022679290363403006217927211257782345065101645447343343299782815525132234892412631316922585660099256128786300617930853341609588826485809160148169001698279353098407314749177<179>] Free to factor
4×10200-3 = 3(9)1997<201> = 397 × 1591080945026496112917339112958930463606304590528911569<55> × 633252932990278223069090414959637564981283096491029523470488470154265459768968029261042716837602446043281857774800232294214750266149540233317729<144> (Wataru Sakai / Msieve / 626.57 hours / December 6, 2008 2008 年 12 月 6 日)
4×10201-3 = 3(9)2007<202> = 7 × 29 × 28663 × 2090750288080015059847<22> × 2330082518637233481228931<25> × 46856702191880789007097991806729637684419<41> × 3011598855699598071151625486968596848471071678142658545952126968331471634833200049073377848121174521051598431<109> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=775643045 for P41 / March 20, 2013 2013 年 3 月 20 日)
4×10202-3 = 3(9)2017<203> = 232 × 37 × 4129 × 5077 × 19501 × 1379639989526695106325647538991007<34> × [3623496886882157385533754490420340641545791104069751230621273857796214198295322804574188072647769287143144148327406327050825808698880935235446520869728519<154>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=804843122 for P34 / March 20, 2013 2013 年 3 月 20 日) Free to factor
4×10203-3 = 3(9)2027<204> = 13 × 1719291941937964699<19> × [17896454940949744298786450883441074515339765224441039510052425530410450777491242227178496522725027220389002227185018621743684205355105051588102530949405937340848331541448843173424704931<185>] Free to factor
4×10204-3 = 3(9)2037<205> = 419 × 107773 × 133944829 × 555372469 × 482169552880549<15> × 2469596005992001620746645314444626302852716787568033868657889014614690932792939609885770171496149145047492746575697108394965957138697769406818473247270147600372832719<166>
4×10205-3 = 3(9)2047<206> = 19 × 37 × 839 × 1129 × 25618511 × 355554854881<12> × 61983903312636037163<20> × 106392091094381727912916839758097376587320712171358026885224309612754266122544403808750136431875585316510670583616825597120775737678631490289962077650976807513<159>
4×10206-3 = 3(9)2057<207> = 683 × 9868796963<10> × 15829567263599<14> × 791524085816826752053<21> × 4736329370189566615035160497589321507426880258075843675684379736309572708886392076748432793630149783153629079295605605071770978091966718635214314715849971858119<160>
4×10207-3 = 3(9)2067<208> = 7 × 42437239597<11> × 13465262511300740119424044531559106454372350146725577292534486698945774236179723012358951773303026682924977726878434963267656397265564384644097391418476323394673802996663167449784318058659130664743<197>
4×10208-3 = 3(9)2077<209> = 37 × 70336392684251<14> × 8506440046481915423<19> × 1806884243582925913513895439283086670754195255072767713629475575162088640501633082964041860387611125062583978885787635690515913677792392191049582663719857863530607545641172197<175>
4×10209-3 = 3(9)2087<210> = 13 × 107 × 2657 × 21911 × 27895933803593<14> × 3159424662082742971<19> × [56044138853456037524090330246912450640469433430748997663596863156110715977631475565288359475979856249181230253441534377606318106657765348647113353872093443867437961607<167>] Free to factor
4×10210-3 = 3(9)2097<211> = 6154210827082201197522655333<28> × 3431353117210616330501280155754076747850232841<46> × 3142916137495335145294364794230667601713425082370109479<55> × 60268365765110488409452647085714459841742817465419193799019829725093188239880941031<83> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2439796343 for P46 / March 25, 2013 2013 年 3 月 25 日) (Erik Branger / GGNFS, Msieve gnfs for P55 x P83 / May 20, 2014 2014 年 5 月 20 日)
4×10211-3 = 3(9)2107<212> = 37 × 1151 × 63543461 × 164704353721<12> × [89744325669048042911139453143418918652979412950347345156304866056925759072498304400779350524836283516729261436588043166608769113714234944448698571603511653943635091339797059958184755308051<188>] Free to factor
4×10212-3 = 3(9)2117<213> = 275358944512162957357367015050275313055209<42> × 1452649379916298624310249792586760462253299945710487449071079615919133567148324891947719820392803152245132343622166772500419874279637328912708440056342516304730825738610933<172> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=893454024 for P42 / March 25, 2013 2013 年 3 月 25 日)
4×10213-3 = 3(9)2127<214> = 7 × 139 × 29429 × 1206500747<10> × 22444405982293684765365886124533<32> × [5158648479100259170818054364303197925814031875330221529824616559953158840260775644126474632905549517067535304881971259641888539940321369446029317028513401487604262091<166>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3224966958 for P32 / March 19, 2013 2013 年 3 月 19 日) Free to factor
4×10214-3 = 3(9)2137<215> = 37 × 59 × 97 × 491 × [384727321769513689564735955242977858336686632700181488381316637116562596804006658052557811026960238363967839450518588865196846070819778227590275520644030458823591760221851471189102991032746729647042210098417<207>] Free to factor
4×10215-3 = 3(9)2147<216> = 132 × 17 × 443 × 42426302472697231237<20> × 7407735298080293375752527863997664468204743851018531684628689857887324596747829778669631701927550650451249948026688320451950073669331173959541549084593769820223410256188832067313412591176979<190>
4×10216-3 = 3(9)2157<217> = 11987 × 12224188490538589637173<23> × 270675599881445468884942811<27> × 543579564463872369276493054721622609175569103201<48> × 19908205731456826539052940025491068433262821979493597<53> × 9319338760453768484785456879744583150887539719939897393270232541<64> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2192195301 for P48, NFS for P53 x P64 / March 20, 2013 2013 年 3 月 20 日)
4×10217-3 = 3(9)2167<218> = 37 × 1061 × 56717673331134002837332148993<29> × 5304421748735442838522170610939694351<37> × [3386775655642202564438718488309730890041436203373149222804338752301168190671206303097197979559016826870889243147734222236106059314257633890129015147<148>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=40276203 for P37 / March 25, 2013 2013 年 3 月 25 日) Free to factor
4×10218-3 = 3(9)2177<219> = 10067831582637022132817905111256783184575163431814522785441218512027016129455219736741<86> × 39730501718944109275533248415809468732659894963488711511851403087021043769617025638792340956819600016474235519149275235236442233719417<134> (NFS@Home + Lionel Debroux / ggnfs-lasieve4I14e on the NFS@Home grid + msieve 1.53 SVN for P86 x P134 / September 24, 2015 2015 年 9 月 24 日)
4×10219-3 = 3(9)2187<220> = 72 × 1246612768507574610673925215234477<34> × [65483568854307364858591061353745838644763192360921850964445040988688378593507665385450169619548705780793170382024412780613289569992092618153890464004124984380757840913163914211691214689<185>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=969435131 for P34 / March 19, 2013 2013 年 3 月 19 日) Free to factor
4×10220-3 = 3(9)2197<221> = 37 × 131 × 601 × 309125928983<12> × 72070815572721926275001962564127<32> × 616336131884305043803315200341692880412921733794801412902763944974434685535922496702796960092699977969842089948100992504762318462224390239768390769589994461343110915586611<171> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=866281183 for P32 / March 20, 2013 2013 年 3 月 20 日)
4×10221-3 = 3(9)2207<222> = 13 × 14197 × 14952127 × 1177543439<10> × 123094923423024065452039018668116266453406853252054274460151514046615019349789939929090290776032987839542608196846070933290614768671854667948994623673236226455635721387260175724671451165407421515887709<201>
4×10222-3 = 3(9)2217<223> = 10069 × 125113 × 305481277 × 24548232864263<14> × 393886438489543573877593<24> × 223035807665583287889849404921823227<36> × 4819708353534051502665747978121034351625741975799558660604331149441142172135112905085070941010399416481189542559972958171805763732241<133> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2297520921 for P36 / March 20, 2013 2013 年 3 月 20 日)
4×10223-3 = 3(9)2227<224> = 19 × 37 × 9739994593213<13> × 5841790128618094886811335014930485772880429647051836771186692488871544341397291504914051749140669286289239062098049806093812833413450965137333008099006891994917515957196675265796748175606462583989637782401023<208>
4×10224-3 = 3(9)2237<225> = 23 × 1229983875570725778468387135347<31> × 14139457185775166562285035496492411824083412912895583989544473078372809254352278566729271081962949944469815925487061515995970151126797115732602176495941411743089233604956377547038043697491593737<194> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=3123167193 for P31 / March 1, 2013 2013 年 3 月 1 日)
4×10225-3 = 3(9)2247<226> = 7 × 65677 × 8700588812347875642484105111813441974685636850473855818192496177178790574652139583546316496968932372498308823049599881671992152068891262216170479337189144275338833555560872582051990368448184730901663770095641222519734023<220>
4×10226-3 = 3(9)2257<227> = 37 × 157 × 749500334856574271<18> × [9187276427029102349163695740036260975378164042342605966092797232945345169491319618900076347178940226307457149089177344009941689282950854195331942759778262532989175969648609375114483827165820029572679545523<205>] Free to factor
4×10227-3 = 3(9)2267<228> = 13 × 1543 × 19801 × 4378271 × [230017537536693018454303014150419206077930454225295371490143159036110390919331199449326251122057277492956301398175135722762196558115425779920148357747126581576813370802968067602101193438972915633667221751297575873<213>] Free to factor
4×10228-3 = 3(9)2277<229> = 83 × 79201 × 2795989746190549<16> × 186165299680291024599949741<27> × [1169006499352578198525690517431493618054375953829479585470402398221089728390454236064938879641461960215466536926906860547646501967164259735226527147072752604595192842266258142684351<181>] Free to factor
4×10229-3 = 3(9)2287<230> = 29 × 37 × 1655463447677955633749<22> × [22518563016659922703722107154622647163779876897640348549547911759067272343964700357989788651299927373125698253763376929159654747820156822137394984213853112245038242310859277408961531398994531927478556867161<206>] Free to factor
4×10230-3 = 3(9)2297<231> = 268729 × 760645057289650031<18> × 332471928843535440235743944231<30> × [5885839629441864086350648683894161386602538514753687975494496325589542151815282399868938848631356649238793515051474248422336839697556287812051750200808302021945748763717076502813<178>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=4039395337 for P30 / March 1, 2013 2013 年 3 月 1 日) Free to factor
4×10231-3 = 3(9)2307<232> = 7 × 17 × 71 × 25958430003118348353527711<26> × 18237960003209099607005017577430584843512045454129466656979036144470260363507951467028332753623591857343608913749941881353417274786113080249193385515236566559035319324660507862820571504231827258936215523<203>
4×10232-3 = 3(9)2317<233> = 37 × 346660654351789<15> × 3118557204314300291871478716196922235624934823820014152353910122256480232344441825881001873365845877194887902647782637300742745635303888097964419091490769683093699768521268448344739391469369221508083671981919915832829<217>
4×10233-3 = 3(9)2327<234> = 13 × 243701 × 365255531283607259069<21> × [345670665940936223013973126326300617269444324166040746755002156872712158229996603019922978046268038520527486689186489766218761575957013857350936120409952196842312646278861036785926736299492947419001704315601<207>] Free to factor
4×10234-3 = 3(9)2337<235> = 47 × 3667362831252726937<19> × [23206425678271950445835592711491490549603238235018520678641524781311631560958724727207695637224421209324091251532586105073434738542673839556024169051654975480369695714518811389569073477132629151650108851004623814923<215>] Free to factor
4×10235-3 = 3(9)2347<236> = 37 × 1109 × 1709 × 22391847221311050664336660065689307107<38> × 25473858734494385118046428291843859591024320113483126223184458766126155533013800194305744399645247290851064248248636723003213487525081351098571084093305189573347221520288132187872132957316643<191> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2526242207 for P38 / March 25, 2013 2013 年 3 月 25 日)
4×10236-3 = 3(9)2357<237> = 6307762081<10> × [63413932685391657529766617714635391302736739984533985469449731453813849070570231610484231895683003963953725413189058422255986798053742255596656515681920502036132519754750718220692509343869781888813761046482945176891810545763037<227>] Free to factor
4×10237-3 = 3(9)2367<238> = 7 × 68832651473<11> × 8301707971437327876294819531810881292729546621232064369112590547156408370301579874875430088481557096744609208952716576235549724970109774178383822309168703619080888800916748444539882056281795916158148595581000401417277703835627<226>
4×10238-3 = 3(9)2377<239> = 37 × [1081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081081<238>] Free to factor
4×10239-3 = 3(9)2387<240> = 13 × [30769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769<239>] Free to factor
4×10240-3 = 3(9)2397<241> = 602573669803468557142109149<27> × 79349947136857964305668137506688317<35> × 83657175759470924823693263439826465083136882480613079419002053388178698340504033830068281799588771303765978244755348829683856580231030075491812320049247559206858722044086071040309<179> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1745716713 for P35 / March 20, 2013 2013 年 3 月 20 日)
4×10241-3 = 3(9)2407<242> = 19 × 37 × 18701 × 115434841 × 249802181 × 211100086656608807111<21> × 108008530106947381244923767476259797371<39> × [4627647112161213796803303050186459001719592262813332647430682976158857980733089981569542156850652824224010444060356321590859140521089787325700327813334244628599<160>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2295438255 for P39 / March 25, 2013 2013 年 3 月 25 日) Free to factor
4×10242-3 = 3(9)2417<243> = 3529 × [113346557098328138282799659960328705015585151601020119013884953244545196939642958345140266364409181071124964579200906772456786625106262397279682629640124681212808160952111079625956361575517143666761122130915273448568999716633607254179654293<240>] Free to factor
4×10243-3 = 3(9)2427<244> = 7 × 947 × 308242174871<12> × 391148271174733<15> × 1107461614273030837<19> × 39445442058434347163<20> × 1116057707099624213130629762575971433721779<43> × 102651745017231922769321319293535454050199954655215497668536209630320785327089075742019401192220923777396685226798295827836109293443199<135> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1704325369 for P43 / March 20, 2013 2013 年 3 月 20 日)
4×10244-3 = 3(9)2437<245> = 37 × 1069 × 101691627639521635365213121<27> × [9944784201136793635565867304885017744354497045873807886105544734033049376364688897549263181203275773937010404459037602130507515558678186563889674638998594156592074617926991086983547393383646550007429714000051387069<214>] Free to factor
4×10245-3 = 3(9)2447<246> = 13 × 165721 × 15943673 × [11645300915449701868914795276236466234406941272979754649222820225441097971821989751300027252205462118325516992178311830494424901882198686663196937557904156499553893893007631244327787286194540033422918418893776006504414366395221269793<233>] Free to factor
4×10246-3 = 3(9)2457<247> = 23 × 130473594318359<15> × 7967857811869411093007<22> × 167289218871941038886415593267487009568716891312210345658992912548307926214444388101909803585750717254190473151360398561002765370791694938614434810513111260656447774447722664010134224901787759725412548301190403<210>
4×10247-3 = 3(9)2467<248> = 17 × 37 × 3821 × 698063983739909<15> × 1302880934933551458494198693845196266651<40> × [18299210279240090196329674836447761834668004162087269082755337622736940561028637087943471978670864020359365090278631819863915298592576434689180172274476040207222078036833739689555209556587<188>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2724775150 for P40 / March 25, 2013 2013 年 3 月 25 日) Free to factor
4×10248-3 = 3(9)2477<249> = 61 × 4150849173185756299743926377<28> × 1579767603106516461335190226212595836928196290954080257181913642608681202796067550798478843574262105113290621517458014304183233643740349738410925918576695962627283693558359650264582853522275444527310373122028964135503001<220>
4×10249-3 = 3(9)2487<250> = 7 × 9587 × 35281 × 87964439 × 619287569532142649068937<24> × 9859890000758151500364257584249<31> × [3145333986665746441343186218347376991352568895757343791641157789369007326951412566718314788972102056523375602462736044789298287824881016671304975482203162826880013221213009407999<178>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=602926246 for P31 / March 20, 2013 2013 年 3 月 20 日) Free to factor
4×10250-3 = 3(9)2497<251> = 37 × 1849338482347739<16> × [584577183355124059933098604933483077382973426513602005237820835754223223629833736147424378046826300391371918799062659320044274616348033723697116135626041449125383556261102735551252903049266644648576640248396501370020120573672058792379<234>] Free to factor
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