Table of contents 目次

  1. About 600...007 600...007 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 600...007 600...007 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 600...007 600...007 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 600...007 600...007 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

60w7 = { 67, 607, 6007, 60007, 600007, 6000007, 60000007, 600000007, 6000000007, 60000000007, … }

1.3. General term 一般項

6×10n+7 (1≤n)

2. Prime numbers of the form 600...007 600...007 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. 6×101+7 = 67 is prime. は素数です。
  2. 6×102+7 = 607 is prime. は素数です。
  3. 6×103+7 = 6007 is prime. は素数です。
  4. 6×108+7 = 600000007 is prime. は素数です。
  5. 6×109+7 = 6000000007<10> is prime. は素数です。
  6. 6×1019+7 = 6(0)187<20> is prime. は素数です。
  7. 6×1058+7 = 6(0)577<59> is prime. は素数です。
  8. 6×10121+7 = 6(0)1207<122> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 4, 2004 2004 年 12 月 4 日) (certified by: (証明: Makoto Kamada / PFGW / January 4, 2005 2005 年 1 月 4 日)
  9. 6×10187+7 = 6(0)1867<188> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 4, 2004 2004 年 12 月 4 日) (certified by: (証明: Makoto Kamada / PFGW / January 4, 2005 2005 年 1 月 4 日)
  10. 6×10806+7 = 6(0)8057<807> 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: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006 2006 年 5 月 31 日)
  11. 6×10855+7 = 6(0)8547<856> 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 4, 2005 2005 年 1 月 4 日)
  12. 6×101019+7 = 6(0)10187<1020> 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 4, 2005 2005 年 1 月 4 日)
  13. 6×102593+7 = 6(0)25927<2594> 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: suberi / PRIMO 3.0.4 / September 29, 2007 2007 年 9 月 29 日)
  14. 6×102749+7 = 6(0)27487<2750> 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: suberi / PRIMO 3.0.4 / October 16, 2007 2007 年 10 月 16 日)
  15. 6×103016+7 = 6(0)30157<3017> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 18, 2004 2004 年 12 月 18 日) (certified by: (証明: Maksym Voznyy / Primo 3.0.9 / December 26, 2012 2012 年 12 月 26 日)
  16. 6×104295+7 = 6(0)42947<4296> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 19, 2004 2004 年 12 月 19 日)
  17. 6×109664+7 = 6(0)96637<9665> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / January 6, 2005 2005 年 1 月 6 日)
  18. 6×1014927+7 = 6(0)149267<14928> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  19. 6×1034562+7 = 6(0)345617<34563> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  20. 6×1064387+7 = 6(0)643867<64388> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  21. 6×1071299+7 = 6(0)712987<71300> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  22. 6×1071951+7 = 6(0)719507<71952> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)

2.3. Range of search 捜索範囲

  1. n≤100000 / Completed 終了 / Dmitry Domanov / March 8, 2010 2010 年 3 月 8 日
  2. 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. 6×106k+7 = 13×(6×100+713+54×106-19×13×k-1Σm=0106m)
  2. 6×1015k+12+7 = 31×(6×1012+731+54×1012×1015-19×31×k-1Σm=01015m)
  3. 6×1016k+12+7 = 17×(6×1012+717+54×1012×1016-19×17×k-1Σm=01016m)
  4. 6×1018k+17+7 = 19×(6×1017+719+54×1017×1018-19×19×k-1Σm=01018m)
  5. 6×1021k+7+7 = 43×(6×107+743+54×107×1021-19×43×k-1Σm=01021m)
  6. 6×1022k+4+7 = 23×(6×104+723+54×104×1022-19×23×k-1Σm=01022m)
  7. 6×1028k+24+7 = 29×(6×1024+729+54×1024×1028-19×29×k-1Σm=01028m)
  8. 6×1032k+30+7 = 353×(6×1030+7353+54×1030×1032-19×353×k-1Σm=01032m)
  9. 6×1033k+1+7 = 67×(6×101+767+54×10×1033-19×67×k-1Σm=01033m)
  10. 6×1035k+31+7 = 71×(6×1031+771+54×1031×1035-19×71×k-1Σm=01035m)

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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 26.59%. 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 26.59% です。

3. Factor table of 600...007 600...007 の素因数分解表

3.1. Last updated 最終更新日

August 22, 2017 2017 年 8 月 22 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, 196, 197, 199, 205, 207, 208, 210, 211, 215, 216, 219, 220, 223, 226, 227, 228, 229, 231, 232, 233, 234, 235, 238, 239, 240, 241, 242, 243, 246 (31/250)

3.4. Factor table 素因数分解表

6×101+7 = 67 = definitely prime number 素数
6×102+7 = 607 = definitely prime number 素数
6×103+7 = 6007 = definitely prime number 素数
6×104+7 = 60007 = 23 × 2609
6×105+7 = 600007 = 83 × 7229
6×106+7 = 6000007 = 133 × 2731
6×107+7 = 60000007 = 43 × 127 × 10987
6×108+7 = 600000007 = definitely prime number 素数
6×109+7 = 6000000007<10> = definitely prime number 素数
6×1010+7 = 60000000007<11> = 66617 × 900671
6×1011+7 = 600000000007<12> = 157 × 51869 × 73679
6×1012+7 = 6000000000007<13> = 13 × 17 × 31 × 2579 × 339583
6×1013+7 = 60000000000007<14> = 47 × 97 × 2441 × 5391553
6×1014+7 = 600000000000007<15> = 9733 × 223589 × 275711
6×1015+7 = 6000000000000007<16> = 587 × 10221465076661<14>
6×1016+7 = 60000000000000007<17> = 59 × 3893753 × 261174541
6×1017+7 = 600000000000000007<18> = 19 × 31578947368421053<17>
6×1018+7 = 6000000000000000007<19> = 13 × 2333 × 3435623 × 57582121
6×1019+7 = 60000000000000000007<20> = definitely prime number 素数
6×1020+7 = 600000000000000000007<21> = 32934247 × 18218118058081<14>
6×1021+7 = 6000000000000000000007<22> = 109 × 55045871559633027523<20>
6×1022+7 = 60000000000000000000007<23> = 616991 × 97246151078378777<17>
6×1023+7 = 600000000000000000000007<24> = 139067 × 4314467127355878821<19>
6×1024+7 = 6000000000000000000000007<25> = 13 × 29 × 61 × 131 × 122869 × 16209381575029<14>
6×1025+7 = 60000000000000000000000007<26> = 76103 × 4544991179<10> × 173466824611<12>
6×1026+7 = 600000000000000000000000007<27> = 232 × 1801 × 629769850608095271583<21>
6×1027+7 = 6000000000000000000000000007<28> = 31 × 547 × 761 × 1733 × 268298973282418927<18>
6×1028+7 = 60000000000000000000000000007<29> = 17 × 43 × 149 × 701 × 6269 × 125352014333343337<18>
6×1029+7 = 600000000000000000000000000007<30> = 197 × 1293307 × 2354959247253604332833<22>
6×1030+7 = 6000000000000000000000000000007<31> = 13 × 353 × 48809 × 26787567770146738858507<23>
6×1031+7 = 60000000000000000000000000000007<32> = 712 × 2267 × 5250286862548452491072981<25>
6×1032+7 = 600000000000000000000000000000007<33> = 32479 × 490513041497<12> × 37661537218645889<17>
6×1033+7 = 6000000000000000000000000000000007<34> = 3461 × 6371264351<10> × 272097170891956164037<21>
6×1034+7 = 60000000000000000000000000000000007<35> = 67 × 89 × 739 × 609997 × 1333480003<10> × 16738933968161<14>
6×1035+7 = 600000000000000000000000000000000007<36> = 19 × 121016711 × 557897477 × 467732886666893599<18>
6×1036+7 = 6000000000000000000000000000000000007<37> = 13 × 9828538733227<13> × 46959011310415298018857<23>
6×1037+7 = 60000000000000000000000000000000000007<38> = 2286513966743<13> × 26240819375123410553567249<26>
6×1038+7 = 600000000000000000000000000000000000007<39> = 1083940060991<13> × 553536142442641784859710777<27>
6×1039+7 = 6000000000000000000000000000000000000007<40> = 21803 × 275191487409989450992982617071045269<36>
6×1040+7 = 60000000000000000000000000000000000000007<41> = 267090643 × 224642837824910249663819185159549<33>
6×1041+7 = 600000000000000000000000000000000000000007<42> = 3577061 × 167735467748523159096252482135473787<36>
6×1042+7 = 6000000000000000000000000000000000000000007<43> = 13 × 31 × 53743900109<11> × 277023763418491029871991637041<30>
6×1043+7 = 60000000000000000000000000000000000000000007<44> = 4999273 × 12001745053730812460131703149637957359<38>
6×1044+7 = 600000000000000000000000000000000000000000007<45> = 17 × 229 × 98878659946139283059<20> × 1558706242266289452361<22>
6×1045+7 = 6000000000000000000000000000000000000000000007<46> = 240623 × 1592823481<10> × 15654761802996888034571030103089<32>
6×1046+7 = 60000000000000000000000000000000000000000000007<47> = 83 × 40459649 × 13903108892221<14> × 1285106507981942768539201<25>
6×1047+7 = 600000000000000000000000000000000000000000000007<48> = 291299 × 750423679 × 2744768539828925176253974934503667<34>
6×1048+7 = 6000000000000000000000000000000000000000000000007<49> = 13 × 23 × 16339 × 129967 × 8330981228849<13> × 1134293227422906087268489<25>
6×1049+7 = 60000000000000000000000000000000000000000000000007<50> = 43 × 127 × 28661 × 74223740263<11> × 5164697614627379771155769652809<31>
6×1050+7 = 600000000000000000000000000000000000000000000000007<51> = 68041 × 204329 × 242175943153<12> × 178204863822727761721765452071<30>
6×1051+7 = 6(0)507<52> = 9623 × 1356557651<10> × 459623800465360714632227548920685144459<39>
6×1052+7 = 6(0)517<53> = 29 × 3739 × 557095242203<12> × 15378961595791<14> × 64586436809647495465189<23>
6×1053+7 = 6(0)527<54> = 19 × 233 × 881 × 28807 × 1812719959518711163<19> × 2946029359829255587544521<25>
6×1054+7 = 6(0)537<55> = 13 × 4388640945277212317<19> × 105166603350210519597612385891603967<36>
6×1055+7 = 6(0)547<56> = 443291 × 135351270384465283527073637858652668337502904412677<51>
6×1056+7 = 6(0)557<57> = 227 × 367 × 174824891 × 2084526673883<13> × 2368188812239<13> × 8345114136392433269<19>
6×1057+7 = 6(0)567<58> = 31 × 20611 × 5053891 × 19169002983219077<17> × 96931536565961966012385392861<29>
6×1058+7 = 6(0)577<59> = definitely prime number 素数
6×1059+7 = 6(0)587<60> = 47 × 33028004917<11> × 386519182096817617422963772305700117711218912293<48>
6×1060+7 = 6(0)597<61> = 13 × 17 × 8819 × 23073121 × 49161272827<11> × 2714002053200343766099337742596564179<37>
6×1061+7 = 6(0)607<62> = 8861 × 81535291 × 381801529 × 754989401345719577<18> × 288100737505429161458329<24>
6×1062+7 = 6(0)617<63> = 353 × 25657 × 66247679537008217251756971270920879181788159574318910367<56>
6×1063+7 = 6(0)627<64> = 431 × 743901487390679<15> × 18713652177151914593889343662127041858671538943<47>
6×1064+7 = 6(0)637<65> = 163 × 337903 × 10473677 × 31450857691482513701<20> × 3307043658817000901713130682019<31>
6×1065+7 = 6(0)647<66> = 617 × 1153 × 872838164347<12> × 9734952510569516749<19> × 99258844355536353257965988369<29>
6×1066+7 = 6(0)657<67> = 13 × 71 × 2713 × 2396071401330378711065337273007177431882685149428996217801293<61>
6×1067+7 = 6(0)667<68> = 67 × 70860556890146739591673559004791<32> × 12637811885221369803175262599750331<35>
6×1068+7 = 6(0)677<69> = 67021 × 76667 × 232749564959<12> × 196664889062801<15> × 2551033536390412699360023131205239<34>
6×1069+7 = 6(0)687<70> = 122693 × 172647815814128989362652642817<30> × 283250298573918348624320510579619547<36>
6×1070+7 = 6(0)697<71> = 23 × 43 × 1299173 × 46696891598140152154365335514516084038798775480175439007615031<62>
6×1071+7 = 6(0)707<72> = 19 × 619 × 35107 × 201577 × 48593214431537025469<20> × 148353116864985518179221507099069971257<39>
6×1072+7 = 6(0)717<73> = 13 × 31 × 530696666431222807064662741<27> × 28054326342583363652026301318927807490980809<44>
6×1073+7 = 6(0)727<74> = 1493 × 61464883 × 391949836591<12> × 29975574563185939388106053<26> × 55650155140249028183226811<26>
6×1074+7 = 6(0)737<75> = 59 × 557 × 47701 × 123433 × 1736639 × 36106877 × 49452220731256776467389766374268449438783991311<47>
6×1075+7 = 6(0)747<76> = 8839 × 678809820115397669419617603801334992646226948749858581287475958818870913<72>
6×1076+7 = 6(0)757<77> = 17 × 467 × 1764227 × 1766465505869<13> × 2425078620192876496847562064201690662770065200014824651<55>
6×1077+7 = 6(0)767<78> = 1373 × 224110457 × 9810155197<10> × 27143383967831581<17> × 30426793632236797<17> × 240670319662076435538703<24>
6×1078+7 = 6(0)777<79> = 13 × 89 × 439 × 90583 × 130408731738032770813552657520713097773626749705905146079761133744523<69>
6×1079+7 = 6(0)787<80> = 125098182497512527503029<24> × 479623275111875024289405200959197453009921778301829553483<57>
6×1080+7 = 6(0)797<81> = 29 × 2111 × 9870377741973879615140003<25> × 992958837882683379516893991296803461210434204985551<51>
6×1081+7 = 6(0)807<82> = 3373 × 630084236494460683919<21> × 4774169927874534851454587<25> × 591341586048224919172763165890903<33>
6×1082+7 = 6(0)817<83> = 821 × 2099 × 326592148199<12> × 20234003509417661095198607<26> × 5268756094296001343414019528487801774081<40>
6×1083+7 = 6(0)827<84> = 44257550537<11> × 16439582756404765583886502633<29> × 824656498495778819328487299653463259463221367<45>
6×1084+7 = 6(0)837<85> = 132 × 61 × 181 × 191 × 1286983 × 13081271466870965349121825716736306322297889012098897771447898368946311<71>
6×1085+7 = 6(0)847<86> = 1002809 × 646263360161<12> × 92581346539308453192519644932096365394857389980930736378852686091743<68>
6×1086+7 = 6(0)857<87> = 7643 × 1209351174553<13> × 2973770932078747623997<22> × 21828678679235618972474638200260884422113067238289<50>
6×1087+7 = 6(0)867<88> = 312 × 83 × 3323473 × 45591841696771091<17> × 496444243731213032623888357592389796431090239865700079122623<60>
6×1088+7 = 6(0)877<89> = 223 × 1543 × 174373490579472171444015937737038963756469983056709165361287341356451383217714021663<84>
6×1089+7 = 6(0)887<90> = 19 × 157 × 199 × 24593 × 65322839 × 629170511364221670694393915388962319777274801612561613739015380586514673<72>
6×1090+7 = 6(0)897<91> = 13 × 857 × 55031119813824061<17> × 237259263206669730062293<24> × 41247302194496926985670125516471012929924724699<47>
6×1091+7 = 6(0)907<92> = 43 × 127 × 948370613 × 2408835000055147304507<22> × 4809433597732420760921554026534822027678205836594058990957<58>
6×1092+7 = 6(0)917<93> = 17 × 23 × 1740689 × 93044027 × 428121805541447492708792000594941<33> × 22130817719931540658054315210254452237508799<44> (Makoto Kamada / msieve 0.83 / 14 minutes)
6×1093+7 = 6(0)927<94> = 2503 × 9431197 × 2882011837<10> × 109520272221985913<18> × 340974271518853605551609693<27> × 2361629141652282450174736296469<31>
6×1094+7 = 6(0)937<95> = 353 × 152083 × 1034123 × 1080746099294760800501838781944914081181596051237101330373844565968086001971559991<82>
6×1095+7 = 6(0)947<96> = 3620164495193<13> × 409250915825321<15> × 404979729270243208306970640482426853068884295817370238518110866469319<69>
6×1096+7 = 6(0)957<97> = 13 × 244239867677743627<18> × 28756980835101615572027064493089709<35> × 65712509692929665288626202307118445254839373<44> (Makoto Kamada / GGNFS-0.70.8 / 0.29 hours)
6×1097+7 = 6(0)967<98> = 1307 × 17231 × 153887 × 9261429562719217979<19> × 10727002677617171773876969<26> × 174263659558134791537877956937023153550583<42>
6×1098+7 = 6(0)977<99> = 965393282677<12> × 2467836249001<13> × 251843437557084610803925643474306154861835726602684996470023236366508774291<75>
6×1099+7 = 6(0)987<100> = 575987 × 142305857 × 141730909753<12> × 44085013092445747<17> × 782255816805778261923871<24> × 14976538375068085340907968227990393<35>
6×10100+7 = 6(0)997<101> = 67 × 47911 × 1131707956861<13> × 16516074863655088332511280544105970849272263247792245807584958716323559409211646951<83>
6×10101+7 = 6(0)1007<102> = 71 × 8450704225352112676056338028169014084507042253521126760563380281690140845070422535211267605633802817<100>
6×10102+7 = 6(0)1017<103> = 13 × 31 × 84229241 × 359188923630123761<18> × 1155515355091075669<19> × 88535722742346450703454489<26> × 4810233109850207171319291017609<31>
6×10103+7 = 6(0)1027<104> = 13898725301<11> × 1274634293942717<16> × 3386808803258319200041713659614439132045571646927340938604254222100640852860071<79>
6×10104+7 = 6(0)1037<105> = 8629566092175419113<19> × 312703414298744945585964596618843105759<39> × 222346177668355476515021026054869613681073668721<48> (Sinkiti Sibata / Msieve v. 1.26 for P39 x P48 / 5.54 hours on Pentiu3 750MHz, Windows Me / October 11, 2007 2007 年 10 月 11 日)
6×10105+7 = 6(0)1047<106> = 47 × 105057221 × 154103230254811<15> × 22932868516167111539<20> × 343840761914218639605270698796545153481252440244853113296873909<63>
6×10106+7 = 6(0)1057<107> = 660354883413107731466749453206421<33> × 90860235166103760559298389079671871752970399872818769276787670766575373867<74> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / October 11, 2007 2007 年 10 月 11 日)
6×10107+7 = 6(0)1067<108> = 19 × 31578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421053<107>
6×10108+7 = 6(0)1077<109> = 13 × 172 × 292 × 1033 × 40697 × 565461449598559<15> × 585412295097782251565954143<27> × 136454071993896072257680312646939448233341474865210603<54>
6×10109+7 = 6(0)1087<110> = 97 × 113 × 421 × 126233 × 2307850135449284867849961733022761<34> × 44631190303135651102220940770960015737268303350902756015757068619<65> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3331727894 for P34 / October 3, 2007 2007 年 10 月 3 日)
6×10110+7 = 6(0)1097<111> = 907 × 519349 × 51668763745561<14> × 24652251691447635748360840959588991742155253060036734783122047278188858370891012873928809<89>
6×10111+7 = 6(0)1107<112> = 35051 × 631227249234675673259<21> × 2147754284301416278826847601681<31> × 126264279537185088818990156269263499590204974826899642383<57> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3297505446 for P31 / October 3, 2007 2007 年 10 月 3 日)
6×10112+7 = 6(0)1117<113> = 43 × 42037675529382231904791550999<29> × 14936485810428385363892834492251<32> × 2222264100043128899370105966054617650050692155163401<52> (Robert Backstrom / GMP-ECM 6.0.1 B1=87500, sigma=730686625 for P29 / October 11, 2007 2007 年 10 月 11 日) (Robert Backstrom / Msieve v. 1.28 for P32 x P52 / October 11, 2007 2007 年 10 月 11 日)
6×10113+7 = 6(0)1127<114> = 1384215170113<13> × 17932606117040429<17> × 3164675015991183313<19> × 580795039765962377462232524578013<33> × 13150801402073216131757713374329839<35> (Makoto Kamada / Msieve 1.28 for P33 x P35 / 1.1 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / October 11, 2007 2007 年 10 月 11 日)
6×10114+7 = 6(0)1137<115> = 13 × 23 × 294199 × 314707 × 2354837 × 13963735493801662655038504422019<32> × 6591283660858015718799436869882276779748116589270476529805242367<64> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 1.60 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / October 12, 2007 2007 年 10 月 12 日)
6×10115+7 = 6(0)1147<116> = 167 × 49531 × 3261899 × 654526358807<12> × 127057720792461074237899253<27> × 932609489502919662147480293<27> × 28672076170935576604150277447855760503<38> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1751136893 for P38 / October 4, 2007 2007 年 10 月 4 日)
6×10116+7 = 6(0)1157<117> = 1433 × 4260569836341526184189932091009434032922764443<46> × 98273714505283129560284285927238795172266087521311216860992588389453<68> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 2.17 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / October 12, 2007 2007 年 10 月 12 日)
6×10117+7 = 6(0)1167<118> = 31 × 2602909783189<13> × 761007481197519851161967935908199514911<39> × 97710562768479463816800500502385687103003804418987111582005841643<65> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 2.20 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / October 12, 2007 2007 年 10 月 12 日)
6×10118+7 = 6(0)1177<119> = 547 × 22157 × 1389121260658598425015693430507<31> × 3563795770363790821874783279229655889340489088375678789667004423756560940534265219<82> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=522870328 for P31 / October 4, 2007 2007 年 10 月 4 日)
6×10119+7 = 6(0)1187<120> = 5923 × 6104077523<10> × 231169767641248649<18> × 71789088746775663738962355886473233275104880922024917361381233516605740920802404266204967<89>
6×10120+7 = 6(0)1197<121> = 13 × 51907 × 4081342551264929<16> × 7645475170771717<16> × 27745952197849913<17> × 971436662429574307<18> × 10572076958192710026894382283226404875642575209479<50>
6×10121+7 = 6(0)1207<122> = definitely prime number 素数
6×10122+7 = 6(0)1217<123> = 89 × 11324894969<11> × 595287907937494370994313973199783519642030692233233226118995513431437496183483777687957175981232128527877109527<111>
6×10123+7 = 6(0)1227<124> = 29599 × 44276447 × 94785961 × 94030172640398981783628806147<29> × 294564344205934739410460391310452991<36> × 1743853595781557178934439081632632390427<40> (Makoto Kamada / Msieve 1.28 for P36 x P40 / 5.1 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / October 11, 2007 2007 年 10 月 11 日)
6×10124+7 = 6(0)1237<125> = 17 × 32141 × 2395941097286059<16> × 185276137155292873<18> × 247370165559100534333875765754251184397696303382907109936597427062208383839050640961233<87>
6×10125+7 = 6(0)1247<126> = 19 × 91943 × 343462225165820700124848518847775824495382436601166512204071515704524027186179995958594483882176428530949094891171131771<120>
6×10126+7 = 6(0)1257<127> = 13 × 353 × 450067 × 1476927445809203<16> × 1966966036403924233198026061443130413186668760102207906907152871089101717620777160156115645881441992363<103>
6×10127+7 = 6(0)1267<128> = 197 × 9720031 × 266168660299<12> × 3583617409332378966987419272264607655669797<43> × 32850260496263134596383389203484134247046587543608521946389524867<65> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 5.28 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / October 12, 2007 2007 年 10 月 12 日)
6×10128+7 = 6(0)1277<129> = 83 × 8699 × 7671569 × 874729021702702382808042889<27> × 123835766281642160716390684992072551487581674041827416419198288771251077509467115913506431<90>
6×10129+7 = 6(0)1287<130> = 109 × 1707274519<10> × 8462035003399<13> × 3810189504834212133480300072234693542750393708193406245365027111585522371594430393229161295758752560006883<106>
6×10130+7 = 6(0)1297<131> = 1294065035287<13> × 46365521333085933642743339436980199052813974586557304899021596309478218657827928443490774431377900368194819972342492561<119>
6×10131+7 = 6(0)1307<132> = 269 × 47659 × 261757 × 178795152596685422443546662136171916524628935206625955055502605816827185441824975919675667565824611566077893146372404381<120>
6×10132+7 = 6(0)1317<133> = 13 × 31 × 59 × 2090009 × 148913261947<12> × 1983329501828473727548585254782922572449329984672734213<55> × 408806495210391060163003461145989705978462625906890077609<57> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 7.78 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / October 13, 2007 2007 年 10 月 13 日)
6×10133+7 = 6(0)1327<134> = 43 × 67 × 127 × 5332753 × 69625163173<11> × 37846168211569<14> × 12102745821141977<17> × 964230242425944265707191283071326618862810503137224231251303744715178672334288013<81>
6×10134+7 = 6(0)1337<135> = 193 × 863 × 23603 × 100586824269101<15> × 16080745011300179212403283434151191<35> × 94355816472667095064977591820097467102390568492729306979142286831385089101801<77> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 5.83 hours on Core 2 Duo E6300 1.83GHz, Windows Vista / October 13, 2007 2007 年 10 月 13 日)
6×10135+7 = 6(0)1347<136> = 2699 × 3418033 × 149900794357<12> × 4338785500770170432459336295952156124948843133536921522475434120937235870774872078708901658644375397702018392316753<115>
6×10136+7 = 6(0)1357<137> = 23 × 29 × 71 × 14479 × 151767013842881<15> × 1158168948961393657<19> × 5164693661409462950941<22> × 85644837827449824843115921<26> × 1125468735569574499089562164457759100973418686937<49>
6×10137+7 = 6(0)1367<138> = 1907 × 2442939067<10> × 2648952475918503289210280331721<31> × 48619865802990135250155684578826868952543880444606150618159122460305331077521458652851641803343<95> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1042357332 for P31 / October 4, 2007 2007 年 10 月 4 日)
6×10138+7 = 6(0)1377<139> = 13 × 8786475728072227386487041599685529123701731718444931<52> × 52528280487235138475680678891847720293425922478509734700005290994634833797311729822369<86> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 6.79 hours on Cygwin on AMD 64 3200+ / October 12, 2007 2007 年 10 月 12 日)
6×10139+7 = 6(0)1387<140> = 383 × 45821 × 46040069 × 326628229 × 69754537981<11> × 2361569787997263997<19> × 1380145840089929495385570317802057204845682330870991559375128906205892605463222976990157<88>
6×10140+7 = 6(0)1397<141> = 17 × 25765322537<11> × 29151135776457323<17> × 6123908191785128062611453979386707666992816396823857<52> × 7673307351852464227438937019759901799643665911557369118867853<61> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 6.19 hours on Core 2 Quad Q6600 / October 13, 2007 2007 年 10 月 13 日)
6×10141+7 = 6(0)1407<142> = 929 × 354874528087<12> × 12214942821740613244063<23> × 1489941682121143839564261158856376527008667789411446331017207080072538446659183701214346429661417181098543<106>
6×10142+7 = 6(0)1417<143> = 33644756517101<14> × 8641435049825201314391470051<28> × 21643763371002936526145083831<29> × 9534879599089550269036402904750689858513859097873661158547832822238665447<73>
6×10143+7 = 6(0)1427<144> = 19 × 43592813251279719249310489<26> × 724407190386915779189861829436160781145141087919370177233761215936470204843140459625954837001793266584748284154980677<117>
6×10144+7 = 6(0)1437<145> = 13 × 61 × 6217 × 17996214744046724344420417956846958165765495333<47> × 67626362611447967176376164281940047499923797596474846813424537050089499416597128887441863259<92> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 7.95 hours on Cygwin on AMD 64 3400+ / October 13, 2007 2007 年 10 月 13 日)
6×10145+7 = 6(0)1447<146> = 163 × 3919572055477532086753025839329335485817252963822084748594102007<64> × 93912844131744392068992466757974562467028071947951869170587151041083038337579227<80> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / October 12, 2007 2007 年 10 月 12 日)
6×10146+7 = 6(0)1457<147> = 4357 × 11418173072097254220419104341228272288444055633023768296587371<62> × 12060548760877474653322042621937488929340653264886088872424357570501388208759630481<83> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 14.29 hours on Cygwin on AMD XP 2700+ / October 14, 2007 2007 年 10 月 14 日)
6×10147+7 = 6(0)1467<148> = 31 × 74460874157397706814885857<26> × 3757810852757300286714196049398151<34> × 691713910870677076891814665811219671401933953308716939722566516154829814248796350852671<87> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 13.31 hours on Core 2 Quad Q6600 / October 18, 2007 2007 年 10 月 18 日)
6×10148+7 = 6(0)1477<149> = 4549 × 787609 × 12956873023<11> × 9540749344069170990484839035782631826167<40> × 135469633078895411887709169907086398273346654936908113597527218378494142638547322866052347<90> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.28 / October 14, 2007 2007 年 10 月 14 日)
6×10149+7 = 6(0)1487<150> = 25747 × 436150417 × 2488433141<10> × 314768938357<12> × 288204824127944521231161772400113432086544229<45> × 236684181525452140035337569045008331845614114346156387833169766487401841<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 11.33 hours on Core 2 Quad Q6600 / October 18, 2007 2007 年 10 月 18 日)
6×10150+7 = 6(0)1497<151> = 13 × 1021 × 51377866217<11> × 38690659722181<14> × 13553397374370467<17> × 75896163172818350563639937211446513525782697<44> × 221071096062905112755419151133504653865878416206951105384644033<63> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs for P44 x P63 / 19.13 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / October 14, 2007 2007 年 10 月 14 日)
6×10151+7 = 6(0)1507<152> = 47 × 5011 × 52900231 × 1576110637<10> × 556773584791355717<18> × 67642040010577081460933<23> × 81131480570091755909002159185243049529697458062736962772191782449522056682821188277358513<89>
6×10152+7 = 6(0)1517<153> = 1840685266806508095129806305318544351784701<43> × 325965557947322722135583311765356705447166321685192963549916970963466614546316438202055770474848508291355137107<111> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 20.05 hours on Core 2 Quad Q6600 / October 12, 2007 2007 年 10 月 12 日)
6×10153+7 = 6(0)1527<154> = 617 × 116959 × 136501 × 1281706931<10> × 48960944861<11> × 9706397746413154942816285850965437463266938427148677567450081254538625255697920228419644778528906240803146393245767461259<121>
6×10154+7 = 6(0)1537<155> = 43 × 131 × 563 × 3697 × 26171 × 101833 × 176066677 × 33378076676768419<17> × 326743022684683871721997154450382375174342428549972196611943834276754091537372975979834494605779073733793368321<111>
6×10155+7 = 6(0)1547<156> = 30253 × 8290186057<10> × 93174093649657<14> × 47369174977499761<17> × 7846580404504329797862521<25> × 11519704348754539604022205034624081555611<41> × 5996609457515185443760101854342559834794121041<46> (Sinkiti Sibata / Msieve v. 1.28 for P41 x P46 / 5.66 hours on Cerelon 750MHz, Windows 2000 / October 11, 2007 2007 年 10 月 11 日)
6×10156+7 = 6(0)1557<157> = 13 × 17 × 599 × 1313827 × 8377112000507<13> × 4118126183757539249516328423677924947386661909125264987502390387259118978508173688739888706726161162250130031760472174392482315204597<133>
6×10157+7 = 6(0)1567<158> = 29575545858739133328361799<26> × 909973554507637615273149646490856241896005712528152743<54> × 2229408796486527839879415799102804165173602971152320543487096830961582839982551<79> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 31.18 hours on Core 2 Quad Q6600 / October 20, 2007 2007 年 10 月 20 日)
6×10158+7 = 6(0)1577<159> = 23 × 353 × 29401 × 13037886666029<14> × 192787736939975697014415352352241238041823265936318055683277403820606339025083974887377475530853350359199599690541467302596538828107190557<138>
6×10159+7 = 6(0)1587<160> = 3256824485114773<16> × 461870997793807749890033<24> × 3988744362838528649608020617147188217861829995936160905676737892791518622532653948351500885921779036841237718725002869723<121>
6×10160+7 = 6(0)1597<161> = 4229 × 482513 × 19099104039013<14> × 2891475901086594031773677024975431<34> × 532441594081401683367165802963920698884830621397625778059323292338660459693626121501287829706854904467897<105> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=3219074435 for P34 / October 13, 2007 2007 年 10 月 13 日)
6×10161+7 = 6(0)1607<162> = 19 × 9857893 × 3203417542513501884386343751998632226133814535055417281520396637336300224761918938298584964513101062105365987597851525515751959529175998199722053341312121<154>
6×10162+7 = 6(0)1617<163> = 132 × 31 × 20563 × 655103 × 14044633 × 2253685369002830003<19> × 97922689079135641938337<23> × 233850288407644268921831<24> × 753662499492278242063877<24> × 155634172304773061490196805203509441649383335703359557<54>
6×10163+7 = 6(0)1627<164> = 4862730147235601142936793501<28> × 12338747613644409159893433799684073847193066197154781962901756043716970052209745162253613944562232213904638320310642873228544740813195507<137>
6×10164+7 = 6(0)1637<165> = 29 × 127031 × 1770843922137685855971883220866292296403759900031873711559753<61> × 91973613665363851062774584215016713526677170996970636469854370682108828520625054063548519257625981<98> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.28 / October 16, 2007 2007 年 10 月 16 日)
6×10165+7 = 6(0)1647<166> = 179 × 359 × 26187244226761893400549<23> × 3565446894909933020524216172376347819304738872207309491635929705904188865649502859437853420976844857453693253629308940681374317488695323263<139>
6×10166+7 = 6(0)1657<167> = 67 × 89 × 10062049304041589803790038571188998826094247861814522891162166694616803622337749454972329364413885628039577393929230253228240818380010062049304041589803790038571189<164>
6×10167+7 = 6(0)1667<168> = 157 × 30141491732912660764138607233343720887304110987<47> × 126790541251891655395868197515952259522258968043055404184000880238481113593670765322134091338218303304135490412872342073<120> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.28 / November 2, 2007 2007 年 11 月 2 日)
6×10168+7 = 6(0)1677<169> = 13 × 162683 × 1905773 × 92496541056236438247583376263031<32> × 1737404675144043985388097795414143<34> × 9263350086582064127298447027451667014374897979566099083674205980098110320670551785060577237<91> (Robert Backstrom / GMP-ECM 6.2.1 B1=226000, sigma=3867865071 for P34, GMP-ECM 6.2.1 B1=226000, sigma=3867865071 for P32 / July 1, 2008 2008 年 7 月 1 日)
6×10169+7 = 6(0)1687<170> = 83 × 227 × 3011 × 1057636780066423467789698303996574949051432894241909841012337491684991839715286999170865646266927322426266014581885068691129182559054780138378023393550647255200757<163>
6×10170+7 = 6(0)1697<171> = 7949 × 460073 × 2163987266008573<16> × 54259207804217377507164325108667689661711419580711023<53> × 1397281332661513419734474128891275205904136412680671506450765242423612261405435404496170098729<94> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 35.86 hours on Core 2 Quad Q6700 / September 8, 2009 2009 年 9 月 8 日)
6×10171+7 = 6(0)1707<172> = 71 × 59218811 × 474552042132264250970127542339833<33> × 3007110393444661684023615721112945500024818563987365700417287479523557838981587406237779335223878760263992906197715985864050125259<130> (matsui / GGNFS-0.77.1-20060513-prescott snfs / 263.39 hours / June 5, 2008 2008 年 6 月 5 日)
6×10172+7 = 6(0)1717<173> = 17 × 16567 × 2986223 × 2612696322781<13> × 27305321012217023351802495384824876436124320021010604434689741263485710169980818357736740790261167875826658097208285298134668472026043677560241813051<149>
6×10173+7 = 6(0)1727<174> = 503 × 12641 × 55614277 × 1319027733109<13> × 284463259801367<15> × 160651840224481703<18> × 28148141420097158589187358878229266603272406253384954285917287167661149735864217715878968895576824795445501232554313<116>
6×10174+7 = 6(0)1737<175> = 13 × 2938517 × 48705822565039097<17> × 51558263803061540107128040800077810447132923147971269<53> × 62546141630142688721859625720172802775487443687178653795039661264814513896323199982417191538910019<98> (Warut Roonguthai / Msieve 1.47 snfs / September 21, 2011 2011 年 9 月 21 日)
6×10175+7 = 6(0)1747<176> = 43 × 127 × 5857 × 369029 × 497754530654158898262482918388193<33> × 10212407401770974562203373259905645116915575153544103149285082741091258068049866810239921241211727728204394618259915974357728769903<131> (Ignacio Santos / GMP-ECM 6.2.3 B1=3000000, sigma=946743402 for P33 / June 7, 2010 2010 年 6 月 7 日)
6×10176+7 = 6(0)1757<177> = 149 × 230266112072425854835615673997286041414191311<45> × 17487790979496472353574388242068301111731661211926813193993672549877478287762758543465832179237070194085811306528123110099573405413<131> (matsui / GGNFS-0.77.1-20060513-prescott snfs / 252.84 hours / June 24, 2008 2008 年 6 月 24 日)
6×10177+7 = 6(0)1767<178> = 31 × 10163 × 37889 × 1055726003533<13> × 137957768547432597600421483945944484145457751898950245102953<60> × 3451096537458573746877784904719289281833843474701496376345681098244629876207369940038932275181879<97> (Robert Backstrom / Msieve 1.44 snfs / January 16, 2012 2012 年 1 月 16 日)
6×10178+7 = 6(0)1777<179> = 65436008381<11> × 270079319397521079231699103763149<33> × 3395026124561532305221449613632037781211754859929786635535396542181035536197808417011117419669125188507000441962994625579397684755006303<136> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3025977912 for P33 / October 8, 2007 2007 年 10 月 8 日)
6×10179+7 = 6(0)1787<180> = 19 × 191 × 165334802976026453568476164232570956186277211352989804353816478368696610636538991457701846238633232295398181317167263709010746762193441719481950950675117112152108018737944337283<177>
6×10180+7 = 6(0)1797<181> = 13 × 23 × 113398657 × 176958794424761339205024601465906072706931334230674254182415421427963356652734494231367936195736374372873837190972875354500561164547302062753989291278920271846413436624149<171>
6×10181+7 = 6(0)1807<182> = 91807 × 500873 × 410017432524380165263628364615764230851743814725679469252361<60> × 3182332185507896285509820418496848430448675599100716022605720663029243697716260322491423099353138680884612531017<112> (Robert Backstrom / Msieve 1.44 snfs / February 2, 2012 2012 年 2 月 2 日)
6×10182+7 = 6(0)1817<183> = 152063 × 165283412363<12> × 70366264293028415911<20> × 866000074200019132192754269<27> × 391756310745498438738510736116586428197746803401800983167145001545777900416713425537774863848865123883901866151264336417<120>
6×10183+7 = 6(0)1827<184> = 4646109535270935651861373920553944113<37> × 1291403044730436574664225203953221354301912479271324672689780038042977651172600578097674193944368819808698887156719580132180993397271065994090189239<148> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=3000000, sigma=1341276002 for P37 / October 13, 2007 2007 年 10 月 13 日)
6×10184+7 = 6(0)1837<185> = 265726569991362252967<21> × 222834435050292754160574629069<30> × 131935204767316660471140556311202389169<39> × 2119070511668868360781759359292368903619451<43> × 3624331062217507668366103060087084969379043502436192911<55> (Makoto Kamada / GMP-ECM 6.1.3 B1=50000, sigma=1469781093 for P30 / September 29, 2007 2007 年 9 月 29 日) (Robert Backstrom / Msieve 1.44 gnfs for P39 x P43 x P55 / May 25, 2012 2012 年 5 月 25 日)
6×10185+7 = 6(0)1847<186> = 9109 × 486119 × 10533650783<11> × 7198232528923<13> × 6020878659975871147<19> × 57715737637649789572192595701<29> × 15856940822896359383771402356889784989979289<44> × 324309472250677628769264887001027044666888119049640084725461111<63> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs, Msieve 1.28 for P44 x P63 / October 16, 2007 2007 年 10 月 16 日)
6×10186+7 = 6(0)1857<187> = 13 × 2543 × 100699 × 78249506389201880801134777<26> × 323264810356988131992461527949813501328632517243183249085555519722893<69> × 71251882380162027040770852139908078618182136926303527150277099348190087274606318507<83> (Dmitry Domanov / Msieve 1.50 snfs / August 25, 2014 2014 年 8 月 25 日)
6×10187+7 = 6(0)1867<188> = definitely prime number 素数
6×10188+7 = 6(0)1877<189> = 17 × 199 × 257 × 3463 × 16649 × 96059 × 61883693 × 90624285000529213<17> × 454041790607190733<18> × 517371257791985827755390629<27> × 3525119596170058088736272803183372325772469391249<49> × 26831479803562967544394299568098567920660248574603957<53> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P49 x P53 / 6.98 hours on Cygwin on AMD 64 3200+ / October 15, 2007 2007 年 10 月 15 日)
6×10189+7 = 6(0)1887<190> = 6209183697097282695749827<25> × 84650755361806968467920668269<29> × 4062121527632102156060091728424317<34> × 1680909826812190287292239045721606212547297<43> × 1671816379013681629754808124264716372502592202633848031929461<61> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=1415196895 for P29 / July 12, 2008 2008 年 7 月 12 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=249225484, Msieve 1.47 gnfs for P34 x P43 x P61 / April 8, 2011 2011 年 4 月 8 日)
6×10190+7 = 6(0)1897<191> = 59 × 353 × 1103 × 7573 × 127271 × 33951908294718475771806931750360129453<38> × 4287985150835009147240230901276407666355812535398225891776259<61> × 18613761531501886916940212646954689821596504368526684251366135903378899692367<77> (Robert Backstrom / Msieve 1.44 snfs / March 5, 2012 2012 年 3 月 5 日)
6×10191+7 = 6(0)1907<192> = 1586857 × 8577215265242096701<19> × [44082594640568368454294015955624041418396330514721274542463248405699515720176035007651007899202436324127702258978496687305094052765765497688323437692609397280932236251<167>] Free to factor
6×10192+7 = 6(0)1917<193> = 13 × 29 × 31 × 3208007417<10> × 15475455343<11> × 310826606681<12> × 40049826089950582237612221318425371<35> × 10102569630990212054844298716593986140238949067257353<53> × 82227811572357690683721133099265358362960911903422547606796172190078277<71> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=407467275 for P35 / October 9, 2007 2007 年 10 月 9 日) (Tyler Cadigan / GGNFS gnfs, Msieve / 74.14 hours on C2Q Q6600 2.4 Ghz, 4 gb RAM, Vista / May 28, 2008 2008 年 5 月 28 日)
6×10193+7 = 6(0)1927<194> = 9431867921209970677263227064224760463<37> × [6361412235753920282712594389572541485300199982510262458997768914548898435588007324833733189857362507423842664895526461468007039663923961796686299905053607689<157>] (Jo Yeong Uk / GMP-ECM 6.1.3 B1=3000000, sigma=177507791 for P37 / October 13, 2007 2007 年 10 月 13 日) Free to factor
6×10194+7 = 6(0)1937<195> = 4880807929<10> × 126110244771031557278809682152871<33> × 974785733093042308010396782144898734663233985206820852016727149290684723767326775717208198754930119035872196205293376228506927605092858346962533362269673<153> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1132209484 for P33 / October 23, 2008 2008 年 10 月 23 日)
6×10195+7 = 6(0)1947<196> = 1800916057<10> × 3331637794376109557892625308520973445904480599564113942485660229748287485006304211101828162554941337834937189412821144056244038474914880499618978076555624824438999379747326002102495552351<187>
6×10196+7 = 6(0)1957<197> = 43 × 263 × 755230781 × 730736822099071379653153<24> × [9613607166989736134299362490031666760532613019805236282573225766833897002722570685520499776745706723160946243107556688566855696310017420714882290020460831410911<160>] Free to factor
6×10197+7 = 6(0)1967<198> = 19 × 47 × 26693 × 28697 × 45083 × [19455979469469794253772848516128838861610097206592201868555527257136441631155698516622220345713779394865237964580168303704305679589414854258492007128363638789307445084309063710662493<182>] Free to factor
6×10198+7 = 6(0)1977<199> = 13 × 5936837 × 1592801512885567<16> × 31002981535411234004171<23> × 335224324447072705491257699413<30> × 5578023513293801818533172337270300793467390504065490987063639<61> × 841921861803218150630322445765550878314463032851719559505591353<63> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3102473160 for P30 / October 10, 2007 2007 年 10 月 10 日) (Erik Branger / GGNFS, Msieve gnfs for P61 x P63 / 105.45 hours / October 3, 2009 2009 年 10 月 3 日)
6×10199+7 = 6(0)1987<200> = 67 × 4027 × 21414629 × 822758849778409381339<21> × [12621521194104600741672319701369468179803954538245274390523021268457371223901198823700830829932612854216290231478862756042220252177081936177877550566997746016108130033<167>] Free to factor
6×10200+7 = 6(0)1997<201> = 25080527931514001037989<23> × 23922941400531381951968563140550725020695739263155141138555507842257974585574379366739574350458731349789471528006653290171558403658459934378875564774015248128689303475832017890363<179>
6×10201+7 = 6(0)2007<202> = 414607 × 4911451 × 2565569261<10> × 1148473717855759047193417603827629995056879294251054197892601657621212819177686162126963507258283811071366829257519671314883142661552539226132389244787764095141764354346017643345591<181>
6×10202+7 = 6(0)2017<203> = 23 × 81017 × 13287941 × 50135752524495184541457597901358271437<38> × 48332808063008793678040931825323467980849094936043097165539122607616056747712751607212659251160353111512279211719189440972973326590999144764412511768281<152> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2171463521 for P38 / December 24, 2012 2012 年 12 月 24 日)
6×10203+7 = 6(0)2027<204> = 852227148677<12> × 7763047107227<13> × 7286361543699457642828310033<28> × 1022383201200087451374353785341135857<37> × 80575352925971965921427696854895450124272565139<47> × 151090453804326234977595485114149605132969713693416689943631794485787<69> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3776163958 for P37, Msieve 1.50 gnfs for P47 x P69 / December 18, 2012 2012 年 12 月 18 日)
6×10204+7 = 6(0)2037<205> = 13 × 17 × 61 × 337 × 607 × 96749 × 178873 × 72335884166029747<17> × 1738062861490895053616374174967781017249582864502393343252558327663325944014714140620588291810536965643694006671513149319261940002298252907006229673101085055311097923807<169>
6×10205+7 = 6(0)2047<206> = 97 × 887 × 95566159390651<14> × 18703363909450595588264733943<29> × [390150384603197270344650340341447864236216583062762717193869527839662085793894520825715316592236137995454193477959232073138116267015487072844569237969001036341<159>] Free to factor
6×10206+7 = 6(0)2057<207> = 71 × 817549 × 134683583927<12> × 53998891706178162221<20> × 47610942844035418799767878506723<32> × 214248538984621315264600790146421585817776256097422353<54> × 139333308068327076745152855141688734786907019507601272338989134167149767438777264021<84> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2750254752 for P32 / December 9, 2012 2012 年 12 月 9 日) (Erik Branger / GGNFS, Msieve gnfs for P54 x P84 / June 10, 2014 2014 年 6 月 10 日)
6×10207+7 = 6(0)2067<208> = 31 × 56131 × [3448154978474892546870483276161008148564906632583570346097062114489089750301857233740656218373953556800594921672286201460753387381246979272565731891008418670379946450153184284918747101394721219543452787<202>] Free to factor
6×10208+7 = 6(0)2077<209> = 1361 × 12129445907<11> × 459964681427<12> × 518300672415152028484941321220462541<36> × [15245648599331745996592669058192303775404127483645189850208123485460061508422522365017347561080246123829808723068874580567406563796796910945663050363<149>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3290846248 for P36 / December 9, 2012 2012 年 12 月 9 日) Free to factor
6×10209+7 = 6(0)2087<210> = 547 × 1922631220291<13> × 1137782236873007657<19> × 400383677009794676198927<24> × 1252369322730719012496031967746390451357399713069074212597733534232116278240760276830597526638212616546317462871082607333232447378957465316454363905070969<154>
6×10210+7 = 6(0)2097<211> = 13 × 83 × 89 × [62479824223427851422977996688569316158323874582166175505826243608834647145192698191209088731763701304786995865918297216523830846289219106330247524236965146671387364496881215440847226416469681665295581635097<206>] Free to factor
6×10211+7 = 6(0)2107<212> = 6271 × 47507 × 2700722009<10> × 10200192133<11> × 466996005461<12> × 604218727370352499<18> × [25909632908178474788170026327228499646822068320556771863929438642458586865958994142627553190505332362850682781361709227017992018711003629202247541890369457<155>] Free to factor
6×10212+7 = 6(0)2117<213> = 1009 × 812910769980379485527556805056653816857468935193<48> × 923330060391395106505455028152903016611472017509<48> × 792246322329103629918165113152644125975451873624978684434629022673568292359875075872501712351503519665955525876579<114> (Bob Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs for P48 x P48 x P114 / August 22, 2017 2017 年 8 月 22 日)
6×10213+7 = 6(0)2127<214> = 11286945642610565012077<23> × 51904770484189620272332488299040351849739<41> × 10241593680731073914768693592931524253818351593487071070786676884899904514228176170513082814256766909591335312479063399953860159681764172622183489244969<152> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1221369521 for P41 / December 24, 2012 2012 年 12 月 24 日)
6×10214+7 = 6(0)2137<215> = 16462483 × 1064190773<10> × 224169297701133267488782110609739503721459<42> × 15277781361018441124375624146465387618855785337429955487895956210453400296039352104145108682713334481495020520140186223409811186730746406204198344443428871347<158> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3648055923 for P42 / December 17, 2012 2012 年 12 月 17 日)
6×10215+7 = 6(0)2147<216> = 19 × 53879304247301227942991396484650214719<38> × [586105329487487161032960042648692907094274529788277892344806774310822702739658960881828060078278700368010611814998198163032257498205100984287431124391794195381469811666140899587<177>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4142575193 for P38 / December 17, 2012 2012 年 12 月 17 日) Free to factor
6×10216+7 = 6(0)2157<217> = 13 × 3364259 × 22402013 × 1303317383<10> × 4292447773<10> × 4968424667<10> × [220321821558736420856749007855627485303809124653270346786657795135423060122799232531439371307606868714438408157968720999981856721520402980110695590574459371654524012646492589<174>] Free to factor
6×10217+7 = 6(0)2167<218> = 43 × 127 × 48694502340406754634991<23> × 342792070439650239645435328155049233326617<42> × 2080555677815757325673232186049060900769894783<46> × 316365438398381068745252650884577558014522141824337962356536063347602221926027411674247137627083692639987<105> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3689526990 for P46 / December 18, 2012 2012 年 12 月 18 日) (Serge Batalov / GMP-ECM B1=11000000, sigma=3420057232 for P42 / May 24, 2014 2014 年 5 月 24 日)
6×10218+7 = 6(0)2177<219> = 29332091 × 82043771 × 2285654708031821875564673827106522501<37> × 109081723307576553355581662332104290160624223603391316943975293045679941850440963532281074175630545942353405781698062711841674258515131161642654163568758333521614133587<168> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=466709234 for P37 / December 17, 2012 2012 年 12 月 17 日)
6×10219+7 = 6(0)2187<220> = 647 × 575928372225606311<18> × [16101950818533836072328102667897378264487948623875621733905720244323462457462183972671534833034594003148018104879603534264281801869817203409134944197485961203577669000786082745649418906919258837854871<200>] Free to factor
6×10220+7 = 6(0)2197<221> = 17 × 29 × 57559 × 20190468568253<14> × 54014963791343<14> × 2535157222789868830501<22> × [764760952859361435362009702598670653527978582498561913037110736580847511369419691114196148279834242349977288052975426537116098177714796363740011992223736803543018859<165>] Free to factor
6×10221+7 = 6(0)2207<222> = 113 × 5059 × 48787 × 29726072911<11> × 578957434819381<15> × 375116415835009255623456737926845795641<39> × 3332374249658153609922134497692955234002645660681724231430899736828849475976800292098305465412620107193385609553522073412170243189476382349846075493<148> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3498679683 for P39 / December 18, 2012 2012 年 12 月 18 日)
6×10222+7 = 6(0)2217<223> = 13 × 31 × 353 × 11257 × 942976676784146003462724794884297876990967<42> × 3973268201484442731602569159720445953338533020612029737863434049689424934041575421076917983616097947067723234492112226308749244586463090824989210444521083942862447846176867<172> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=665896651 for P42 / December 24, 2012 2012 年 12 月 24 日)
6×10223+7 = 6(0)2227<224> = 1693 × 2539 × 649877 × 558396953 × [38464260264253923643670869589199394140521765060733606894279283735658887122855363700938176845553595599878352574466171461005243691038322373122800987512323274778582815291473814619287695405157606744174185661<203>] Free to factor
6×10224+7 = 6(0)2237<225> = 23 × 5942047 × 80879933 × 13595793369628151011277999<26> × 3992473051496197064385254631215978415690251311519481389515673040719659174130392425134528675292254198944151405577569071946832587608182219111060427981511662144066373778263672332308983541<184>
6×10225+7 = 6(0)2247<226> = 197 × 36809 × 9516205097296570135109<22> × 828150831303911795900447<24> × 5683600212987119341680989055787745998973234519<46> × 70649083574242079453813694204868657366881701561<47> × 261473520847779881633776951390716820638872355640408542326525475199661879751288487<81> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2988265646 for P46 / December 24, 2012 2012 年 12 月 24 日) (Warut Roonguthai / Msieve 1.49 gnfs for P47 x P81 / December 27, 2012 2012 年 12 月 27 日)
6×10226+7 = 6(0)2257<227> = 163 × 31121 × 7466287 × 5799207070663<13> × [273172392424641515957960373986378714574857880328803048050509417047622836601576302364142575654341769734802018103146044966481169988779435072384118535058188430132985157327702899031322624170050162913381589<201>] Free to factor
6×10227+7 = 6(0)2267<228> = 287028083 × 16896268591<11> × [123718901509345315538494815118176601918926256776784979024066145841671332768809477243343142272102492442735465192471737473684042767434237037233060562088233734943007304707999950622185778346700545882796273321340019<210>] Free to factor
6×10228+7 = 6(0)2277<229> = 13 × 4572523 × [100937373423482295980039567113924093648416522243510101198296533781997715147969394913587430497678953509574809894130321824179241626895799439054005515453604397060777706648706094744966501325080603960119711051964427179817020393<222>] Free to factor
6×10229+7 = 6(0)2287<230> = 102972538938231708604037<24> × 147575069823312951194913072674807<33> × [3948360804214901593452136975974233553819947352293596346074851620352121459370471774262583685168456135087866656420734519922209718541992943546964380382789806954681471750398539773<175>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3970481557 for P33 / December 10, 2012 2012 年 12 月 10 日) Free to factor
6×10230+7 = 6(0)2297<231> = 592070711 × 1169265664249477155044843<25> × 1865701200420373357866856161420189969161749<43> × 464539218626977770237341002646316320492937115259604427056703551010381726477905968601925868204461149608321560607614122402647032748872460110910855607989477191<156> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2109823584 for P43 / December 17, 2012 2012 年 12 月 17 日)
6×10231+7 = 6(0)2307<232> = 12007 × 8567354997769847<16> × 171264998340487363778155627661<30> × 105660144698444301592851431955691<33> × [3223221573736952413290574710123543918778120489607199054796978108482073392537285116645957174096115495081864311517025095557122038115511669868781649847433<151>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=2472449220 for P30, B1=1e6, sigma=2240155014 for P33 / December 8, 2012 2012 年 12 月 8 日) Free to factor
6×10232+7 = 6(0)2317<233> = 67 × 3967 × 579612410769901<15> × 1906121837532791<16> × 53683493094551801461103<23> × 3520717110051958489320969319<28> × [1081070499706837295606107277227725125598481142498198156835632894422084507331509898145075612158251521538176590369094178875061662750575236581800920849<148>] Free to factor
6×10233+7 = 6(0)2327<234> = 19 × 461 × 1753 × 3331 × [11731138853172308614507737956233398617630052317471193792668978846853211795706095108301511889093642320312107460666303269001633960862964461998227270576602152598007542588007422624794953142108445755254718414708784598912283522611<224>] Free to factor
6×10234+7 = 6(0)2337<235> = 13 × 30504578426579<14> × [15130137354605026034829298757288630705729207718238286699890369222151761156809392315732667201906973412849268951752427500189078762485467988318772660041543239529491766327250727754675061122856006719212636584038442920895464241<221>] Free to factor
6×10235+7 = 6(0)2347<236> = 21937 × [2735105073619911564935952956192733737521083101609153484979714637370652322560058348908237224780051966996398778319733783106167661941012900578930573916214614578110042394128641108629256507270820987372931576788074941879017185576879245111<232>] Free to factor
6×10236+7 = 6(0)2357<237> = 17 × 6287 × 488844995696987<15> × 46486234086947775301<20> × 247037753984946030107151261022728344886099976339530643524849388465114757332250916033580823353258532624773402482716476407162479397872422117016333389421254644259969287065846196573983863630596074357759<198>
6×10237+7 = 6(0)2367<238> = 31 × 109 × 57287 × 2955581 × 46664374432449649<17> × 9684185266325924390407368599881554865321<40> × 23206816881994257570968125792371979284640138757909679074415378178154615623623334043289634787824010717546507198795459779354388018881883333285610769497310990066116599791<167> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2403327309 for P40 / December 24, 2012 2012 年 12 月 24 日)
6×10238+7 = 6(0)2377<239> = 43 × 45291822075849689770643670371<29> × [30807964291490145651610124590377676503276251059175110151017500622967766212000573106504424451017313126414726888483391045387408959810539266935031512843091539643269343175449095519243724418708088090736758121457319<209>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2485191783 for P29 / December 10, 2012 2012 年 12 月 10 日) Free to factor
6×10239+7 = 6(0)2387<240> = 116487474657259<15> × [5150768370293711851877955924656298813006501441194955169700434573058576864205097526704217182148811288311174482639101357070433866161813308445101545464716689876937095641495337565362743870016859724648066402723579740533327242693973<226>] Free to factor
6×10240+7 = 6(0)2397<241> = 132 × 166147 × 543601 × 14840089288785655879737565908187<32> × 251891245678714329222136649937577<33> × [105157973141016190495457124533964308040713855847035782049631536875164756657777525188710805635909819693293298430613365752044587545752060794831559398359644894514147351<165>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=508297748 for P32, B1=1e6, sigma=3097308511 for P33 / December 8, 2012 2012 年 12 月 8 日) Free to factor
6×10241+7 = 6(0)2407<242> = 71 × 617 × [1369644120802611454790330312507133563129180267993699637044307987307964480562467185609605770767228981669596183258383363389412650946195813454470746684319857557011436528408701805647499258109434565252128655237747391969319971694021503412696601<238>] Free to factor
6×10242+7 = 6(0)2417<243> = 61034123 × 679829526684532691465311<24> × [14460340472884442593657334399011628318860565464168508824557934914872192322180731453012528335189895435392980707834904741164209342082499484995593428392741293246808600827078601601416955047330864571543664553204837419<212>] Free to factor
6×10243+7 = 6(0)2427<244> = 47 × 1789 × 167555716039<12> × 819750796297<12> × 3288629079745983309291837019<28> × [157974527069376141799751055612107634140164012122749436961578280143307830695572920678769434003707190317094216598930480471019534670784645346949323226022459397237938015223048737284104783805977<189>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2908901572 for P28 / December 9, 2012 2012 年 12 月 9 日) Free to factor
6×10244+7 = 6(0)2437<245> = 40386578273<11> × 577528122293312700990534210121751<33> × 4719974795083528808794541428174837<34> × 76234499023890294227137520047040645453<38> × 340374848535868432207454029539906306119301643<45> × 21003533461711938728889780983716228008632490062918488191191211829675399647481127432483<86> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=1040943161 for P33 / December 8, 2012 2012 年 12 月 8 日) (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3720176197 for P34 / December 9, 2012 2012 年 12 月 9 日) (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1228133576 for P38, Msieve 1.49 gnfs for P45 x P86 / December 14, 2012 2012 年 12 月 14 日)
6×10245+7 = 6(0)2447<246> = 157 × 3253 × 1332850679124584757997<22> × 29157568050755548497587643469069<32> × 541758093322173451679049014942863<33> × 29357964319838457075067688663418022569899<41> × 1900655439582652228037706909460983682585984497283496962475640489748865941467749735530004862959711794549038569744387<115> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=2705080675 for P32, B1=1e6, sigma=4244620673 for P33 / December 8, 2012 2012 年 12 月 8 日) (Serge Batalov / GMP-ECM B1=11000000, sigma=2165118376 for P41 / November 8, 2013 2013 年 11 月 8 日)
6×10246+7 = 6(0)2457<247> = 13 × 23 × 67036471 × 691936766820634571<18> × [432615933243707421788028654742702459343224668475982802021470847935293058451800436309426393158342058441537998703795820967010657047043591688192317763905497542984876930339336245842782239949998008244807373091425218904957273<219>] Free to factor
6×10247+7 = 6(0)2467<248> = 3200140947573088733151261557163182480217373<43> × 18749174171688463297649465943132331247227466606298693493960428128728935432564985867686251170508873631143866698284356656017362433279181789782476169161740721632679624615760072999833773083738171460831355475059<206> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=4266583001 for P43 / December 24, 2012 2012 年 12 月 24 日)
6×10248+7 = 6(0)2477<249> = 29 × 59 × 36106100456477<14> × 103474902035664010282518276851560011719<39> × 93861098098549281357932681004195038364907003710031086915141086416017577137089440201659853623553116041545049930326480957506908437229223447652504481412723759800041552762094985793209777681201599899<194> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4078096456 for P39 / December 19, 2012 2012 年 12 月 19 日)
6×10249+7 = 6(0)2487<250> = 421 × 41851 × 15679779711225682681863932923<29> × 21718176490046684786589912789944844809783153399933979383239747491315415626130435792541023167329713823476103669097490831669998143275134948743699166151759109624526890927922408628612000082407965669002248694744912014579<215>
6×10250+7 = 6(0)2497<251> = 86353 × 117366302857501<15> × 5920118450137412328110189525702992983798816842958013720493123357906689998879318242124834078211724725460159115833988766117119816406987024157767309342240533911485564882588664386810602675909038682561317581225790607570218478430350015619<232>
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