Table of contents 目次

  1. About 799...991 799...991 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 799...991 799...991 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 799...991 799...991 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 799...991 799...991 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

79w1 = { 71, 791, 7991, 79991, 799991, 7999991, 79999991, 799999991, 7999999991, 79999999991, … }

1.3. General term 一般項

8×10n-9 (1≤n)

2. Prime numbers of the form 799...991 799...991 の形の素数

2.1. Last updated 最終更新日

January 30, 2016 2016 年 1 月 30 日

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

  1. 8×101-9 = 71 is prime. は素数です。
  2. 8×105-9 = 799991 is prime. は素数です。
  3. 8×1011-9 = 7(9)101<12> is prime. は素数です。
  4. 8×1012-9 = 7(9)111<13> is prime. は素数です。
  5. 8×1017-9 = 7(9)161<18> is prime. は素数です。
  6. 8×1028-9 = 7(9)271<29> is prime. は素数です。
  7. 8×1046-9 = 7(9)451<47> is prime. は素数です。
  8. 8×1048-9 = 7(9)471<49> is prime. は素数です。
  9. 8×1061-9 = 7(9)601<62> is prime. は素数です。
  10. 8×1073-9 = 7(9)721<74> is prime. は素数です。
  11. 8×10138-9 = 7(9)1371<139> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / November 29, 2004 2004 年 11 月 29 日) (certified by: (証明: Makoto Kamada / PFGW / January 5, 2005 2005 年 1 月 5 日)
  12. 8×10178-9 = 7(9)1771<179> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / November 29, 2004 2004 年 11 月 29 日) (certified by: (証明: Makoto Kamada / PFGW / January 5, 2005 2005 年 1 月 5 日)
  13. 8×10213-9 = 7(9)2121<214> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / November 29, 2004 2004 年 11 月 29 日) (certified by: (証明: Makoto Kamada / PFGW / January 5, 2005 2005 年 1 月 5 日)
  14. 8×10405-9 = 7(9)4041<406> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Makoto Kamada / PFGW / January 5, 2005 2005 年 1 月 5 日)
  15. 8×10762-9 = 7(9)7611<763> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Makoto Kamada / PFGW / January 5, 2005 2005 年 1 月 5 日)
  16. 8×101053-9 = 7(9)10521<1054> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Makoto Kamada / PFGW / January 5, 2005 2005 年 1 月 5 日)
  17. 8×101157-9 = 7(9)11561<1158> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 13, 2006 2006 年 9 月 13 日)
  18. 8×101427-9 = 7(9)14261<1428> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 8, 2006 2006 年 9 月 8 日)
  19. 8×102865-9 = 7(9)28641<2866> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Sinkiti Sibata / PRIMO 3.0.4 / January 19, 2008 2008 年 1 月 19 日)
  20. 8×103148-9 = 7(9)31471<3149> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Ray Chandler / Primo 4.0.1 - LX64 / February 7, 2013 2013 年 2 月 7 日)
  21. 8×103615-9 = 7(9)36141<3616> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by: (証明: Ray Chandler / Primo 4.0.1 - LX64 / March 31, 2013 2013 年 3 月 31 日)
  22. 8×1013447-9 = 7(9)134461<13448> is PRP. はおそらく素数です。 (Sinkiti Sibata / PFGW / January 20, 2008 2008 年 1 月 20 日)
  23. 8×1048081-9 = 7(9)480801<48082> 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 / January 29, 2016 2016 年 1 月 29 日

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

  1. 8×105k+4-9 = 41×(8×104-941+72×104×105-19×41×k-1Σm=0105m)
  2. 8×106k+2-9 = 7×(8×102-97+72×102×106-19×7×k-1Σm=0106m)
  3. 8×1015k+10-9 = 31×(8×1010-931+72×1010×1015-19×31×k-1Σm=01015m)
  4. 8×1016k+8-9 = 17×(8×108-917+72×108×1016-19×17×k-1Σm=01016m)
  5. 8×1018k+13-9 = 19×(8×1013-919+72×1013×1018-19×19×k-1Σm=01018m)
  6. 8×1022k+16-9 = 23×(8×1016-923+72×1016×1022-19×23×k-1Σm=01022m)
  7. 8×1028k+21-9 = 29×(8×1021-929+72×1021×1028-19×29×k-1Σm=01028m)
  8. 8×1028k+25-9 = 281×(8×1025-9281+72×1025×1028-19×281×k-1Σm=01028m)
  9. 8×1034k+26-9 = 103×(8×1026-9103+72×1026×1034-19×103×k-1Σm=01034m)
  10. 8×1035k+1-9 = 71×(8×101-971+72×10×1035-19×71×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 21.51%. 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 21.51% です。

3. Factor table of 799...991 799...991 の素因数分解表

3.1. Last updated 最終更新日

March 24, 2018 2018 年 3 月 24 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=189, 191, 201, 204, 206, 211, 217, 219, 221, 222, 223, 226, 228, 229, 232, 234, 236, 239, 243, 244, 245, 247, 250 (23/250)

3.4. Factor table 素因数分解表

8×101-9 = 71 = definitely prime number 素数
8×102-9 = 791 = 7 × 113
8×103-9 = 7991 = 61 × 131
8×104-9 = 79991 = 41 × 1951
8×105-9 = 799991 = definitely prime number 素数
8×106-9 = 7999991 = 967 × 8273
8×107-9 = 79999991 = 409 × 195599
8×108-9 = 799999991 = 7 × 17 × 6722689
8×109-9 = 7999999991<10> = 41 × 195121951
8×1010-9 = 79999999991<11> = 31 × 2580645161<10>
8×1011-9 = 799999999991<12> = definitely prime number 素数
8×1012-9 = 7999999999991<13> = definitely prime number 素数
8×1013-9 = 79999999999991<14> = 19 × 4289 × 981703501
8×1014-9 = 799999999999991<15> = 7 × 41 × 263 × 311 × 34079401
8×1015-9 = 7999999999999991<16> = 1675799 × 4773842209<10>
8×1016-9 = 79999999999999991<17> = 23 × 2287 × 124897 × 12177103
8×1017-9 = 799999999999999991<18> = definitely prime number 素数
8×1018-9 = 7999999999999999991<19> = 1097 × 7292616226071103<16>
8×1019-9 = 79999999999999999991<20> = 41 × 1669 × 1169094974352979<16>
8×1020-9 = 799999999999999999991<21> = 72 × 21503 × 759267572536153<15>
8×1021-9 = 7999999999999999999991<22> = 29 × 3659 × 5851 × 45949 × 280429319
8×1022-9 = 79999999999999999999991<23> = 631 × 761 × 5643857 × 29518886393<11>
8×1023-9 = 799999999999999999999991<24> = 892 × 1449911 × 69657619550161<14>
8×1024-9 = 7999999999999999999999991<25> = 17 × 41 × 4793 × 2394692642695992871<19>
8×1025-9 = 79999999999999999999999991<26> = 31 × 281 × 5279 × 9539 × 182375906036101<15>
8×1026-9 = 799999999999999999999999991<27> = 7 × 103 × 401 × 647 × 6143 × 696186429775951<15>
8×1027-9 = 7999999999999999999999999991<28> = 149 × 934484521 × 57455499755447779<17>
8×1028-9 = 79999999999999999999999999991<29> = definitely prime number 素数
8×1029-9 = 799999999999999999999999999991<30> = 41 × 19512195121951219512195121951<29>
8×1030-9 = 7999999999999999999999999999991<31> = 167 × 47904191616766467065868263473<29>
8×1031-9 = 79999999999999999999999999999991<32> = 19 × 359 × 811 × 14461757779657404573639361<26>
8×1032-9 = 799999999999999999999999999999991<33> = 7 × 750784839958567<15> × 152221659526344839<18>
8×1033-9 = 7999999999999999999999999999999991<34> = 26821 × 10457101841<11> × 28523557029547616731<20>
8×1034-9 = 79999999999999999999999999999999991<35> = 41 × 97 × 20115665074176514961025898918783<32>
8×1035-9 = 799999999999999999999999999999999991<36> = 67880932826929<14> × 11785341872653708269479<23>
8×1036-9 = 7999999999999999999999999999999999991<37> = 71 × 151 × 746199048596213039828374218822871<33>
8×1037-9 = 79999999999999999999999999999999999991<38> = 2239 × 35730236712818222420723537293434569<35>
8×1038-9 = 799999999999999999999999999999999999991<39> = 7 × 23 × 47 × 594023 × 177976635383481354116836429951<30>
8×1039-9 = 7999999999999999999999999999999999999991<40> = 41 × 419 × 547529 × 850520881595797450276840512301<30>
8×1040-9 = 79999999999999999999999999999999999999991<41> = 17 × 31 × 190529 × 11358097 × 11009437207<11> × 6371586620636063<16>
8×1041-9 = 799999999999999999999999999999999999999991<42> = 27249245278861<14> × 35397567456959<14> × 829396294603309<15>
8×1042-9 = 7999999999999999999999999999999999999999991<43> = 62355420289<11> × 128296785795400446426778473830519<33>
8×1043-9 = 79999999999999999999999999999999999999999991<44> = 27479 × 2911314094399359510899232140907602168929<40>
8×1044-9 = 799999999999999999999999999999999999999999991<45> = 7 × 41 × 117161489 × 23791575796659867978333882574698137<35>
8×1045-9 = 7999999999999999999999999999999999999999999991<46> = 8831 × 246941 × 5574659 × 47097319 × 13972444945424990795401<23>
8×1046-9 = 79999999999999999999999999999999999999999999991<47> = definitely prime number 素数
8×1047-9 = 799999999999999999999999999999999999999999999991<48> = 59 × 5801 × 1112821 × 405526799 × 844624751 × 6132342937092969881<19>
8×1048-9 = 7999999999999999999999999999999999999999999999991<49> = definitely prime number 素数
8×1049-9 = 79999999999999999999999999999999999999999999999991<50> = 19 × 29 × 41 × 34428131 × 30558252794071<14> × 3365988015361238290310101<25>
8×1050-9 = 799999999999999999999999999999999999999999999999991<51> = 7 × 233 × 97241 × 2658539176833697<16> × 1897332932889844300996750193<28>
8×1051-9 = 7(9)501<52> = 48221 × 26677546787920154045429<23> × 6218818534577130616030199<25>
8×1052-9 = 7(9)511<53> = 337 × 203969 × 2289289183<10> × 3178323848335799<16> × 159954740879521114991<21>
8×1053-9 = 7(9)521<54> = 281 × 6011 × 8437955501<10> × 321736062761<12> × 174461645974232174414899241<27>
8×1054-9 = 7(9)531<55> = 41 × 439 × 370009 × 4083097 × 124387346130881<15> × 2365175778566451733599593<25>
8×1055-9 = 7(9)541<56> = 31 × 463181 × 1285396974161<13> × 1013264190720409<16> × 4277771563314497600069<22>
8×1056-9 = 7(9)551<57> = 7 × 17 × 123669018721<12> × 54360333292502183505219244380113912722610209<44>
8×1057-9 = 7(9)561<58> = 911101 × 551882813827062449307119<24> × 15910234977365532901871647789<29>
8×1058-9 = 7(9)571<59> = 333730871 × 1565783633701658213991193<25> × 153095299166497563176949097<27>
8×1059-9 = 7(9)581<60> = 41 × 4651 × 59281 × 216829 × 326382528666337693827299007147935099725975249<45>
8×1060-9 = 7(9)591<61> = 23 × 103 × 70777087 × 163759903 × 4035985489551607103<19> × 72189672813064424616233<23>
8×1061-9 = 7(9)601<62> = definitely prime number 素数
8×1062-9 = 7(9)611<63> = 73 × 199 × 11989727 × 971207539674582700991<21> × 1006517779281554641726959085559<31>
8×1063-9 = 7(9)621<64> = 61 × 179 × 661 × 1871760833268196608149<22> × 592182141415822078693178687948812601<36>
8×1064-9 = 7(9)631<65> = 41 × 20919785872470060025360820966977<32> × 93271485859847177417170026791263<32> (Makoto Kamada / msieve 0.81 / 44 seconds)
8×1065-9 = 7(9)641<66> = 66644880098786039<17> × 12003922864204722219976697486636863671956327424769<50>
8×1066-9 = 7(9)651<67> = 33777704057965423<17> × 236842622170865054103044684831127931485869669658617<51>
8×1067-9 = 7(9)661<68> = 19 × 89 × 727720664593370519<18> × 65010225418715864344106284159765521018650193779<47>
8×1068-9 = 7(9)671<69> = 7 × 770690898889<12> × 148289949252630878778974321104809666834951929676795041417<57>
8×1069-9 = 7(9)681<70> = 41 × 3259481 × 939902008319<12> × 3608971856869<13> × 290614655588953079<18> × 60725918399552760659<20>
8×1070-9 = 7(9)691<71> = 31 × 1151 × 106024454208401<15> × 21146910345096644999228598470944171893279394404875111<53>
8×1071-9 = 7(9)701<72> = 71 × 10729 × 3621851 × 28894794847199<14> × 10035111396951100345999007745790481780041022101<47>
8×1072-9 = 7(9)711<73> = 172 × 391273 × 70747689975168179861003251590361642470234479157319312367473547903<65>
8×1073-9 = 7(9)721<74> = definitely prime number 素数
8×1074-9 = 7(9)731<75> = 7 × 41 × 26962625044119759366833<23> × 103382235276863139833918318517928986627005732022521<51>
8×1075-9 = 7(9)741<76> = 6306961 × 563587711760553941<18> × 2250651882793755714334856008817847409708892401539691<52>
8×1076-9 = 7(9)751<77> = 886868023 × 90205078912851952042925331630769598736564211426078218179256644593217<68>
8×1077-9 = 7(9)761<78> = 29 × 320941 × 1248721 × 68833740816123924171951117799540680787757002604451811504337865439<65>
8×1078-9 = 7(9)771<79> = 549874015052564724254396210642322507913<39> × 14548787142151547233300156646070128174207<41> (Makoto Kamada / GGNFS-0.70.1 / 0.06 hours)
8×1079-9 = 7(9)781<80> = 41 × 3265631 × 27965002730233229<17> × 144230033847648137089<21> × 148138672560012127132811640310939141<36>
8×1080-9 = 7(9)791<81> = 7 × 152729 × 140451137 × 175680383 × 3516616465807<13> × 137769557177099770217<21> × 62595576288885612734971553<26>
8×1081-9 = 7(9)801<82> = 281 × 599 × 1879 × 2951188939<10> × 8571030688695841716198860742889417003443178176564851093752902269<64>
8×1082-9 = 7(9)811<83> = 23 × 2729 × 21943 × 3705521 × 721209405157286611950819481<27> × 21734615003010862251049972897803349868311<41>
8×1083-9 = 7(9)821<84> = 17479720834139<14> × 106592318311181<15> × 1518615850072269680457701<25> × 282736357314082634224042281970549<33>
8×1084-9 = 7(9)831<85> = 41 × 47 × 743 × 7687 × 726879762394621211801391909089571161326438709545182340258424983318202584513<75>
8×1085-9 = 7(9)841<86> = 19 × 31 × 831191 × 9266189641<10> × 5278434208099237339320904563821<31> × 3340931437534264759700107191327783569<37> (Makoto Kamada / msieve 0.81 / 1.3 minutes)
8×1086-9 = 7(9)851<87> = 7 × 13371286561<11> × 31383767836172558959<20> × 272341401630430485534738797795860281929962816838801664287<57>
8×1087-9 = 7(9)861<88> = 320497711 × 620807981 × 1246611371500128661<19> × 32253487377531502986851358726659894965202028002674441<53>
8×1088-9 = 7(9)871<89> = 17 × 3361 × 5209 × 114031 × 7176344935019271474213060241<28> × 328467161637485477643402556200157335015038739937<48>
8×1089-9 = 7(9)881<90> = 41 × 131501 × 148380583584544752604125610841130578437593259515229504885523452385876319961213315451<84>
8×1090-9 = 7(9)891<91> = 191 × 396887 × 1566996511<10> × 1829684258089<13> × 36808283463413323401114896495621325375167752741758226649480537<62>
8×1091-9 = 7(9)901<92> = 5261 × 31189 × 51479210339<11> × 14856858480653089<17> × 637472378808260277486500944606583265307060061109032280749<57>
8×1092-9 = 7(9)911<93> = 7 × 1308863 × 1396657 × 62518419992876019825917869749138387550201480930570359069179266062109072179074143<80>
8×1093-9 = 7(9)921<94> = 40709 × 18874781380531563299<20> × 1050305013776143544881251969047909<34> × 9912933300716956352196073332931121989<37> (Makoto Kamada / msieve 0.83)
8×1094-9 = 7(9)931<95> = 41 × 103 × 109609 × 172831416755703831564705877752575524590824483351211195115269124861877722563349071196513<87>
8×1095-9 = 7(9)941<96> = 42839 × 5696681 × 71959379 × 10430065508761<14> × 81962564607799<14> × 53289148392320131181336208217453853689614795752029<50>
8×1096-9 = 7(9)951<97> = 3847 × 28727057 × 157923959 × 458383146858058083640569189274783699802299405974652739034285101997489595090631<78>
8×1097-9 = 7(9)961<98> = 181 × 441988950276243093922651933701657458563535911602209944751381215469613259668508287292817679558011<96>
8×1098-9 = 7(9)971<99> = 7 × 42473 × 1795039 × 288190519 × 5201462017139773407532948000368590335525019793021247677164543946625822841735041<79>
8×1099-9 = 7(9)981<100> = 412 × 252400679 × 357291259901<12> × 52772705784956691325475970159058388447295718892389579642066632828255512523509<77>
8×10100-9 = 7(9)991<101> = 31 × 148513 × 12661801 × 199640305759<12> × 6874167530995116418962276664987443820628599521956149749350162344306288430783<76>
8×10101-9 = 7(9)1001<102> = 109 × 7339449541284403669724770642201834862385321100917431192660550458715596330275229357798165137614678899<100>
8×10102-9 = 7(9)1011<103> = 49474853752019561<17> × 161698305165246504829176369287613785871274807254827355179107196688724463197592027937631<87>
8×10103-9 = 7(9)1021<104> = 19 × 809 × 1081922211214987353245001119627142180481<40> × 4810517819513914829026450136873524978585031656841214920313541<61> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 snfs / 0.68 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / January 12, 2008 2008 年 1 月 12 日)
8×10104-9 = 7(9)1031<105> = 72 × 17 × 23 × 41 × 12339525360577763311<20> × 82534369499492775539504164901993157698019211796802044264858135701867736475272599<80>
8×10105-9 = 7(9)1041<106> = 29 × 59 × 839 × 3833339 × 21150143453099<14> × 35078619954211<14> × 1959498667062999031926704741614139593738179779293723784466025712749<67>
8×10106-9 = 7(9)1051<107> = 71 × 14635097 × 2507524927653294391235106031<28> × 30703704237119309157206525676455637656338375135978941052412088778620503<71>
8×10107-9 = 7(9)1061<108> = 19227376621<11> × 253197206069634762046679<24> × 164327801377612366280851970862226784680540787850498357916385079147268929349<75>
8×10108-9 = 7(9)1071<109> = 11897 × 6595030913<10> × 74285794073<11> × 10784808302586663079660355798191<32> × 127267493166302734542256662357223329760676931011149417<54> (Robert Backstrom / GMP-ECM 6.0.1 B1=894000, sigma=353689614 for P32 / January 12, 2008 2008 年 1 月 12 日)
8×10109-9 = 7(9)1081<110> = 41 × 281 × 3739 × 662762029 × 302221898661149<15> × 9271730439680033210909506370965412733241317224833674180076775917438590150778909<79>
8×10110-9 = 7(9)1091<111> = 7 × 431 × 13855092257<11> × 9998334610991140900879<22> × 1914157140475983078381850722025574846690912817235800539519111123350958670641<76>
8×10111-9 = 7(9)1101<112> = 89 × 151 × 5879 × 183965453731<12> × 14732146478761<14> × 4596843431298289<16> × 59666213875095059<17> × 136216298961351150346613817476555834066220530671<48>
8×10112-9 = 7(9)1111<113> = 1481801 × 12879455609353<14> × 100082971494652293793<21> × 48579937690634404245880879<26> × 862155200536747669407680255056557135875893230601<48>
8×10113-9 = 7(9)1121<114> = 60281424871<11> × 390808792124933992905008532836460473489137122991<48> × 33958003771356934218524016876132944905551552683170456031<56> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 1.88 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / January 12, 2008 2008 年 1 月 12 日)
8×10114-9 = 7(9)1131<115> = 41 × 113 × 1249 × 181457 × 8379447418092713<16> × 106724771260208334463<21> × 337024070459655651343248393473<30> × 25278423742542254086178637648393531097<38> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3473905617 for P30 / January 5, 2008 2008 年 1 月 5 日)
8×10115-9 = 7(9)1141<116> = 31 × 1952641829846445891880391633628571<34> × 183792537662905341244235989253778248189<39> × 7190810275475399982758739592384651846401319<43> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 1.28 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / January 12, 2008 2008 年 1 月 12 日)
8×10116-9 = 7(9)1151<117> = 7 × 601 × 2399 × 17618927 × 4498914823027589954502177767264828194440402177682568398889575566184859392258189367911634448562824481481<103>
8×10117-9 = 7(9)1161<118> = 372829 × 673801 × 946886201 × 23054579733001<14> × 1203266767824644239<19> × 1212360365626907637766017430542379738743344113366637302699512357061<67>
8×10118-9 = 7(9)1171<119> = 929 × 86114101184068891280947255113024757804090419806243272335844994617868675995694294940796555435952637244348762109795479<116>
8×10119-9 = 7(9)1181<120> = 41 × 269 × 318811 × 3667183621<10> × 62042301017400996603275075014367355962058187966895330526278921138045829639685408286473804485966277709<101>
8×10120-9 = 7(9)1191<121> = 17 × 140980436176722049147831<24> × 201912898514421863519033<24> × 16531724244739797677094769294070330025691469189992376341763977264010111801<74>
8×10121-9 = 7(9)1201<122> = 19 × 16931 × 66190937999157259563309327452865130078561271454954931<53> × 3757121508638448333172650338258137145904700516674921367147594549<64> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2.07 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / January 12, 2008 2008 年 1 月 12 日)
8×10122-9 = 7(9)1211<123> = 7 × 433 × 479 × 79629799 × 65511205542191<14> × 105627579118010198961241542572400153835355663333650886864897190806568868681245992047348899374951<96>
8×10123-9 = 7(9)1221<124> = 61 × 1531 × 24997684759<11> × 3426771721360181654428953629771676679324560568343517918235996281132700620340567184773687381191136855559393039<109>
8×10124-9 = 7(9)1231<125> = 41 × 471528184675037636079943<24> × 4138076101516266611399553899059299501642320547257280706598333192612670982383463605435787583592516457<100>
8×10125-9 = 7(9)1241<126> = 226832719 × 3526828067515251183847071021531069333961473168251357953347109505838088551942984909509461022684298026688116364729552089<118>
8×10126-9 = 7(9)1251<127> = 23 × 217581248286592871920703441696601910487<39> × 1598603233024812172766526043763336942138049668499189186436388071437141249364595430510791<88> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 1.48 hours on Core 2 Quad Q6600 / January 12, 2008 2008 年 1 月 12 日)
8×10127-9 = 7(9)1261<128> = 379 × 162668538905134917251<21> × 657946460633670262464217847012752777057361<42> × 1972225892515966800861803327069244574222166958428213389132029239<64> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 3.10 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / January 13, 2008 2008 年 1 月 13 日)
8×10128-9 = 7(9)1271<129> = 7 × 103 × 404614087 × 2742292167422427287690729889200973292113433766197069877178938634243448046654360596538083213446535921526403923849564033<118>
8×10129-9 = 7(9)1281<130> = 41 × 12539 × 4536100568863046394901<22> × 3430524720802701163401847697876439169825244483784746397694403874743878437063770501147648944784823642809<103>
8×10130-9 = 7(9)1291<131> = 31 × 47 × 97 × 16230463228990793<17> × 34876089691677833342903508989503146475849040917539833934310381258702986387517749678035697172214214885763853903<110>
8×10131-9 = 7(9)1301<132> = 41191035001<11> × 151997412884823871<18> × 17395137635564948101611492468769441<35> × 7345531358476291840454011461466485796613423585618958953378377111100081<70> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1735415070 for P35 / January 5, 2008 2008 年 1 月 5 日)
8×10132-9 = 7(9)1311<133> = 569 × 183377 × 3598279 × 2772456103<10> × 1215962505406241644361<22> × 6320525105922331840657645991538739365276883820530221672189240436176226633667347386033751<88>
8×10133-9 = 7(9)1321<134> = 29 × 131 × 821 × 134230471 × 3084425618477467829<19> × 61951542000835037581279737010663806153811192081745810634853918906334299802153961473899362472992866831<101>
8×10134-9 = 7(9)1331<135> = 7 × 41 × 2991559 × 51611423 × 547886259883585498357025117689672145168225517346471<51> × 32951430664648770389924301340174201074562936491053050907418208102919<68> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 5.77 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / January 13, 2008 2008 年 1 月 13 日)
8×10135-9 = 7(9)1341<136> = 2242280133867389847297408619<28> × 3567796850700335413658530902418118705283912299168086494635422463658210156038995743562306889260792981443809189<109>
8×10136-9 = 7(9)1351<137> = 17 × 4337 × 31319 × 22064536663081199635553<23> × 414874359200499062591640749476962066365515367<45> × 3784707754227857968375340111961975566863294728841184192955991<61> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 3.02 hours on Core 2 Quad Q6600 / January 13, 2008 2008 年 1 月 13 日)
8×10137-9 = 7(9)1361<138> = 281 × 45259 × 6783449 × 146011951 × 9029523373784041010808525557981<31> × 1221423363891302373996983840134301<34> × 5758491037866755216905701730446521364185825908289891<52> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=4274360394 for P31, Msieve v. 1.28 for P34 x P52 / 25.3 minutes on Core 2 Quad Q6600 / January 12, 2008 2008 年 1 月 12 日)
8×10138-9 = 7(9)1371<139> = definitely prime number 素数
8×10139-9 = 7(9)1381<140> = 19 × 41 × 229 × 15695249 × 24527989 × 110631601 × 10529498738541754816202736159753808310781106211950284172182702169963716947647307740186077642356246030618409273341<113>
8×10140-9 = 7(9)1391<141> = 7 × 2445390769<10> × 37242387217387908233<20> × 388536296915994985391902206726511<33> × 3229792119842628898676018383831983166364802105671842667810158223564146032892279<79> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 5.41 hours on Core 2 Quad Q6600 / January 13, 2008 2008 年 1 月 13 日)
8×10141-9 = 7(9)1401<142> = 71 × 18461264067532624519<20> × 6103377099523147226220507515885566424858188379663517431659052822574508103751414373958897894353550287072113312752076445159<121>
8×10142-9 = 7(9)1411<143> = 9137 × 618833 × 1079521573057<13> × 13106344268257660385799848873815145070735015267291497911795837660217251149657750668426132396884498862251018484795471198903<122>
8×10143-9 = 7(9)1421<144> = 1931 × 57197513924989<14> × 152883219893830842959<21> × 47377347201491538911343208462784817336284594135413608953377398657081612022941678337443698538488935259754311<107>
8×10144-9 = 7(9)1431<145> = 41 × 356977 × 12418519760749442070754470311<29> × 1202396689032442891861982410658929<34> × 36605664115474603832272688375093831327326195191011201019483886504026399481577<77> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 15.54 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / January 14, 2008 2008 年 1 月 14 日)
8×10145-9 = 7(9)1441<146> = 31 × 3769 × 7489 × 279971682391<12> × 7742337301078104200488978966281420202696958368400348371<55> × 42178597070720342821424007221144098406947930977765023595765919575211661<71> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 13.98 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / January 14, 2008 2008 年 1 月 14 日)
8×10146-9 = 7(9)1451<147> = 72 × 74209 × 233102762089<12> × 458430639997432973730641<24> × 2237064275354436560413927703682193<34> × 920317772467855578861737276438457302528107277025704935144084694913195343<72> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=930593696 for P34 / January 12, 2008 2008 年 1 月 12 日)
8×10147-9 = 7(9)1461<148> = 71569 × 15914071 × 77519441 × 211293311 × 3128994342837361<16> × 757574316234139695166249827153995203794288161<45> × 180907822053975968030490364262581021587417735195779858011279<60> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 21.13 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / January 13, 2008 2008 年 1 月 13 日)
8×10148-9 = 7(9)1471<149> = 23 × 2351 × 5417 × 18204143 × 1811121196799<13> × 1947542272318766199929<22> × 1698869895271211983854184427647893889<37> × 2503720935946036989300856832502895816091759303149812092199359903<64> (Sinkiti Sibata / Msieve v. 1.30 for P37 x P64 / 11.01 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / January 14, 2008 2008 年 1 月 14 日)
8×10149-9 = 7(9)1481<150> = 41 × 387128561 × 506448962913497763293952892565556348977959<42> × 51909484898783796991431617515193618122604873161<47> × 1917204817158045773364919500838723218822870408926609<52> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.32 / January 15, 2008 2008 年 1 月 15 日)
8×10150-9 = 7(9)1491<151> = 193 × 247601 × 3624571477934606884159<22> × 96315157891755373030439425392135709447474977307786081<53> × 479544565961051555887991852543525630193846540227492360552478340319353<69> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 11.20 hours on Core 2 Quad Q6600 / January 13, 2008 2008 年 1 月 13 日)
8×10151-9 = 7(9)1501<152> = 81001 × 1259231 × 1739471 × 87802863301<11> × 30791592289433442832144020953926711999042958399<47> × 166777008939323811795992782279128050360042974145183252503836734575392545775709<78> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 21.10 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / January 15, 2008 2008 年 1 月 15 日)
8×10152-9 = 7(9)1511<153> = 7 × 17 × 4660787009<10> × 138804112174759<15> × 8716632273706955002066316578892953673433856501001<49> × 1192154963555103648416832707448716501053570407831671868210179818737805091325919<79> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 25.77 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / January 15, 2008 2008 年 1 月 15 日)
8×10153-9 = 7(9)1521<154> = 1399 × 1140091 × 5015713889921615670987135108295711210577412813759259823678007710091441235411108841619002499536502581664115297358770395081557354259801198205019699<145>
8×10154-9 = 7(9)1531<155> = 41 × 59281 × 547957391 × 12119965852433<14> × 461939553236586484114536733702650233023<39> × 10728951295727690102209746621884683736435695534177888595486933153914001471840926288450159<89> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 18.01 hours on Core 2 Quad Q6600 / January 14, 2008 2008 年 1 月 14 日)
8×10155-9 = 7(9)1541<156> = 89 × 39076948619<11> × 17285468921447286611<20> × 630937457078491523522125157973689<33> × 21091713323420107009957029361942912268853049172167108976864637180884556752573488461477765719<92> (Robert Backstrom / GMP-ECM 6.0 B1=1358000, sigma=3048894762 for P33 / January 14, 2008 2008 年 1 月 14 日)
8×10156-9 = 7(9)1551<157> = 13001 × 1295988165151587695336675852925431<34> × 474801621105532083834700125189778681342962201400810891482867919304452802278015894667986382020302929101025045361916944761<120> (Robert Backstrom / GMP-ECM 6.0.1 B1=2822000, sigma=3560430649 for P34 / January 16, 2008 2008 年 1 月 16 日)
8×10157-9 = 7(9)1561<158> = 19 × 2099 × 7229 × 18859 × 603401 × 56949044155789<14> × 428188103946864618973346395991416136526087129783255206465681135573022188697491171059758709198279405275825079559867921294146909<126>
8×10158-9 = 7(9)1571<159> = 7 × 4323841 × 4714903 × 462997341128773543<18> × 410562561244534563981430142949031<33> × 46763860302718914140271163284841847599644741791<47> × 630639651843465146374746113429199687582690077977<48> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=2488992415 for P33 / January 13, 2008 2008 年 1 月 13 日) (Jo Yeong Uk / Msieve v. 1.32 for P47 x P48 / 3.43 hours on Core 2 Quad Q6600 / January 14, 2008 2008 年 1 月 14 日)
8×10159-9 = 7(9)1581<160> = 41 × 819895751 × 144046589869251451<18> × 1652131125410027750230091445891361988713569097781279733909762092164628552597079591796479256940617241534675316425849653189664647062251<133>
8×10160-9 = 7(9)1591<161> = 31 × 57073 × 162324131850327948485434438093621716953<39> × 278557273407351934069599866763595027872975703442508848781459154897177077473859196381772941462840739464361826004563169<117> (Robert Backstrom / GMP-ECM 6.0 B1=460000, sigma=2066832104 for P39 / January 14, 2008 2008 年 1 月 14 日)
8×10161-9 = 7(9)1601<162> = 29 × 199 × 571 × 1692365724601<13> × 428383815004193749871857607077279<33> × 334869450332200636093078292799339933789697545275221769023019937305594987180395275406031737563279818152065360169<111> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=4020806271 for P33 / January 13, 2008 2008 年 1 月 13 日)
8×10162-9 = 7(9)1611<163> = 103 × 885679 × 27972713 × 20174793473<11> × 128513348641<12> × 6739247979073<13> × 1849901488629672000658219697<28> × 29004454390043890346738171836159<32> × 3343949795648324158059774855467139266458728235931156713<55> (Sinkiti Sibata / Msieve v. 1.30 for P32 x P55 / 5.81 hours on Pentium3 750MHz, Windows Me / January 13, 2008 2008 年 1 月 13 日)
8×10163-9 = 7(9)1621<164> = 59 × 1871 × 56422890657214170461<20> × 542641511977858280491601<24> × 875566100557163004027901<24> × 27033787953781187764242225330412868305230762710162197083926926782390962622491739968985386579<92>
8×10164-9 = 7(9)1631<165> = 7 × 41 × 1143403361<10> × 261891714717420247<18> × 11046278788929908087<20> × 308636832720759777975330569373913552783<39> × 2730380120299666574824672795496309223735144601900062623583012669777090797192599<79> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P39 x P79 / 32.49 hours on Core 2 Quad Q6600 / January 16, 2008 2008 年 1 月 16 日)
8×10165-9 = 7(9)1641<166> = 281 × 18039899370116253132365185259<29> × 1578154639645101849715900601142746848194561974023738373087552898239995805944710078341227436286841880064814566233260954631456666425083629<136> (Robert Backstrom / GMP-ECM 6.0 B1=508000, sigma=1694339146 for P29 / January 14, 2008 2008 年 1 月 14 日)
8×10166-9 = 7(9)1651<167> = 1039921 × 76928920562235015929094613917787985818153494351974813471407924255784814423403316213443136545949163446069461045598656051757777754271718717094856243887756858453671<161>
8×10167-9 = 7(9)1661<168> = 2371 × 3152099 × 68098319 × 39805790809<11> × 328122692405400099376586451015551<33> × 120348219501465859000916415860703533989146155732677824787903392809000729377628019185401396804542816303837799<108> (Robert Backstrom / GMP-ECM 6.0 B1=726000, sigma=2355788295 for P33 / February 9, 2008 2008 年 2 月 9 日)
8×10168-9 = 7(9)1671<169> = 17 × 168837552669242694718423<24> × 11681215841603794478271720614912632360063687<44> × 238607433000818367820061770438598453100921190268658947143978441159074725390668672932146359772318330023<102> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.36 / 43.83 hours on Cygwin on AMD 64 X2 6000+ / July 21, 2008 2008 年 7 月 21 日)
8×10169-9 = 7(9)1681<170> = 41 × 311 × 6744493062860975247569<22> × 153259559622294960992443672324849<33> × 4793749476605961545931498988840397341<37> × 1266174380191027066904884727886512981316500532551514322249230638281825634221<76> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2143804591 for P33 / January 10, 2008 2008 年 1 月 10 日) (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 146.83 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / January 19, 2008 2008 年 1 月 19 日)
8×10170-9 = 7(9)1691<171> = 7 × 23 × 26017 × 2214715267511<13> × 86236077562737196330146826425772970067888786441365007847722264766881105680234692955925454854605262572454517069721363351702050706318228050577829986173313<152>
8×10171-9 = 7(9)1701<172> = 193889600710609<15> × 41260593506200698279599462767637384171982231491177858236262250974719211845842972441210726085997841796337501541838264491008556974220898578912233981285000963399<158>
8×10172-9 = 7(9)1711<173> = 2887 × 183569 × 20014529 × 128714305601821727214220447<27> × 58596498982001952975845798701288109708106382244239018345980820975809202876122374448730226233013938124947800132473133749936923060319<131>
8×10173-9 = 7(9)1721<174> = 762946411 × 25759368564863328438503015111<29> × 23660900021573994987453189462396384397709<41> × 1720400179231385795985452436310629205021018478432220686288060649998543845046452046194341069059519<97> (Serge Batalov / GMP-ECM 6.2.1 B1=5000000, sigma=3442877901 for P41 / August 8, 2008 2008 年 8 月 8 日)
8×10174-9 = 7(9)1731<175> = 41 × 173743074481<12> × 19106912458400837994080317241<29> × 451656251742733916273683704772193<33> × 592251998082554341409369753785202370375115807<45> × 219732123875349514938455918437129730022904144914165154681<57> (Serge Batalov / GMP-ECM 6.2.1 B1=2000000, sigma=1366989160 for P33 / August 29, 2008 2008 年 8 月 29 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P45 x P57 / 4.00 hours on Core 2 Quad Q6700 / August 30, 2008 2008 年 8 月 30 日)
8×10175-9 = 7(9)1741<176> = 19 × 31 × 149 × 20059681 × 343336352573371<15> × 132356298264951304247691216083342406871276098976976067296888785159636102953289446576228151348035488494413741550290799505424221421961676806586976243781<150>
8×10176-9 = 7(9)1751<177> = 7 × 47 × 71 × 2006614343<10> × 3761131926862762109033<22> × 4537882651626232824466406254647044203827101931656789392057764811180770931956296544596453833901873187582314737218252795726330076899175702962071<142>
8×10177-9 = 7(9)1761<178> = 991 × 115981 × 36714255936236869753284963919<29> × 293404665016948568264301967590385417545820782950131890352575649<63> × 6461416521356221327173118082655938446851161197468240636540461926587279552388291<79> (Warut Roonguthai / Msieve 1.48 snfs / January 31, 2012 2012 年 1 月 31 日)
8×10178-9 = 7(9)1771<179> = definitely prime number 素数
8×10179-9 = 7(9)1781<180> = 41 × 19512195121951219512195121951219512195121951219512195121951219512195121951219512195121951219512195121951219512195121951219512195121951219512195121951219512195121951219512195121951<179>
8×10180-9 = 7(9)1791<181> = 826115977894170609050375729157582021497<39> × 9990207070327391855783197701498143287718371662893791939986474480751<67> × 969336296313865853470535064289775123620533028668230038800912477861614266753<75> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=3000000, sigma=1512967684 for P39 / January 15, 2008 2008 年 1 月 15 日) (matsui / Msieve 1.41 snfs / 110.65 hours / May 19, 2009 2009 年 5 月 19 日)
8×10181-9 = 7(9)1801<182> = 6701381 × 11937837887444393924177717995738490320129537478916659118471252417971758358463725611183724668094531559987411549947689886606954596373493761957423402728482382959572064325248780811<176>
8×10182-9 = 7(9)1811<183> = 7 × 55034647 × 80872862999<11> × 12505279122703<14> × 4610751791149583<16> × 300977981458113710336063<24> × 791520676525556756558287<24> × 1869350855022326145848482156629783632895446606870285042910755179464118848856103721317809<88>
8×10183-9 = 7(9)1821<184> = 61 × 6301 × 20813766224981202567378063851431336686084176074055380228483118734731151183392695929087498471489042852942936458173435910511212115693319561558014470770967918181084969598892707636831<179>
8×10184-9 = 7(9)1831<185> = 17 × 41 × 53881 × 525199 × 19560201548737<14> × 47291522362212610363688449301629559<35> × 16036893578982114464326470006735731329<38> × 273414034698599650866625624274832254903897139353621479873467317551382470700435628639391<87> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3256196919 for P35 / January 10, 2008 2008 年 1 月 10 日) (Robert Backstrom / GMP-ECM 6.0.1 B1=1836000, sigma=2743095310 for P38 / January 26, 2008 2008 年 1 月 26 日)
8×10185-9 = 7(9)1841<186> = 191 × 1417159 × 2076771549705598050703621<25> × 1423145536052120102382132019368305719940062530797523306346723844255178216935965167603016558787305428873887986189012205606784622894763594805151285500405859<154>
8×10186-9 = 7(9)1851<187> = 151 × 847274600419839100841<21> × 7792689731598829239462487148882553000521530686313<49> × 8024194874485047703519917845528012680760042092666387174497595573580873743456741120481696442116176478200628281751377<115> (Rich Dickerson / GMP-ECM 6.4.4 [configured with GMP 6.0.0, --enable-asm-redc] [ECM] B1=11000000, sigma=2999268530 for P49 / April 18, 2014 2014 年 4 月 18 日)
8×10187-9 = 7(9)1861<188> = 4799 × 2538299 × 6567445211308539305752531218104327527054666278838120571641421811856386013228494084794165546954678894087650150445996423381980253401263025335072242978079596518324777346300066182091<178>
8×10188-9 = 7(9)1871<189> = 72 × 7602311 × 173736791 × 24708429609994175097734154407390913318412121051201351269847898750755065188688709610697<86> × 500277919901286123788847387177898953814010750877712565143716310335071116668731990013647<87> (Kenji Ibusuki / Msieve v. 1.49 (SVN unknown) + GGNFS-0.77.1-VC8 with factMsieve.pl (decomposed + modified) snfs (without procrels.exe, matbuild.exe for "finalFF" calculation) / March 23, 2018 2018 年 3 月 23 日)
8×10189-9 = 7(9)1881<190> = 29 × 41 × 2596385003143837715582911<25> × [2591427364336719491235389806977115681555038614279184025366308696610268250530517408044902827364339063789302198421776397419940583459949469105359168620438392722790229<163>] Free to factor
8×10190-9 = 7(9)1891<191> = 31 × 257 × 30319 × 2445649 × 568034078420777<15> × 1118584622077795641597568510231<31> × 5956694674603727915072852316779388032674317487<46> × 35779774073720156830334101164802233650029559245191540826257705794588243741259881976407<86> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1248440662 for P31 / January 11, 2008 2008 年 1 月 11 日) (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=3143978648 for P46 / April 21, 2009 2009 年 4 月 21 日)
8×10191-9 = 7(9)1901<192> = 2838215384488977187840273748749501<34> × [281867262214153842659280716998882524780880662933308691584296839537167821919759679358142157019600539866645046737600020701546566244595946561032467565638861495491<159>] (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=301425253 for P34 / January 12, 2008 2008 年 1 月 12 日) Free to factor
8×10192-9 = 7(9)1911<193> = 23 × 18679 × 88554291281<11> × 21761061683787691129<20> × 1019205584347682443153199<25> × 9481063224206527308752297561166297518388025260180897213130338632814005914190654888873107270178108977355433010461160592720741029966273<133>
8×10193-9 = 7(9)1921<194> = 19 × 281 × 4418326058451689<16> × 28635389649731171<17> × 4005799549560803338611269<25> × 47530447988775454504196992466925654385332702204589<50> × 622025352119764712028843316628216948512092949996598055244945354900245093351541822511<84> (Sinkiti Sibata / Msieve 1.40 gnfs for P50 x P84 / 379.04 hours / May 23, 2009 2009 年 5 月 23 日)
8×10194-9 = 7(9)1931<195> = 7 × 41 × 27333617 × 101979055534180908398804937583005844284932836783323810289051858283389497739408541687601081217588453295187071615330580713221651435519603254808356223825144965499662669282257266479646758329<186>
8×10195-9 = 7(9)1941<196> = 3889 × 15610275261869941441<20> × 435897677914358674687851179<27> × 1045513792226296340499906371<28> × 19119580804026448034824934992231<32> × 15123377562818027057411188140424291585847836807190418568871815626881749196170735312717121<89> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=3290480722 for P32 / January 15, 2008 2008 年 1 月 15 日)
8×10196-9 = 7(9)1951<197> = 103 × 167 × 954991 × 81414877802867842804171020513313290804837130370072920417469071886006761367<74> × 59818185753980978199058118896566485703373129613222157612388667504251304310190969765131248916109490387978301091103<113> (Robert Backstrom / Msieve 1.44 snfs / March 15, 2012 2012 年 3 月 15 日)
8×10197-9 = 7(9)1961<198> = 1741 × 91944989 × 1234814714173888079<19> × 1427215094366113765241891957567569<34> × 1908958733856301694391969850590058850504946851<46> × 1485509331511250677828481937411850202310266579344367442824439124264860593989565789479246459<91> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=188830890 for P34 / October 23, 2010 2010 年 10 月 23 日) (Wataru Sakai / GMP-ECM 6.2.3 B1=11000000, sigma=2042445678 for P46 / December 3, 2010 2010 年 12 月 3 日)
8×10198-9 = 7(9)1971<199> = 1616047 × 866083792778492543<18> × 48379420295302544573687953<26> × 118145022102909943944592172563135540794145409774164176463071726333370430757513105962769532160781285167609778415980091915961386815871399074195238846807<150>
8×10199-9 = 7(9)1981<200> = 41 × 89 × 1951 × 11237219243344651554198723760917485239561360765445663198907629917354466422416342063201211259862240119991027080434189295733972319076907388036210253428791637935672257510992458561700550862533832809<194>
8×10200-9 = 7(9)1991<201> = 7 × 17 × 887 × 4759 × 1592588960531259966185315080796009486471142914121708678264296297337967446036372259364172752846575093743717920866273157709165652258833522111197559273010770935945042796816980833273480190513534033<193>
8×10201-9 = 7(9)2001<202> = 53741904157986199<17> × 453999315412948545613489<24> × [327885143288386481356764937818611038150393207814738326466843212365548611446743777078639510000143948799595718681805691140882502761381039938670637533649485305968881<162>] Free to factor
8×10202-9 = 7(9)2011<203> = 3943 × 53099360729<11> × 382097254672614913340202368026272144023459536191136002678102550589232823417532364619639237993486813223934078753254472001296857965821164493009722760529934297557570715413022046567446618996953<189>
8×10203-9 = 7(9)2021<204> = 1471 × 59382805939<11> × 120354795269<12> × 60394682658835190656773536992949<32> × 53694954854754892804718221745868071<35> × 403474286370117420764849993380133628803096457592087361<54> × 58157422897196965521108495629688569153637861218663306686349<59> (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=2119101525 for P32 / February 5, 2012 2012 年 2 月 5 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1015594997 for P35, Msieve 1.48 gnfs for P54 x P59 / February 8, 2012 2012 年 2 月 8 日)
8×10204-9 = 7(9)2031<205> = 41 × 23833 × 16205329375756221583103465311673<32> × [505207227237265374887558002728015292695785941385988850601995045775830174065319994869178937526427979697918458667522201603126308966220899905162535335181384817442229537839<168>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2633903517 for P32 / February 7, 2012 2012 年 2 月 7 日) Free to factor
8×10205-9 = 7(9)2041<206> = 31 × 51225707609<11> × 320273508689<12> × 3057792190289<13> × 7819375344968024371452336693179<31> × 6578687870510139660523303659740199724518015232584287023187088745718684824935935284311888116432008122491166508382345814269560719137651116931<139> (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=1066738707 for P31 / February 5, 2012 2012 年 2 月 5 日)
8×10206-9 = 7(9)2051<207> = 7 × 4463 × 462308604473<12> × 632035769279<12> × [87637791811927250111542225322134702996575595676457834151333815582046951216898499480746579815431661200478211669687319634870224970124658744168034333653774958255851751403489014596553<179>] Free to factor
8×10207-9 = 7(9)2061<208> = 29022289 × 231481619423005561<18> × 5891042753158565579<19> × 383563553224667129883891866576590009<36> × 2359994481905721143616232585850367032270519<43> × 223306475654755621082958334503634416321951702625374202668692208032859353866554246722531<87> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2460805740 for P36 / February 8, 2012 2012 年 2 月 8 日) (Warut Roonguthai / Msieve 1.48 gnfs for P43 x P87 / February 14, 2012 2012 年 2 月 14 日)
8×10208-9 = 7(9)2071<209> = 16425041 × 109820965184612658553334561<27> × 16676835144464689281490881595951<32> × 2659405929581831293565068128847269042687244750493538621421776967444578619579170149805010981249277469626588751271440227953337250531318602167044041<145> (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=3755180555 for P32 / February 5, 2012 2012 年 2 月 5 日)
8×10209-9 = 7(9)2081<210> = 41 × 109 × 1360359379<10> × 131590936325342026559291494366315030725946976988397839708462165966663128760843627792172881678530204632706782793630062234233158789660889365686898556613157113451038753684429413499110123935490234645241<198>
8×10210-9 = 7(9)2091<211> = 359 × 352585123213688238209088624642086390941252550482654312659488413481<66> × 63202106656010406556759667715580889046487196378902614899075518260479266518560510682320966550634695977417478810669857055435308396255452706606729<143> (Kenji Ibusuki / GGNFS-0.77.1-VC8 with factLat.pl (decomposed + modified) snfs / March 4, 2012 2012 年 3 月 4 日)
8×10211-9 = 7(9)2101<212> = 19 × 71 × 409 × 461 × 381239 × 44323901911430299<17> × [18613090848619154380747271992252774832320724349757780448634635913376328957004719385849927304596388114074857107498755574435378571356359451432286829189704031242269523182345302462533131<182>] Free to factor
8×10212-9 = 7(9)2111<213> = 7 × 26183 × 169313 × 415320089 × 1900689590953<13> × 1851356479454681782943182282432079535581617393<46> × 31928351621138747939762429657064506409514168353797424553<56> × 552486351302421971067972087000414597054715852617904914334871053835933092571523679<81> (Cyp / GMP-ECM 6.4.4 B1=11000000, sigma=3731307205 for P46 / February 14, 2014 2014 年 2 月 14 日) (Erik Branger / GGNFS, Msieve gnfs for P56 x P81 / June 17, 2014 2014 年 6 月 17 日)
8×10213-9 = 7(9)2121<214> = definitely prime number 素数
8×10214-9 = 7(9)2131<215> = 23 × 41 × 182687 × 848423 × 91060340977<11> × 195064932800671<15> × 2886040652293261121<19> × 10640290587464849006471302367<29> × 207349464913336188675367467608513<33> × 108949257441081492745795054103854289<36> × 44418778933365391401581679676288297409967491417272068628919489<62> (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=3200188585 for P33 / February 5, 2012 2012 年 2 月 5 日) (Warut Roonguthai / Msieve 1.48 gnfs for P36 x P62 / February 8, 2012 2012 年 2 月 8 日)
8×10215-9 = 7(9)2141<216> = 125523691 × 14750700551<11> × 432067539018221815137592217173370298877795799944486578143120893421828183766243999826033245033194470228899636678951978407138655947171340828649534603631240039297792280827538998381697058019482355771251<198>
8×10216-9 = 7(9)2151<217> = 17 × 16527160925826955714456519<26> × 28473628193377757499689835180671069975436684001365746159516865145605963012482072255300603684210781437647928059614192221779732467968558000851473755036311784268453766759808701987053990372542017<191>
8×10217-9 = 7(9)2161<218> = 29 × 63311 × 20114021 × 34349179 × 85899031 × [734191395993309381497216879725179244650425417587853108879355218409852620652981417516277294448912787522030981370791382184656473446407878294958954942864285825434910200422009007289212109220941<189>] Free to factor
8×10218-9 = 7(9)2171<219> = 7 × 3271 × 901528497316355772074058337256364994351<39> × 7403565714962559282672850667451919621111<40> × 35594522000963558448843039644723038426729<41> × 147064497301686100463326295785520523913687470636240970765830801402569209267305122035506041699687<96> (Serge Batalov / GMP-ECM B1=2000000, sigma=2798145354 for P39 / February 8, 2012 2012 年 2 月 8 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2436595440 for P41 / February 10, 2012 2012 年 2 月 10 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3431402457 for P40 / February 28, 2012 2012 年 2 月 28 日)
8×10219-9 = 7(9)2181<220> = 41 × 12161 × 1800449461<10> × 58779051569787581<17> × [151611914687635167550066182144371296288992678919781849346958585430303232068246349937793833719798598955519768833450463963233705183006536738749648722658629923481835403768141597017160113951551<189>] Free to factor
8×10220-9 = 7(9)2191<221> = 31 × 223 × 1211647 × 1622280868927<13> × 1517630966915612671<19> × 4394614115734335254718367974861097<34> × 882743129427351530264106926864560648240553136372071098686185119035170557604353129690648662635308325532181922284556948631456584937424490041655630369<147> (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=1710193540 for P34 / February 5, 2012 2012 年 2 月 5 日)
8×10221-9 = 7(9)2201<222> = 59 × 281 × 13829 × 124339 × 28945309 × 6377253754843809216010092323801<31> × [152027313216263896477811644021367687518556641276753454397573777124752499389233502731666854072626344217975318003128625312839581053484872377216654451788936806379330111096951<171>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2972292649 for P31 / February 7, 2012 2012 年 2 月 7 日) Free to factor
8×10222-9 = 7(9)2211<223> = 47 × 10273 × 67961 × 11196313 × 194245282193<12> × 623348773457<12> × [179836756303062185404946640083916108828101636370242388366661066365157259702408772974208063934708906852468204182366603772405008514663552846493778272244404936392633441732858287688940777<183>] Free to factor
8×10223-9 = 7(9)2221<224> = 56671 × 43512761 × 262227619 × [123718326818921983698997674215499215221431040281039247186093180170142898244187288715754502343620260298708158057661745158675726245270689728702571753657637140775022760971244216967967144580820715570949800219<204>] Free to factor
8×10224-9 = 7(9)2231<225> = 7 × 41 × 42069507863<11> × 66258356410310911815218099063285147715919526998981310080499212600366947939624840698066275898033707549507098898506014634117220037849080063979093508456019930514060766096556441131896175789035186152621023947475256511<212>
8×10225-9 = 7(9)2241<226> = 1085609492839<13> × 7369132319466950629764048177305328479239963577913954494172930628160822310655579714993841099466148843831130688037205696002503652624565883445673873851021578797132418025326091453105505152348540056040312231336107401969<214>
8×10226-9 = 7(9)2251<227> = 97 × 113 × 313 × 401 × 6271 × 606947959 × 1741466113963086055081<22> × [8772993644271341727972676483705398147165081262589997769724266257247856928734461397250428940881199588856832560066133641078964251044364291898018852344673395667384595436437539681797350143<184>] Free to factor
8×10227-9 = 7(9)2261<228> = 345599 × 5197081 × 116256056369<12> × 604164697454869<15> × 192574188519105839<18> × 32929794156322879495338602885034114500361855923369776780459048536652587097029854535071878735945627738212538053435821609716899316179951995825523601656876213272969721481289491<173>
8×10228-9 = 7(9)2271<229> = 108743377 × 41616076348182715121<20> × [1767771140477338183069259974923011841261647771746466429215109924708677504748493534139888055538324611074999001795781404348735517144952584936558090210236861853812992933547919779550521354022916535678410423<202>] Free to factor
8×10229-9 = 7(9)2281<230> = 19 × 41 × 1211326541<10> × 53904499871<11> × 5748854973854004570911695555422280559069<40> × [273580363632063644237674800354809013169225887004252328477631732172085995981949538957645870072542082707750073440439786164959496645103118598132072854810452152931841335731<168>] (Serge Batalov / GMP-ECM B1=3000000, sigma=3491332925 for P40 / May 26, 2014 2014 年 5 月 26 日) Free to factor
8×10230-9 = 7(9)2291<231> = 72 × 103 × 983 × 2734620647767<13> × 58966598455289505522980087414186412048349735188851147643824007342507394838437520856472953831646741861243742500616405559806337088769953842113987788066289525781110611888769765836361049074934463464278519959253591473<212>
8×10231-9 = 7(9)2301<232> = 15990809 × 477144268831<12> × 9664832021043839<16> × 72240364729753375595168862739<29> × 1501742940789884201986989326585660564191974652998924731158598315151703404542838467100129509102329022714957089445674920267449381698968908183861967333270578224550405124149<169>
8×10232-9 = 7(9)2311<233> = 17 × 672167 × 2753311711<10> × 2099169905378344609049<22> × 1867590180864495694715339047<28> × [648603552754392107855201313994300282462211794002566243794942684228417721777466170243335756933488946299245721251109289864102384367351830331949073683987140515295023702993<168>] Free to factor
8×10233-9 = 7(9)2321<234> = 1049 × 723551 × 3001919 × 178613861 × 423899143891<12> × 251911124751709<15> × 18408624377862604712452484699993587841385214242251823222941428222544174924488806012656147491993373652708493831912876685454329510681075410224514001958994326931963112555434850552241834629<185>
8×10234-9 = 7(9)2331<235> = 41 × 1645487 × [118580062449300538455758823686966303563151524257026613531138316572510885538564037243210983857740566300136187719472241052159708312019184712563484986215141852807843217354571595654971564723362274823316818638627659893467375445392273<228>] Free to factor
8×10235-9 = 7(9)2341<236> = 31 × 66549405191<11> × 133646570909<12> × 80069180150681<14> × 137509233770861569<18> × 14583331384644655834766246191<29> × 1807058892093786699381504846069706577618906976995238561396323867816796794003754607130458592182312439364937154992266129236062191022071491811436709821986781<154> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1805905473 for P29 / February 7, 2012 2012 年 2 月 7 日)
8×10236-9 = 7(9)2351<237> = 7 × 23 × 4191329 × 440887850221447107185182731517512171773959<42> × [2688959293550758662803569792022591608403827595158597311087987901215976507023612733452358425694282459361151017241557827798561799687428462958410688972618333472524697448336433125490091410321<187>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2655642556 for P42 / May 14, 2012 2012 年 5 月 14 日) Free to factor
8×10237-9 = 7(9)2361<238> = 289065319 × 25894478668908317059<20> × 1068776326142634441297644177312849557501061145203191186202359491819463149958043337782610799913613766242648999471416256623697095563844804673372272082132311549465350026883084687688298615807588813204957717437051771<211>
8×10238-9 = 7(9)2371<239> = 13241 × 6041839740200891171361679631447775847745638546937542481685673287516048636809908617173929461521033154595574352390302847216977569669964504191526319764368250132165244316894494373536741937920096669435843214258741786874103164413563930216751<235>
8×10239-9 = 7(9)2381<240> = 41 × 1511 × 224071 × [57630981175722401310804391442815588942766682031463250782783373502358937381991097452598028299725147455584750297220637420867105958470090141851680331833046147216254739631954179604356990669256208860844024733219918967409982779818881071<230>] Free to factor
8×10240-9 = 7(9)2391<241> = 67694653936875193<17> × 118177722091022813983146314113415991921175350135296550750492330663076193994386421890718312339290020712468684373519188008883458564652425986048786252029803191602614361806163486476232547022978943329025219077250242720557219517487<225>
8×10241-9 = 7(9)2401<242> = 179 × 719 × 3830053391<10> × 35086382558119<14> × 1277217812163820649<19> × 3621593288176758115661547929806607212528138969785922864294706512058994634063557632672937145725189419075822824509273984088920455530901769714499315764869686981513226163195079312428723381534928723571<196>
8×10242-9 = 7(9)2411<243> = 7 × 218233 × 523686675643529098322827960417142621483853103269048611870274955142963189408960671785267515519127328523707623110554839486760873535559307188712457393179373814749766141168907936537030212138926219748093616848571415479261680340343970500729561<237>
8×10243-9 = 7(9)2421<244> = 61 × 89 × 52466789 × 3339482969<10> × 6671486959<10> × 59944667953710342148831<23> × 271559403294699179670218434082719<33> × [77440541380532099964643908223547652135647118368266604354825028597548440104155320264822440498466721043420792895390909338561476691035397536718340644692941554169<158>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2391588249 for P33 / February 7, 2012 2012 年 2 月 7 日) Free to factor
8×10244-9 = 7(9)2431<245> = 41 × 5849 × 15217 × 12222230187396067903<20> × 738488395587427276690376057<27> × [2428853577019143317742668732352135856193568495188566337240658521054003621588586276356525012060377364041593830091517639539403776405198621158259196356980845414385414230103991839500223197844257<190>] Free to factor
8×10245-9 = 7(9)2441<246> = 29 × 4139 × 26234467408092023483878578044093422379955221<44> × [254052990120208972101761884523720999588342322295526614696921697856658355347523277089578810438611748037727855407054329101947615900136134098294436271648047544076998963090108708646874865172433277259141<198>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=295852664 for P44 / March 10, 2012 2012 年 3 月 10 日) Free to factor
8×10246-9 = 7(9)2451<247> = 71 × 304151 × 1134714472201<13> × 326479409055421069722430093360460511028839253435322567485696067533843494123413010248886102713589673505514128296209938823407540382059759842651701269139016600449145492498849221929844286083585063241382716923141243263915913166392671<228>
8×10247-9 = 7(9)2461<248> = 19 × 307360637263252973156539<24> × 602879792468421145513441<24> × 3289354456996380061493927389528425569<37> × [6907911034266074829693664448291777900488674949890473738502974168097412771201004057373822750743309555552070130728113585432038424473092582387418775485488290995056919<163>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3662303517 for P37 / February 8, 2012 2012 年 2 月 8 日) Free to factor
8×10248-9 = 7(9)2471<249> = 7 × 17 × 24012575406493670317851540947007249176239<41> × 279965349897964273260793367265069054397992529434839860924127865483005125350966554138174669635748250394873452193938689380241881710323277247788220624473980379054466247947188461097513390330222777489472917785551<207> (Lionel Debroux / GMP-ECM 6.5-dev (SVN r1712). for P41 / February 10, 2012 2012 年 2 月 10 日)
8×10249-9 = 7(9)2481<250> = 41 × 281 × 59281 × 2458169232233878471960429665052435189<37> × 228344099195616997070047101106338562309649<42> × 20868090794823982690731484557044344475803309155709141084654258831633234104523317900122016313878697697890790361570063183473784399973979227645471029508076711855303131<164> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=762661468 for P42 / February 8, 2012 2012 年 2 月 8 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2710449089 for P37 / February 8, 2012 2012 年 2 月 8 日)
8×10250-9 = 7(9)2491<251> = 31 × 863 × 62958160036904213969<20> × 102594635678422265258751823<27> × 3189958354459564644304445748083579858411050653119<49> × [145129534857487163405564510505225401666554618120264589295941012986763713523687920179573011749752475101956040265140788219615512875040547683780718443129399<153>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1446469063 for P49 / February 8, 2012 2012 年 2 月 8 日) Free to factor
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