Table of contents 目次

  1. About 811...119 811...119 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 811...119 811...119 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 811...119 811...119 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 811...119 811...119 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

81w9 = { 89, 819, 8119, 81119, 811119, 8111119, 81111119, 811111119, 8111111119, 81111111119, … }

1.3. General term 一般項

73×10n+719 (1≤n)

2. Prime numbers of the form 811...119 811...119 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. 73×101+719 = 89 is prime. は素数です。
  2. 73×104+719 = 81119 is prime. は素数です。
  3. 73×107+719 = 81111119 is prime. は素数です。
  4. 73×109+719 = 8111111119<10> is prime. は素数です。
  5. 73×1019+719 = 8(1)189<20> is prime. は素数です。
  6. 73×1022+719 = 8(1)219<23> is prime. は素数です。
  7. 73×1070+719 = 8(1)699<71> is prime. は素数です。
  8. 73×10102+719 = 8(1)1019<103> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 6, 2004 2004 年 12 月 6 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 6, 2005 2005 年 1 月 6 日)
  9. 73×10121+719 = 8(1)1209<122> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 6, 2004 2004 年 12 月 6 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 6, 2005 2005 年 1 月 6 日)
  10. 73×10123+719 = 8(1)1229<124> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 6, 2004 2004 年 12 月 6 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 6, 2005 2005 年 1 月 6 日)
  11. 73×10235+719 = 8(1)2349<236> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 6, 2004 2004 年 12 月 6 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 6, 2005 2005 年 1 月 6 日)
  12. 73×10360+719 = 8(1)3599<361> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 6, 2004 2004 年 12 月 6 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 6, 2005 2005 年 1 月 6 日)
  13. 73×10594+719 = 8(1)5939<595> 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 / June 1, 2006 2006 年 6 月 1 日)
  14. 73×101614+719 = 8(1)16139<1615> 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 / August 12, 2006 2006 年 8 月 12 日)
  15. 73×102410+719 = 8(1)24099<2411> 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: Ray Chandler / Primo 3.0.9 / September 22, 2010 2010 年 9 月 22 日)
  16. 73×1016048+719 = 8(1)160479<16049> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 10, 2010 2010 年 9 月 10 日)
  17. 73×1016174+719 = 8(1)161739<16175> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 10, 2010 2010 年 9 月 10 日)

2.3. Range of search 捜索範囲

  1. n≤30000 / Completed 終了 / Ray Chandler / September 19, 2010 2010 年 9 月 19 日
  2. n≤50000 / Completed 終了 / Erik Branger / May 1, 2013 2013 年 5 月 1 日
  3. n≤100000 / 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. 73×103k+2+719 = 3×(73×102+719×3+73×102×103-19×3×k-1Σm=0103m)
  2. 73×106k+2+719 = 7×(73×102+719×7+73×102×106-19×7×k-1Σm=0106m)
  3. 73×106k+2+719 = 13×(73×102+719×13+73×102×106-19×13×k-1Σm=0106m)
  4. 73×1013k+10+719 = 53×(73×1010+719×53+73×1010×1013-19×53×k-1Σm=01013m)
  5. 73×1015k+6+719 = 31×(73×106+719×31+73×106×1015-19×31×k-1Σm=01015m)
  6. 73×1016k+12+719 = 17×(73×1012+719×17+73×1012×1016-19×17×k-1Σm=01016m)
  7. 73×1018k+6+719 = 19×(73×106+719×19+73×106×1018-19×19×k-1Σm=01018m)
  8. 73×1022k+3+719 = 23×(73×103+719×23+73×103×1022-19×23×k-1Σm=01022m)
  9. 73×1028k+27+719 = 29×(73×1027+719×29+73×1027×1028-19×29×k-1Σm=01028m)
  10. 73×1032k+3+719 = 353×(73×103+719×353+73×103×1032-19×353×k-1Σm=01032m)

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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 19.12%. 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 19.12% です。

3. Factor table of 811...119 811...119 の素因数分解表

3.1. Last updated 最終更新日

March 8, 2015 2015 年 3 月 8 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=202, 203, 204, 206, 208, 209, 212, 213, 214, 216, 217, 218, 219, 221, 224, 225, 227, 228, 232, 233, 236, 237, 240, 241, 242, 245, 246, 247, 249 (29/250)

3.4. Factor table 素因数分解表

73×101+719 = 89 = definitely prime number 素数
73×102+719 = 819 = 32 × 7 × 13
73×103+719 = 8119 = 23 × 353
73×104+719 = 81119 = definitely prime number 素数
73×105+719 = 811119 = 3 × 167 × 1619
73×106+719 = 8111119 = 19 × 31 × 47 × 293
73×107+719 = 81111119 = definitely prime number 素数
73×108+719 = 811111119 = 3 × 7 × 13 × 2971103
73×109+719 = 8111111119<10> = definitely prime number 素数
73×1010+719 = 81111111119<11> = 53 × 1530398323<10>
73×1011+719 = 811111111119<12> = 32 × 90123456791<11>
73×1012+719 = 8111111111119<13> = 17 × 477124183007<12>
73×1013+719 = 81111111111119<14> = 683 × 25847 × 4594619
73×1014+719 = 811111111111119<15> = 3 × 7 × 13 × 43591 × 68158633
73×1015+719 = 8111111111111119<16> = 61 × 7440127 × 17871877
73×1016+719 = 81111111111111119<17> = 109 × 10639 × 69944415269<11>
73×1017+719 = 811111111111111119<18> = 3 × 4643 × 19463 × 2991924497<10>
73×1018+719 = 8111111111111111119<19> = 601 × 13496025143279719<17>
73×1019+719 = 81111111111111111119<20> = definitely prime number 素数
73×1020+719 = 811111111111111111119<21> = 33 × 72 × 13 × 47160364620682081<17>
73×1021+719 = 8111111111111111111119<22> = 31 × 3727 × 51929 × 1351914744503<13>
73×1022+719 = 81111111111111111111119<23> = definitely prime number 素数
73×1023+719 = 811111111111111111111119<24> = 3 × 53 × 547 × 2677 × 10651 × 327082376189<12>
73×1024+719 = 8111111111111111111111119<25> = 19 × 58831189 × 7256365068455809<16>
73×1025+719 = 81111111111111111111111119<26> = 23 × 3364253 × 1048247574813540701<19>
73×1026+719 = 811111111111111111111111119<27> = 3 × 7 × 13 × 49417 × 538871 × 2364281 × 47190809
73×1027+719 = 8111111111111111111111111119<28> = 29 × 487 × 798403 × 719335065514775951<18>
73×1028+719 = 81111111111111111111111111119<29> = 17 × 8626172730211<13> × 553112252593237<15>
73×1029+719 = 811111111111111111111111111119<30> = 32 × 1792 × 14323 × 31586003 × 6217318487879<13>
73×1030+719 = 8111111111111111111111111111119<31> = 12211 × 173548906093<12> × 3827429843443753<16>
73×1031+719 = 81111111111111111111111111111119<32> = 727 × 47779 × 2335118281753945215124643<25>
73×1032+719 = 811111111111111111111111111111119<33> = 3 × 7 × 132 × 53327 × 4285753603100422650628853<25>
73×1033+719 = 8111111111111111111111111111111119<34> = 4828308966121<13> × 1679907223838550504439<22>
73×1034+719 = 81111111111111111111111111111111119<35> = 139 × 877 × 665374200069818717431983717473<30>
73×1035+719 = 811111111111111111111111111111111119<36> = 3 × 353 × 9109 × 84084062915197456044739356049<29>
73×1036+719 = 8111111111111111111111111111111111119<37> = 31 × 53 × 997 × 748677143 × 6613830408275036508223<22>
73×1037+719 = 81111111111111111111111111111111111119<38> = 773 × 11003 × 9536516044972694276500518218201<31>
73×1038+719 = 811111111111111111111111111111111111119<39> = 32 × 7 × 13 × 443 × 2007827 × 1113439009072670965596417941<28>
73×1039+719 = 8111111111111111111111111111111111111119<40> = 1353197 × 5994035688160046993239795174768427<34>
73×1040+719 = 81111111111111111111111111111111111111119<41> = 197 × 210856693069433<15> × 1952660465689929246003419<25>
73×1041+719 = 811111111111111111111111111111111111111119<42> = 3 × 2741 × 437077518501107683<18> × 225679230175529164091<21>
73×1042+719 = 8111111111111111111111111111111111111111119<43> = 19 × 59 × 113 × 499 × 1180009 × 144827317 × 750861685597672647049<21>
73×1043+719 = 81111111111111111111111111111111111111111119<44> = 1429 × 4967 × 1889754121<10> × 1923563012759<13> × 3143708310588347<16>
73×1044+719 = 811111111111111111111111111111111111111111119<45> = 3 × 7 × 13 × 17 × 441523 × 984847 × 185479584827<12> × 2166958374119705057<19>
73×1045+719 = 8111111111111111111111111111111111111111111119<46> = 89 × 11731 × 343906727 × 22589917159798838943582421805083<32>
73×1046+719 = 81111111111111111111111111111111111111111111119<47> = 6481 × 32119 × 276028502203<12> × 1411634893691852811123032507<28>
73×1047+719 = 811111111111111111111111111111111111111111111119<48> = 33 × 23 × 523543 × 380266435013997739<18> × 6560673121264033092007<22>
73×1048+719 = 8111111111111111111111111111111111111111111111119<49> = 990544955336147871917<21> × 8188534066440783407510448107<28>
73×1049+719 = 81111111111111111111111111111111111111111111111119<50> = 53 × 69899 × 481144762074049<15> × 45504857238487214757260791673<29>
73×1050+719 = 811111111111111111111111111111111111111111111111119<51> = 3 × 7 × 13 × 9694963 × 333153455333<12> × 919871631780359634723216854657<30>
73×1051+719 = 8(1)509<52> = 31 × 18043 × 14501399186372180992559193022959687898105620643<47>
73×1052+719 = 8(1)519<53> = 47 × 74693897 × 99233983700377<14> × 232828933084518375163412300033<30>
73×1053+719 = 8(1)529<54> = 3 × 97 × 2643144059<10> × 22235185811<11> × 47427012056409328624695263382341<32>
73×1054+719 = 8(1)539<55> = 1554463217952069558477619559<28> × 5217949847534578171759018841<28>
73×1055+719 = 8(1)549<56> = 29 × 5195974438070477<16> × 538288804003243666789323705170887971143<39>
73×1056+719 = 8(1)559<57> = 32 × 7 × 13 × 19391 × 51073573154263508895382788769755231859644559694411<50>
73×1057+719 = 8(1)569<58> = 457 × 619 × 3350040343732889045881<22> × 8559008632854594197760222097453<31>
73×1058+719 = 8(1)579<59> = 307 × 26113 × 2611403 × 43813387 × 88430988584372385335640500808859888669<38>
73×1059+719 = 8(1)589<60> = 3 × 607 × 4606963 × 5995991 × 165500281 × 97430733650224057036320023624621543<35>
73×1060+719 = 8(1)599<61> = 17 × 19 × 9769 × 2570559842932455230090987606626734251966909640912861437<55>
73×1061+719 = 8(1)609<62> = 15643 × 16113685860529<14> × 321784716247288491597249362293057867599098477<45>
73×1062+719 = 8(1)619<63> = 3 × 72 × 13 × 53 × 32059 × 14239811 × 229549637503<12> × 7242130108284077<16> × 10552288668991279447<20>
73×1063+719 = 8(1)629<64> = 163 × 2082729246919612747<19> × 1250171405658851405879<22> × 19111306131727563101801<23>
73×1064+719 = 8(1)639<65> = 4813 × 127946261 × 8415994816883<13> × 15650615816522249777124890059901421355301<41>
73×1065+719 = 8(1)649<66> = 32 × 50739566433473<14> × 1776196824785416780267976450508522301094234218871767<52>
73×1066+719 = 8(1)659<67> = 31 × 36781527516551085129970158907<29> × 7113591065568867697044938003575719907<37>
73×1067+719 = 8(1)669<68> = 353 × 3089 × 10718666427353<14> × 6939800428797568408148080559057107783992485103319<49>
73×1068+719 = 8(1)679<69> = 3 × 7 × 13 × 90085231 × 32981021840338857575567553033226624050851387294582961140113<59>
73×1069+719 = 8(1)689<70> = 23 × 352657004830917874396135265700483091787439613526570048309178743961353<69>
73×1070+719 = 8(1)699<71> = definitely prime number 素数
73×1071+719 = 8(1)709<72> = 3 × 37847 × 283930143684241<15> × 25160318447494385892790549401746087850780212816388499<53>
73×1072+719 = 8(1)719<73> = 1211027 × 1148464911089<13> × 14373319723384218620501<23> × 405743627615235480100209452979473<33>
73×1073+719 = 8(1)729<74> = 461 × 68737 × 2559698722478562023532025668813072225689912703859446760813998640267<67>
73×1074+719 = 8(1)739<75> = 35 × 7 × 13 × 20470361377<11> × 13298230498051<14> × 3000820575285787<16> × 44902786229364766507929677475487<32>
73×1075+719 = 8(1)749<76> = 53 × 61 × 1031 × 2433413879332739247002409113074976115042741248068644405463154163736153<70>
73×1076+719 = 8(1)759<77> = 17 × 223 × 84914624768471<14> × 1943207432733067<16> × 129665640147627780192188727114991146991865237<45>
73×1077+719 = 8(1)769<78> = 3 × 25541 × 4623341 × 21525520298707<14> × 160691869001080958757711233<27> × 661938608439068419459959143<27>
73×1078+719 = 8(1)779<79> = 19 × 96731 × 29558190942991<14> × 350135201897737965806471979769<30> × 426429700989180419199902699849<30>
73×1079+719 = 8(1)789<80> = 18169 × 1799631403<10> × 3110797699<10> × 5509157905164724529<19> × 144746734046895573046570125828388755127<39>
73×1080+719 = 8(1)799<81> = 3 × 7 × 13 × 139 × 24169 × 36936651541403710267<20> × 892116603030995402567153<24> × 26838922566326970593273504383<29>
73×1081+719 = 8(1)809<82> = 31 × 361936793 × 177034806842197<15> × 52765754286455711<17> × 77388265097449482991486660817611950498379<41>
73×1082+719 = 8(1)819<83> = 193 × 691 × 3529 × 70951 × 1476581 × 30465646035547<14> × 594287703708325304443<21> × 90859512614846635281926005447<29>
73×1083+719 = 8(1)829<84> = 32 × 29 × 160619 × 3415051 × 44218500167381<14> × 128127314640138729269525111912956426868992333216809452111<57>
73×1084+719 = 8(1)839<85> = 57605357 × 16461279187<11> × 895516635752225860273<21> × 9551690451252422595443049020201753730969697817<46>
73×1085+719 = 8(1)849<86> = 26367826695431227<17> × 132928266417155273453<21> × 864076430408612544869<21> × 26781599747059965493964013821<29>
73×1086+719 = 8(1)859<87> = 3 × 7 × 13 × 769 × 5309 × 63059 × 14990074530267924089<20> × 769888383829591157408602270590367376242018937529718193<54>
73×1087+719 = 8(1)869<88> = 54402887242802994298107005537<29> × 149093394159592827841913489111415992955265704610084632906287<60>
73×1088+719 = 8(1)879<89> = 53 × 1530398322851153039832285115303983228511530398322851153039832285115303983228511530398323<88>
73×1089+719 = 8(1)889<90> = 3 × 89 × 217331561663<12> × 536091504721<12> × 39815202495923<14> × 4348321336187043973<19> × 150604103128419797068522703933821<33>
73×1090+719 = 8(1)899<91> = 158060718403787<15> × 51316425694018456435206631432031904505616914169032018376255759555754559633037<77>
73×1091+719 = 8(1)909<92> = 23 × 2269 × 1554239774486196008797422942708166997741029588041295937898540079159773719721599461764637<88>
73×1092+719 = 8(1)919<93> = 32 × 7 × 13 × 17 × 9266977 × 117769836114493393<18> × 1380636212902920116260385926657<31> × 38663050021077919019473347904876789<35> (Makoto Kamada / msieve 0.81 / 44 seconds)
73×1093+719 = 8(1)929<94> = 3559 × 2581837 × 99501822271806996799<20> × 73968698914679730906628393661513<32> × 119934610265400019540009200162539<33> (Makoto Kamada / msieve 0.81 / 59 seconds)
73×1094+719 = 8(1)939<95> = 12260065561<11> × 6615879067492950016787525326603847768046296103416988172100290378790667799032588803879<85>
73×1095+719 = 8(1)949<96> = 3 × 3739 × 19754303 × 932287501 × 16422137600058218609025611<26> × 239090528183841595798277463730670000149203944673679<51>
73×1096+719 = 8(1)959<97> = 192 × 31 × 4343771 × 160698553 × 1038323222288262201295567800185422276240776296276391063480993680725694949364643<79>
73×1097+719 = 8(1)969<98> = 383 × 25121 × 1290491 × 23195033 × 68199075668623<14> × 4129677997883319482606116919245390723401225787206634778973607157<64>
73×1098+719 = 8(1)979<99> = 3 × 7 × 13 × 47 × 16519 × 366936867555082108170330217<27> × 106198736846979304681051510567<30> × 98203144024586234421144182430440089<35> (Makoto Kamada / GGNFS-0.71.4)
73×1099+719 = 8(1)989<100> = 353 × 120017 × 46320037507732985147<20> × 4133271906126162821272506669094546957325936289914262839905838313033086477<73>
73×10100+719 = 8(1)999<101> = 59 × 886979 × 125046073 × 3798589769831183<16> × 50949691954580556233846231<26> × 64044374295283095978848825495299945933574351<44>
73×10101+719 = 8(1)1009<102> = 33 × 53 × 2577961492877413283<19> × 219869146693855693212510893598980999453259779554650641199178603525458599999826403<81>
73×10102+719 = 8(1)1019<103> = definitely prime number 素数
73×10103+719 = 8(1)1029<104> = 469993 × 523984466989<12> × 329359767999476850570267181706884039996967064918529132169038510428789021411804587626547<87>
73×10104+719 = 8(1)1039<105> = 3 × 72 × 13 × 58771 × 121453 × 1002469005991553<16> × 139304713557256721<18> × 2642733503160737872549<22> × 161123245132623042831366776500363821859<39>
73×10105+719 = 8(1)1049<106> = 2917 × 6211 × 20431 × 261799 × 1186739 × 49995659663592396558234966635096208038207<41> × 1410708448527736521757464750138001672539901<43> (Dmitry Domanov / YAFU v1.14, Msieve 1.38 for P41 x P43 / December 28, 2009 2009 年 12 月 28 日)
73×10106+719 = 8(1)1059<107> = 887 × 91444319178253789302267318050858073405987723913315796066641613428535638231241387949392458975322560440937<104>
73×10107+719 = 8(1)1069<108> = 3 × 6719 × 8095652043826199<16> × 5444629730607944278837<22> × 912923256800170268794749758672994420857847302468287607967482501609<66>
73×10108+719 = 8(1)1079<109> = 17 × 1527397514831<13> × 963680538208470157819<21> × 324150175656483149520722081454839521597738961575053960442538029177442412163<75>
73×10109+719 = 8(1)1089<110> = 52048121 × 1573940689<10> × 694063859623<12> × 100634992774847<15> × 56187569532533993<17> × 21812976670106836929443<23> × 11566002989640497390852661629<29>
73×10110+719 = 8(1)1099<111> = 32 × 7 × 132 × 709 × 2547341 × 33315831953447122333279<23> × 1266103218806878107667124135561432759114217468458227833480982086712429759127<76>
73×10111+719 = 8(1)1109<112> = 29 × 31 × 422069 × 27008287 × 2268375173096507<16> × 152980744201498975913677<24> × 2280806851651637301775986598889171454041242659810777708593<58>
73×10112+719 = 8(1)1119<113> = 61211 × 3302837372239566620159277439<28> × 657203837720481811071319980173<30> × 610468972019395909948250818212723090657778589444207<51> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=4158229372 for P30 / December 27, 2009 2009 年 12 月 27 日)
73×10113+719 = 8(1)1129<114> = 3 × 23 × 359 × 164809 × 1151579146357<13> × 172528996131406252860654665843324514423405058371358506575893765062377685886066599415204404553<93>
73×10114+719 = 8(1)1139<115> = 19 × 53 × 547 × 563 × 663601 × 34718343145649<14> × 1135243792496590671402816043714451858841531794771073231555891252737849680928226533711753<88>
73×10115+719 = 8(1)1149<116> = 423483149 × 506230857469<12> × 8370561436337<13> × 45200268475551288516042126564696370679038744138311147521472830931767598137389192727<83>
73×10116+719 = 8(1)1159<117> = 3 × 7 × 13 × 76915343 × 38628222344441356817080084673131745677466496783391723325879245849595588528690601706124759828102215849222321<107>
73×10117+719 = 8(1)1169<118> = 5717 × 328847 × 93568744514117<14> × 46109187764932983023053937710802481140708966182574324555703563439958931160818992101299601299993<95>
73×10118+719 = 8(1)1179<119> = 391896889 × 23890504111<11> × 8473908764310713<16> × 1481306808136397833<19> × 690167362921337251081854871479702799527244356683536858418211100009<66>
73×10119+719 = 8(1)1189<120> = 32 × 131 × 233 × 583783 × 71065409 × 252664025101<12> × 912416376915226297109<21> × 61766562211443283932362136619<29> × 4998169825435385057877242607897000788441<40>
73×10120+719 = 8(1)1199<121> = 126568067 × 19128010199<11> × 100948139351740979<18> × 38635848423056691401128572469<29> × 859008846547825157061697641276255328143139250987733239693<57>
73×10121+719 = 8(1)1209<122> = definitely prime number 素数
73×10122+719 = 8(1)1219<123> = 3 × 7 × 13 × 4675923890753766574950360259<28> × 125922173315620459129615946304065183<36> × 5046009448427061833923834492113085685821350901354727155499<58> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1840428412 for P36 / December 27, 2009 2009 年 12 月 27 日)
73×10123+719 = 8(1)1229<124> = definitely prime number 素数
73×10124+719 = 8(1)1239<125> = 17 × 109 × 991 × 149021 × 883117 × 9980267138107704887730042889694227<34> × 33629730920297742691078397896650160299356842863654300111169191240765092927<74> (Dmitry Domanov / GGNFS/msieve snfs / 2.08 hours / December 29, 2009 2009 年 12 月 29 日)
73×10125+719 = 8(1)1249<126> = 3 × 11971033 × 721054861 × 31322697692787700194452469737042864683688123410031182595192008048137256137718554349082895229785004295342633921<110>
73×10126+719 = 8(1)1259<127> = 31 × 139 × 1453 × 3515042664115886887854529<25> × 9592985653134869875034205541801392613<37> × 38419689146399931009836098745774037510137112400250221617811<59> (Sinkiti Sibata / Msieve 1.40 snfs / 3.03 hours / December 28, 2009 2009 年 12 月 28 日)
73×10127+719 = 8(1)1269<128> = 53 × 181 × 907 × 588575976406774289161<21> × 1951817711276690451151<22> × 8114781544512228919114973038896918842895584864248039201824773201702249043642979<79>
73×10128+719 = 8(1)1279<129> = 33 × 7 × 13 × 14771 × 280069 × 33176599 × 693784300022328341243608052747<30> × 3466920827688321979998057094981445170611358248054011270569879480535484053774861<79> (Dmitry Domanov / GGNFS/msieve snfs / 2.80 hours / December 29, 2009 2009 年 12 月 29 日)
73×10129+719 = 8(1)1289<130> = 14923 × 9362574254222563477<19> × 5152414849636451359903<22> × 11267254740836007683936506060879526360043269528861179868616758268062621140141048203463<86>
73×10130+719 = 8(1)1299<131> = 311 × 16631 × 887128283 × 964643991739<12> × 240933276602510273<18> × 15106658509912640223271<23> × 29315128750666750426667<23> × 171747768961963388418428548111995920585587<42>
73×10131+719 = 8(1)1309<132> = 3 × 353 × 58819357 × 13021593029222227422709343698713690334129702891339061197851514030377088950090359358702607818234068181359566622491760859113<122>
73×10132+719 = 8(1)1319<133> = 19 × 24109 × 4893113 × 13209347 × 224439919343497211412546079<27> × 1214461439292902885919855851535820745800129<43> × 1005071885008421453825553937454888865893101189<46> (Sinkiti Sibata / Msieve 1.42 for P43 x P46 / 0.93 hours / December 28, 2009 2009 年 12 月 28 日)
73×10133+719 = 8(1)1329<134> = 89 × 13967 × 301391813770722620093<21> × 2507078869821283497743<22> × 9037532917613329690393464518353329398343601<43> × 9555157941091744081965785390646249746120387<43> (Dmitry Domanov / YAFU v1.14, Msieve 1.38 for P43 x P43 / December 28, 2009 2009 年 12 月 28 日)
73×10134+719 = 8(1)1339<135> = 3 × 7 × 13 × 681796099 × 5385378989499177856319113462639669954090587510631531<52> × 809183316368663220645496503880342340532984567530432543516576506517395487<72> (Dmitry Domanov / GGNFS/msieve snfs / 4.34 hours / December 29, 2009 2009 年 12 月 29 日)
73×10135+719 = 8(1)1349<136> = 23 × 61 × 142867 × 5074213991659715059285624333<28> × 42194339287273134134712956567369<32> × 189002602864580679180891001473346390943938127774955938480662659596947<69> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1951978891 for P32 / December 27, 2009 2009 年 12 月 27 日)
73×10136+719 = 8(1)1359<137> = 38851 × 119293 × 1374606113<10> × 12731656638865799150059718883624425267713240433187784157946474013103498558930107732440063058096439188134673140955292041<119>
73×10137+719 = 8(1)1369<138> = 32 × 41999635791847<14> × 873846754541779134666154613<27> × 2455596689909319807102579395371620951315538791996674025511856202407353203273892009772750619532781<97>
73×10138+719 = 8(1)1379<139> = 197 × 22271 × 44129611 × 1972934323<10> × 52732938259<11> × 360615192993721<15> × 193408834228430341613<21> × 14925053767496421729188416670285533<35> × 386824058271141944598213722244333359<36> (Makoto Kamada / Msieve 1.44 for P35 x P36 / December 28, 2009 2009 年 12 月 28 日)
73×10139+719 = 8(1)1389<140> = 29 × 2838289 × 27212567 × 11779445463889<14> × 3074194785421980803132764999896112175700613511273528323569480089187705512753746504498332535634508077597937253373<112>
73×10140+719 = 8(1)1399<141> = 3 × 7 × 13 × 17 × 53 × 1097 × 84551 × 99881 × 154175261940187589<18> × 2308713060991776510081360076355326016373955687009419350317173836354851157696597877244973452251878653404961<106>
73×10141+719 = 8(1)1409<142> = 31 × 15787 × 5093201 × 3254080049076716023017775351823366343919620677645362483994805151762825095954013737048464776166048652276605414877612263764944717827<130>
73×10142+719 = 8(1)1419<143> = 1981739 × 407148199367003<15> × 751392292468339<15> × 43269576374595547736173243979<29> × 7893242038747909008491434810029877<34> × 391720749273976260262849373015548243175374411<45> (Makoto Kamada / Msieve 1.44 for P34 x P45 / December 28, 2009 2009 年 12 月 28 日)
73×10143+719 = 8(1)1429<144> = 3 × 1063 × 1201 × 5653691 × 20884511651<11> × 26015266776968395111523501<26> × 68944265175692779490005562257497867718814938976908696960794843693551023762111711635125851305631<95>
73×10144+719 = 8(1)1439<145> = 47 × 163 × 863 × 55787 × 6506140428703<13> × 245835641351411<15> × 13749370186518038351720671169093072976197062983792743626162702687801701179790900819163639479131633657651323<107>
73×10145+719 = 8(1)1449<146> = 149 × 389 × 126013 × 734995979 × 2376330223512719<16> × 1834335947182066612841569310054514075686985313<46> × 3466238950960290194166180093999899461688609729212517793472907985191<67> (Lionel Debroux / ggnfs + msieve snfs / 19.81 hours on Core 2 Duo T7200, 2 GB RAM / December 30, 2009 2009 年 12 月 30 日)
73×10146+719 = 8(1)1459<147> = 32 × 72 × 13 × 7434503437<10> × 392034149537<12> × 1850807995846475557968504768409426147704346319<46> × 26227758482708608599358967079336782429782746125013969055315410569969216974913<77> (Dmitry Domanov / GGNFS/msieve snfs / 8.70 hours / December 29, 2009 2009 年 12 月 29 日)
73×10147+719 = 8(1)1469<148> = 467 × 571 × 829 × 18077 × 1515347 × 9775583281<10> × 8625121370475241<16> × 25756743140680881319598253147331<32> × 616787463342535551103992442128068409311527714759838090915497941410476967<72> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2756011460 for P32 / December 27, 2009 2009 年 12 月 27 日)
73×10148+719 = 8(1)1479<149> = 3001 × 27028027694472212966048354252286274945388574178977377911066681476544855418564182309600503535858417564515531859750453552519530526861416564848754119<146>
73×10149+719 = 8(1)1489<150> = 3 × 97 × 7105946748371<13> × 2587120697286311<16> × 151617287524761366379080459493275196120371591039520298402353286449046661910746835792982200092881957688064490679252170689<120>
73×10150+719 = 8(1)1499<151> = 19 × 787 × 160238028638641<15> × 154201133328636808853<21> × 116540331761190366881238622528144717<36> × 3720228068650720686461137688852033063<37> × 50635259867568960551818897795436216399281<41> (Sinkiti Sibata / Msieve 1.40 snfs / 20.04 hours / December 29, 2009 2009 年 12 月 29 日)
73×10151+719 = 8(1)1509<152> = 587 × 226201852469<12> × 320611563700643<15> × 649198280543771753408969721683516753<36> × 2934874595875161758042711750294074136406835672145013423416199808748252191780482255915587<88> (Dmitry Domanov / GGNFS/msieve snfs / March 23, 2010 2010 年 3 月 23 日)
73×10152+719 = 8(1)1519<153> = 3 × 7 × 13 × 293 × 599 × 244553 × 1999061 × 659566483 × 5716081932955821182123<22> × 5322069687668780403105271441<28> × 381991140650198618583376646303887<33> × 4517866031744013550341433300017318495804871<43> (Makoto Kamada / Msieve 1.45 for P33 x P43 / March 20, 2010 2010 年 3 月 20 日)
73×10153+719 = 8(1)1529<154> = 53 × 791321824140050171<18> × 3016269803400184939770812414730349201233819511742954597<55> × 64118174826706780157550457294753095106772211039321321833390864304025400384741429<80> (Sinkiti Sibata / Msieve 1.42 snfs / March 22, 2010 2010 年 3 月 22 日)
73×10154+719 = 8(1)1539<155> = 113 × 4691 × 8584910713<10> × 98546412238457<14> × 180867224418415537834618082324103892236965130943057219815218664917946251563670818392829229646577372784086570628350653222691573<126>
73×10155+719 = 8(1)1549<156> = 34 × 379 × 54167 × 76270710632573980933262856242243184545465711647884313<53> × 6395338640776689288090398414743305535067265521240616855130180119126584540849110303070503998611<94> (Sinkiti Sibata / Msieve 1.40 snfs / March 22, 2010 2010 年 3 月 22 日)
73×10156+719 = 8(1)1559<157> = 17 × 31 × 2017 × 12000588293<11> × 16269652186828099<17> × 8334826595479844606357732067142478308577<40> × 4689067269448324198060047798659843863179399021743490046243744990815319640523525833519<85> (Sinkiti Sibata / Msieve 1.40 snfs / March 22, 2010 2010 年 3 月 22 日)
73×10157+719 = 8(1)1569<158> = 23 × 11813194287240574685494529756410456614431<41> × 169097506711717860632323234677739370185882088167<48> × 1765419681120603888754290889693436499117110767738478402422497711718289<70> (Dmitry Domanov / ECMNET/GMP-ECM 6.2.3, GGNFS/msieve B1=11000000, sigma=3659556059 gnfs for P41 x P48 x P70 / March 21, 2010 2010 年 3 月 21 日)
73×10158+719 = 8(1)1579<159> = 3 × 7 × 13 × 59 × 16979968073<11> × 15018125201343264860491<23> × 24805636188366137938334637581360208871<38> × 2106865835629139024769587699298834367861<40> × 3778555899273683689933322821806695945733173749<46> (Sinkiti Sibata / Msieve 1.40 snfs / March 24, 2010 2010 年 3 月 24 日)
73×10159+719 = 8(1)1589<160> = 313 × 474989509 × 2834764698684673<16> × 634416991318515583535069257610316336529<39> × 30336129789368056537994274277444444259653058880044767599301074144106537495471218874266134238571<95> (Sinkiti Sibata / Msieve 1.42 snfs / March 24, 2010 2010 年 3 月 24 日)
73×10160+719 = 8(1)1599<161> = 1223 × 723063890523385279928377579631<30> × 26094469215590555810286618364998509<35> × 219281365079609140825051597505734534116290927<45> × 16029760239056102147107890808188453316076487285341<50> (Dmitry Domanov / ECMNET/GMP-ECM 6.2.3 B1=11000000, sigma=1192380505 for P30 / March 20, 2010 2010 年 3 月 20 日) (Sinkiti Sibata / Msieve 1.40 snfs / March 24, 2010 2010 年 3 月 24 日)
73×10161+719 = 8(1)1609<162> = 3 × 1847 × 3301 × 44345205948218078715522764158909429649030960966262355629853821981783730508133065675389727083140196293385914355228997458952877623894445920289346515620091559<155>
73×10162+719 = 8(1)1619<163> = 509 × 15935385287055228116131848941279196681947173106308666230080768391180964854835188823401004147566033617114167212399039511023793931456013970748744815542457978607291<161>
73×10163+719 = 8(1)1629<164> = 353 × 514561 × 5116201427<10> × 87281287515522620298297300927016839262639974366073223693012641771311815786453093840436801505919832185536362941210606875550112176927533501585040309<146>
73×10164+719 = 8(1)1639<165> = 32 × 7 × 13 × 4903 × 157513 × 4876768582181<13> × 1308836643251379738840811752451457<34> × 200909540176671826398163862912942850525870156003328247652388305575984510666880969685100950665754885604581327<108> (Serge Batalov / GMP-ECM B1=1000000, sigma=1899502385 for P34 / March 22, 2010 2010 年 3 月 22 日)
73×10165+719 = 8(1)1649<166> = 19631999 × 227638054891477<15> × 1485978401618924901429923399<28> × 908777620815932727836561553460523488695544035222835713517<57> × 1344004864375804619963978594024872315991755133969521757612791<61> (Sinkiti Sibata / Msieve 1.40 snfs / March 27, 2010 2010 年 3 月 27 日)
73×10166+719 = 8(1)1659<167> = 53 × 1663 × 9227 × 22550554421<11> × 730564567922213<15> × 10926147436516769903147270310874897947513674795745184831561<59> × 554075345116965317809376196641109773870039465475100829831179449901195385591<75> (Sinkiti Sibata / Msieve 1.40 snfs / March 28, 2010 2010 年 3 月 28 日)
73×10167+719 = 8(1)1669<168> = 3 × 29 × 400307 × 13587839 × 139699193 × 534391643 × 8905457063693<13> × 6901954536203986763928693998157238393067937016586420795198531<61> × 373538747025304453489596309560240921659812714841516661553591257<63> (Sinkiti Sibata / Msieve 1.40 snfs / March 29, 2010 2010 年 3 月 29 日)
73×10168+719 = 8(1)1679<169> = 19 × 373 × 67477 × 776219057 × 528372892591<12> × 192838425402163<15> × 105576070585008765246725446861<30> × 46259354439507947687759406121313<32> × 43911541593266390715124617325956279475958334003954011857668903157<65> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1680471515 for P32 / March 15, 2010 2010 年 3 月 15 日) (Ignacio Santos / GMP-ECM 6.2.3 B1=11000000, sigma=3267219035 for P30 / March 20, 2010 2010 年 3 月 20 日)
73×10169+719 = 8(1)1689<170> = 172199 × 41152123 × 52187507 × 177026747 × 263887817 × 1120311692399<13> × 3850571317282793<16> × 107898984614743811359396927485333962240322006001<48> × 10086751052653309603849303117734291539731633946535963978197<59> (Dmitry Domanov / Msieve 1.40 gnfs for P48 x P59 / March 23, 2010 2010 年 3 月 23 日)
73×10170+719 = 8(1)1699<171> = 3 × 7 × 13 × 40816441 × 762654173 × 48152453459731<14> × 8098986351536887250777<22> × 199073909004114409087838059995602923784953407296551<51> × 1229395127503956453110320892174282744371363133381675250834912569183<67> (Markus Tervooren / Msieve 1.39 gnfs for P51 x P67 / March 24, 2010 2010 年 3 月 24 日)
73×10171+719 = 8(1)1709<172> = 31 × 167 × 6269 × 3490062618945437<16> × 71609509123671864937748104527167000162729593386713128332545380603171837724812163062073136936115428403226884401604823338693380585640881688472491301999<149>
73×10172+719 = 8(1)1719<173> = 17 × 139 × 11974985326789<14> × 6834369813389795228000051231<28> × 13324300128770220679363512021008285679469<41> × 31477393078303577192338852747323144561271038064664956144484487895034781518338342136686403<89> (Ignacio Santos / GMP-ECM 6.2.3 B1=11000000, sigma=3881978367 for P41 / March 25, 2010 2010 年 3 月 25 日)
73×10173+719 = 8(1)1729<174> = 32 × 3833 × 109921362229403379317906076629202024169983679713342589<54> × 213903021924709700966725531874392013593509801982320886329878519207658021547473078621047504495471576430072545726869243<117> (Wataru Sakai / Msieve / April 11, 2010 2010 年 4 月 11 日)
73×10174+719 = 8(1)1739<175> = 337 × 883 × 5492639 × 6765859013856517<16> × 733475726926629789624639743841196871367189862844058311717409631824546903607451313446291575949459522623571747538682028668356886077985196481384055103<147>
73×10175+719 = 8(1)1749<176> = 5326415459186924171<19> × 615372942444724421742301622852266259289250502392937608623668190389457346687<75> × 24746108667306825892150263612358114824355465819510480863545451091251296975012452147<83> (Robert Backstrom / Msieve 1.44 snfs / October 1, 2010 2010 年 10 月 1 日)
73×10176+719 = 8(1)1759<177> = 3 × 7 × 13 × 12487245503947891010267<23> × 403575435619433143165823<24> × 589557718091102670397574507702572541680449302030172688686056259531804103123345716503406431159958178137970923195575512438984613683<129>
73×10177+719 = 8(1)1769<178> = 89 × 1811 × 432959 × 3205236259417<13> × 574396743979679<15> × 15343004196366191<17> × 2341177347359578449146897594973923<34> × 89431210159523054761511299251599119467930611<44> × 19652566780013531408077346917236765410161450211<47> (Ignacio Santos / GMP-ECM 6.2.3 B1=1000000, sigma=66588169 for P34 / March 20, 2010 2010 年 3 月 20 日) (Markus Tervooren / yafu 1.16 / March 21, 2010 2010 年 3 月 21 日)
73×10178+719 = 8(1)1779<179> = 1031 × 4179298895184504894455453743<28> × 18824274762801881157934425266726498504175811546082491872345271284240370841003641029761916379200740870339959620023385758476470831686052871854862521943<149>
73×10179+719 = 8(1)1789<180> = 3 × 23 × 53 × 2090317 × 37307723 × 317609229239<12> × 418007939801<12> × 181752199409458861117669154124804770857<39> × 117865627939428159284170436744413355698232193335027149918042074350680989005736615277112389110260960719<102> (Robert Backstrom / Msieve 1.44 snfs / September 30, 2010 2010 年 9 月 30 日)
73×10180+719 = 8(1)1799<181> = 336045999778278361468391969869<30> × 10386321462700568540425420443421528815354802853614457593<56> × 2323912973932756983724631095665817181922892562606143545631583211265004361372826006976229260396707<97> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1505205109 for P30 / March 15, 2010 2010 年 3 月 15 日) (Robert Backstrom / Msieve 1.44 snfs / September 30, 2010 2010 年 9 月 30 日)
73×10181+719 = 8(1)1809<182> = 10808657 × 121317036925390572829<21> × 35252946975361538516688670009973<32> × 13147348290245991062072054295243276024194393<44> × 133460646752294643798066604926464546579671078112544808831269222913583727078726007<81> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=134833877 for P32 / March 16, 2010 2010 年 3 月 16 日) (Luigi Morelli / Msieve 1.44-GPU for polybomial selection Msieve 1.44 for LA GGNFS 0.77.1 for sieving factmsieve.py for automation / March 25, 2010 2010 年 3 月 25 日)
73×10182+719 = 8(1)1819<183> = 33 × 7 × 13 × 6629113 × 6892585283282467724482193660744448506322729576216573632623329989779223<70> × 7224996211590542705856809999220894510332841550074603613386420237692412812930457163482858397449460559033<103> (matsui / Msieve 1.47 snfs / September 18, 2010 2010 年 9 月 18 日)
73×10183+719 = 8(1)1829<184> = 66803507081<11> × 3718348300193<13> × 32653596345249616045497209214012519056103753309479729366865755313130406182700772076893117471921075382735319008683150786022713973748093183718501254100367525932343<161>
73×10184+719 = 8(1)1839<185> = 2417 × 2707 × 24903763 × 96044609 × 81002358555891581<17> × 63985241360335882041311845560276433167884300254022806645280164203977242362968278787613916683577051267266445439050732983630820776327146022829664563<146>
73×10185+719 = 8(1)1849<186> = 3 × 6991 × 7271582161<10> × 251723078195984291874958793<27> × 219669271682175451617021375736320952183499<42> × 2923088295786972486300125649576748937217643<43> × 32904598830433764759349230757719616714741337644102413899504923<62> (Robert Backstrom / Msieve 1.44 snfs / September 29, 2010 2010 年 9 月 29 日)
73×10186+719 = 8(1)1859<187> = 19 × 31 × 10796787151<11> × 15215666293<11> × 18041681281108844462411821<26> × 52593897983982633765289356677210831<35> × 11697732234420333258671146321369687245228756659<47> × 7552061175018540120341108340869899034360620024154378035033<58> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1809670543 for P35 / March 16, 2010 2010 年 3 月 16 日) (Dmitry Domanov / Msieve 1.40 gnfs for P47 x P58 / March 23, 2010 2010 年 3 月 23 日)
73×10187+719 = 8(1)1869<188> = 1417727 × 3480428356907<13> × 281058495879176993399901151002829941325214371<45> × 5798303789731656169461409227895093868122231985568611<52> × 10086891714165103585270799664092952494368167310071179401134235381838853691<74> (Robert Backstrom / Msieve 1.44 snfs / September 29, 2010 2010 年 9 月 29 日)
73×10188+719 = 8(1)1879<189> = 3 × 72 × 132 × 17 × 2437 × 641279 × 709901 × 114212877036568549<18> × 133511174509886350806748681<27> × 268325269005618510033734242274281<33> × 1899842397191770810723806788623538606419<40> × 222697436487626525196820465796436832258574649762401293<54> (Ignacio Santos / GMP-ECM 6.2.3 B1=1000000, sigma=3801813955 for P33 / March 21, 2010 2010 年 3 月 21 日) (Robert Backstrom / Msieve 1.42 for P40 x P54 / March 22, 2010 2010 年 3 月 22 日)
73×10189+719 = 8(1)1889<190> = 915391641457<12> × 211037023797959<15> × 2378929041358395440570388305691413527<37> × 16745449919378812904772880514993263516725189546710466059<56> × 1053989891803546867331821719596720764892901851071881856793059148655031741<73> (Robert Backstrom / Msieve 1.44 snfs / September 28, 2010 2010 年 9 月 28 日)
73×10190+719 = 8(1)1899<191> = 47 × 7496978611399826992455954336521573069359668309961900039224111224953942825609<76> × 230195177413047059659441039403278277652620483014205313141683306096676569285407621213308806340434888879386009321753<114> (Robert Backstrom / Msieve 1.42 snfs / March 24, 2010 2010 年 3 月 24 日)
73×10191+719 = 8(1)1909<192> = 32 × 1487 × 699007553 × 1213878817<10> × 1578101062073616097817<22> × 96094606459575327752508385732998430439451617<44> × 471016202673307634040226107058357315164887792708789395878207443000259702157273289091174488149526384423137<105> (Robert Backstrom / Msieve 1.44 snfs / September 26, 2010 2010 年 9 月 26 日)
73×10192+719 = 8(1)1919<193> = 53 × 1657421 × 237630011 × 12372543056971<14> × 530923960542041853706277789<27> × 366523956355671874129507039010384399339<39> × 161390025676248894619031522077227942750232711830937806052262159386512238871340527822289140501889113<99> (Robert Backstrom / Msieve 1.44 snfs / September 25, 2010 2010 年 9 月 25 日)
73×10193+719 = 8(1)1929<194> = 2503 × 160807 × 1298989 × 5681311 × 360419933218637<15> × 75762049104256011445556911197294530729433215296081256212363457151714915051488507884659626536508828037460222921743554283480446867872775998321565042373063943993<158>
73×10194+719 = 8(1)1939<195> = 3 × 7 × 13 × 18935314456125229<17> × 539306303757739067709520386122194699963<39> × 290944187480008503753361597257435609869095574941470512565658904614134175315637778381697901031634201112946972718652382630672776881701842689<138> (Robert Backstrom / Msieve 1.44 snfs / September 24, 2010 2010 年 9 月 24 日)
73×10195+719 = 8(1)1949<196> = 292 × 61 × 353 × 447898712945868673385429598399840739488874064055050261383565137176619660187590902347607110636264848202800585485834844270556665761481774599488510713893671434769347532507890364727419243141123<189>
73×10196+719 = 8(1)1959<197> = 433 × 29443 × 2656681 × 6434200369<10> × 9397216147747601<16> × 37756865892370643047<20> × 1049013918848203009063140482706515043166625562126496192927829612505125837634223453751455635065437753235519231169381854256517543486527779947<139>
73×10197+719 = 8(1)1969<198> = 3 × 647 × 797 × 110939 × 4892051 × 85643781889503911<17> × 11280424271281963599926601625425825868662565432906739602726447550289591798096586437773609085222788754857526928585646252597157051069204635515728864642508972835331193<164>
73×10198+719 = 8(1)1979<199> = 279539271932317<15> × 3352284571152846830118245947046747189941725918269344568618460499291<67> × 8655589327660395444439146878956179283514660603962780433777407376546134001432980859314049759960603858809145479882277377<118> (Robert Backstrom / Msieve 1.44 snfs / September 23, 2010 2010 年 9 月 23 日)
73×10199+719 = 8(1)1989<200> = 317320846555790721689707265209124086042995871333587511<54> × 255612299007434787227951883926880089100593501794351086681386748513524528985678312669078680409663386409205947285045497066341365429585108683464620329<147> (Robert Backstrom / Msieve 1.42 snfs / March 24, 2010 2010 年 3 月 24 日)
73×10200+719 = 8(1)1999<201> = 32 × 7 × 13 × 3203 × 614021978664118356973<21> × 1224338533730394224447247509110331<34> × 411295611031908342163002374866003999670835852329885052523088252550051262801763471870564995367025345471806591310857370409606162674852248044409<141> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1567209574 for P34 / March 16, 2010 2010 年 3 月 16 日)
73×10201+719 = 8(1)2009<202> = 23 × 31 × 21436690189<11> × 7724182114067<13> × 68703772515689804100926334965166713500596533245070358179439807888068812957648190261163518536708876002005387862164930226773524810469177880310757257781520656052098940438061677601<176>
73×10202+719 = 8(1)2019<203> = 997 × 24587740717<11> × [3308769910070880374997742244102348605422449652556063138730848241119325103448298209418414257246722321997275953758180595087822829094482382705001253445083425062568317752939135065148060767849231<190>] Free to factor
73×10203+719 = 8(1)2029<204> = 3 × 394523 × 2343549323<10> × 225689450702712260774227<24> × [1295690908057830538687292299245766791601388249220164401286543680776247548379987648052826925663960772311617951211231547384377799242780806749899997267294392793482506031<166>] Free to factor
73×10204+719 = 8(1)2039<205> = 17 × 19 × 18253 × 26903517551<11> × [51136913107536238696017073218444170806053791322538388389759000538347172991099254292281509568321279037563895643007492181474545406892801375109435073838896134184042869592818924119331573666551<188>] Free to factor
73×10205+719 = 8(1)2049<206> = 53 × 547 × 1579 × 10067 × 6154769 × 42894022771053017887<20> × 666693806241746151914430420141918932432575571829058703908892087711874115972595018100175490913424136708824178761458079378556265994820821243397634706331686126784201801071<168>
73×10206+719 = 8(1)2059<207> = 3 × 7 × 13 × 79023961922291<14> × 329549860738834850434099172387<30> × [114087423318336988045431624193116294023998383051271102341016499323033114919567617443007607559004910235408213364793580983753361416280544906654531018107274596563159<162>] (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=110134751 for P30 / November 17, 2010 2010 年 11 月 17 日) Free to factor
73×10207+719 = 8(1)2069<208> = 179 × 24667823 × 31831981 × 17843766365423<14> × 3234046805105052459517211602014706595377630542524854972531783999463975652161573483765468329235218858542680376036709858707110994931175772584193752294203118850130144184387176446089<178>
73×10208+719 = 8(1)2079<209> = 761 × 2593 × 1591553 × [25826887547530910130009019428989740770518498333130383741741018314811770176555217586753995300786714575998734297642866609289828765314268288698989128886844739809172985740415269408357758073492567661351<197>] Free to factor
73×10209+719 = 8(1)2089<210> = 33 × 457 × 5774873724031<13> × 148342299393474493<18> × [76734892265529098249576894046999247818415729630519435479779769871981330807464720529901366324986122796966085271122922436584310130589958953912749603803781002379206273566534150887<176>] Free to factor
73×10210+719 = 8(1)2099<211> = 234539 × 232586450790051429503727527786658809022841<42> × 148689694804900261435988892509679074524672603890222244730943538446300992786432947303886353200691251950883351320538850072998602765400037363496706132191928732400348181<165> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2744833427 for P42 / November 26, 2010 2010 年 11 月 26 日)
73×10211+719 = 8(1)2109<212> = 307 × 34123 × 135647297329<12> × 24283073347217<14> × 570589345455928459<18> × 137037202278734319534491<24> × 13663049011549680367274455192111<32> × 2200240753456168818403181688961567688244740542413528405806723271968970023750685846919754379690387018660339017<109> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=327971039 for P32 / November 23, 2010 2010 年 11 月 23 日)
73×10212+719 = 8(1)2119<213> = 3 × 7 × 13 × 495619 × 677600377 × 42497873227148333<17> × 2253998429255954471<19> × [92358168451149912016111447864599162540288632671568280270499029393948905375392603800382146353868350726263100412033846808153177408047101595903699359506523635990567<161>] Free to factor
73×10213+719 = 8(1)2129<214> = 329309880516853681<18> × [24630633913506261359519381291856334524711585600913469799121688310574635479676284046525488434367159447161190078268908964459697974977908456908530140294932626376799741086615657965217649891194879420799<197>] Free to factor
73×10214+719 = 8(1)2139<215> = 2357 × 694238890221387649<18> × 15959727733735083945273849239<29> × [3105892009439617495848294984893431707668205404865213344289388845729057102183263515421635469798533504686243311014100541962794971663933448328939504730531101622319924997<166>] Free to factor
73×10215+719 = 8(1)2149<216> = 3 × 41766247642999368779127870829<29> × 183642094245528835212060093737<30> × 35250184948949947160512545702369260171534498238431036379655515245218324904416238413561275435288349733867076858761803452436120276327369844787819942027561478801<158> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=1770192900 for P30 / November 17, 2010 2010 年 11 月 17 日)
73×10216+719 = 8(1)2159<217> = 31 × 59 × 2243 × 5433215629<10> × 33364967299492916166529447526196465331<38> × [10906608566728826105057954494114497932743438696193878406232509869239462381306200532636418804852903207174157984155728649153682805538415974378285700852845980605044423<164>] (Serge Batalov / GMP-ECM B1=3000000, sigma=2426130124 for P38 / January 9, 2014 2014 年 1 月 9 日) Free to factor
73×10217+719 = 8(1)2169<218> = 90527 × 552737517362766273145704797<27> × [1621000984904232259576398393045964392934997014854201672121450803559029624983860058847185860188064048919018176655240944267425335363187611398651507836213595762851714305846828483150884144901<187>] (Serge Batalov / GMP-ECM B1=2000000, sigma=1665061202 for P27 / November 23, 2010 2010 年 11 月 23 日) Free to factor
73×10218+719 = 8(1)2179<219> = 32 × 7 × 13 × 53 × 139 × 15108197952359<14> × [8898014571326872488216021000302325045594502246471836501374775162687824146717763349632376817695603999414146147808472188586739658147907174076547152664343233154041330847394117014624172369250494507153317<199>] Free to factor
73×10219+719 = 8(1)2189<220> = 13899640752804972926989<23> × [583548255337050639477787930465511211528416611975676626510587100891363415786629997600562054587570007374693282796418272754245438291497680138999828744431216260526312207230346581262984421530532589764171<198>] Free to factor
73×10220+719 = 8(1)2199<221> = 17 × 153574144507725141184644968721793<33> × 31068002008797482021990941048726398288529276547998900509874983220580782653580694003698545534656335343512265499762007336929153692378808561773165597409955514739063272129740104780998553653599<188> (Serge Batalov / GMP-ECM B1=2000000, sigma=1676103107 for P33 / November 23, 2010 2010 年 11 月 23 日)
73×10221+719 = 8(1)2209<222> = 3 × 89 × 229 × 11411 × 1520681 × 219153421855409<15> × [3488377894734596170175004508986887533455160924009510762286067168105778669606874113752914925415396734502704677755991555353360029119975523643465828132521869358795689409086536603152656041863824107<193>] Free to factor
73×10222+719 = 8(1)2219<223> = 19 × 103681 × 550127 × 28451147 × 263066067329524912237445395165509632013345144631484350429853266845000475289088034650149290286482033128352718641791768628561083105516575624787453507609259505719973554725080346708155148767994222783925707409<204>
73×10223+719 = 8(1)2229<224> = 23 × 29 × 557 × 19457 × 22468606868843<14> × 10412289164053984436254007<26> × 649159157722396676815492141<27> × 514249715672073859794526521886223319724173480502323152759088545591<66> × 143673220997188922577118402337989402640026256542427142425127212190734735626923081103<84> (Maksym Voznyy / factMsieve.py, gnfs-lasieve4I14e, Msieve v. 1.53 (SVN 967) for P66 x P84 / March 8, 2015 2015 年 3 月 8 日)
73×10224+719 = 8(1)2239<225> = 3 × 7 × 13 × 2296727 × 368635339 × 2205603728213<13> × [1591050169780434366119021782976545934087944864459335540320610367298204637010149935122704142304709174153745336617407887201763356507385011254256884975040982732849567249725770068847144722821785076127<196>] Free to factor
73×10225+719 = 8(1)2249<226> = 163 × 77689090610688710373358160127303433331549<41> × [640520019843442932505874698863733328094878409737361607796119159115279259361287943619562679071885899517989498394073290814684594542691069828144536299162464353188078830416180415452439337<183>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=170158555 for P41 / June 10, 2011 2011 年 6 月 10 日) Free to factor
73×10226+719 = 8(1)2259<227> = 135301478262941<15> × 507153620781021063559<21> × 1182056617509355095083890277714276341478501895346716541877307218376198996149561199302081905905411155629352741743801063073151972231233543264667322834478953882547186509285661132190878240378133901<193>
73×10227+719 = 8(1)2269<228> = 32 × 269 × 353 × 7963230883<10> × 82171789121<11> × [1450436784046930570347636281780452788663706068095462506047616330235143564820966722041315602436241377407415364309104734586937160206020241613774172164670721758773899053393896041536350808380674291529057041<202>] Free to factor
73×10228+719 = 8(1)2279<229> = 1823 × 3847160191659054899<19> × [1156520703677932561651070836728448438189307307047783609808380614461870755940925155444515921361200691587029770405206515286038384148957397689553214277696673465902194669716586268080410889961599512854050544848747<208>] Free to factor
73×10229+719 = 8(1)2289<230> = 2505941101<10> × 63238566439<11> × 511832047643360377333509941314788571815308520486502564215727119753921704291962945573094124650706063845005313034037181910771918564481286185979960440134939084561280205794344258523465027879608774435190357286285021<210>
73×10230+719 = 8(1)2299<231> = 3 × 73 × 13 × 773 × 78440820843862267417459222512421023390741161419937458166462575470680653245270295195051643556012962248936586925339994484858122421815428125325952503395278694272806794917838559098426564170947305831272354492250471340684398740739<224>
73×10231+719 = 8(1)2309<232> = 31 × 53 × 1303 × 4204698879592132039<19> × 901080253132326070082025256674968254024765572014847608313567254052451960713443155966052386198456802490331685234882267682693222577836292361734185451884720843634357006037566311264891687224617883494763813407949<207>
73×10232+719 = 8(1)2319<233> = 109 × 112571143132460521<18> × 135498853562457399373<21> × [48785544410324464562796921889878804329914871193310059551740458019696901202600063005877200721162941029006343564259848774543624409058335667557387784046725095362624000604653610954986643182790779327<194>] Free to factor
73×10233+719 = 8(1)2329<234> = 3 × 4127 × 318313 × 2019504881980615442408252747323823906995900701559<49> × [101912004552457573576522098316186508353856361793501395587516179878762363321254922686911599249087503321383707554312991223126442913011531999649462449244684585648713280439893950197<177>] (Ha Seok woo / GMP-ECM B1=110000000, sigma=3916377619 for P49 / December 8, 2011 2011 年 12 月 8 日) Free to factor
73×10234+719 = 8(1)2339<235> = 781545267739127<15> × 8753397836245328700767<22> × 1185630998802581267788288725077821424728448361622206481565900815443750128160273731616548477120188962915528256193609185045704017931172146127202860719687187243994702053484372748997352870981007411947191<199>
73×10235+719 = 8(1)2349<236> = definitely prime number 素数
73×10236+719 = 8(1)2359<237> = 34 × 7 × 13 × 17 × 47 × 197 × 84482443 × 1018949747069<13> × [8121228016759516059372987793655549886374421394465569669566529420028487044609657891018438451417006714812850327276618227507299947467138927533114346294023200066528627386779824568483525691836647812424742148827689<208>] Free to factor
73×10237+719 = 8(1)2369<238> = 776665485361<12> × [10443506585516678694353966434403003280481334801246316807629465784174603771692106479445601566846052062529450908376570040558927794337787750868277264886649389971321670527774242537100267247253706188388844364704501186186722566791679<227>] Free to factor
73×10238+719 = 8(1)2379<239> = 367 × 3787513 × 283283285134599695324489696609340732911<39> × 205986711418370119700727781351409819649347810930783139943107704213306176367156105081703474372820302077997710807258735825012107451865038083464669148939903997524388118956489490002432708444056999<192> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=4253215987 for P39 / November 25, 2010 2010 年 11 月 25 日)
73×10239+719 = 8(1)2389<240> = 3 × 2969 × 3583 × 14694773190616343695402421<26> × 1729574218485238057609095776751651518263910465024869908535562623579925814211285782844647180925664780593312988120888874928229716666463631311109164686922176148443186240364751665417640242771285170649106414678919<208>
73×10240+719 = 8(1)2399<241> = 19 × 1651493 × 314026723 × 1456487368445387565310585704433<31> × [565166853296857323371548261312178490248128736103418767162794529129252327319384248656209718045152862389239990123589723998738487702073847357383054519569683333375436147285681150424624213251633259723<195>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3710569134 for P31 / November 23, 2010 2010 年 11 月 23 日) Free to factor
73×10241+719 = 8(1)2409<242> = 257 × 9528157 × 43650331 × 44694547487<11> × 5578993703623<13> × [3043269164308166954322232258911748753796531855713395740023764383337825829124717532221267435440703562422948957086458284487412397591576127920003190565393137236326353496309310438897533049039113628061193001<202>] Free to factor
73×10242+719 = 8(1)2419<243> = 3 × 7 × 13 × 148847217100141081<18> × 196651270445493831283<21> × [101503315400987099450210655718254783539703115962258504083872797000758416533598311029984768171380557410030762044050316244802073435947532309864551564509550610171833083039240380247452475958498811741120255661<204>] Free to factor
73×10243+719 = 8(1)2429<244> = 263 × 192991 × 60509219 × 63509479025629873<17> × 41584113551204831468822029033375364490317677336630758087780327940401709622756911706407734800096734330682650366703327571010062903020182368691641058601978695396429528202665500096249424176397686216490855646057008189<212>
73×10244+719 = 8(1)2439<245> = 53 × 305387435436792887<18> × 5011333621706597586396750372504732245735201841379554149685106609908544947776831016933020179941981117392724030108752410278181332501573754989021676084668635135329417674767729057489420564567072801004758969316488028045224135185829<226>
73×10245+719 = 8(1)2449<246> = 32 × 23 × 97 × 2557 × 21841 × 2494061 × 1937859450277717<16> × 393772063983289715497172339<27> × [380067536207154385323552059614019239486110286727060749879217286690633031158277476788771230297384468787809698236165912395115009566741550785078133627642413359268445732742347052802464558071<186>] Free to factor
73×10246+719 = 8(1)2459<247> = 31 × 2677 × 1105315987<10> × 2872237052813<13> × [30786729339642233542303872840616346735944079703536245234904360475523661615371115442178072692206987047968339251715499547577613414733966345857744388316732337612660198983985919044123177024075997290558550909120413803148839227<221>] Free to factor
73×10247+719 = 8(1)2469<248> = 2473 × 66343 × 2712617598245899<16> × 364591649716863078605617563872673979<36> × [499880085488008501631204955959372249632756824551462321633322671524074909864594574522146429046349848317225817744252794145549067005091578299411612520642703521021794220682816800081502054597801<189>] (Serge Batalov / GMP-ECM B1=2000000, sigma=275747159 for P36 / November 23, 2010 2010 年 11 月 23 日) Free to factor
73×10248+719 = 8(1)2479<249> = 3 × 7 × 13 × 103769599 × 28631728364903588988245998436430029020070733540205461360326765559756775228273773815999530873884392394182530309007968423420149315322139493889449288236171858994763032389697979877238447949509481124342621494595648413087757726643726386290680097<239>
73×10249+719 = 8(1)2489<250> = 131 × 2819 × [21964128666467485116294043719447671366087565866059132850182678366025284021758327789647433611916713227610654828903950865341537687586446146814855333116099074467723412046151147505371432972850832575871772815088213055658606433203022865861455692184471<245>] Free to factor
73×10250+719 = 8(1)2499<251> = 2221127 × 1483240014369035198518789425703014375349<40> × 24620423897340243405387762055493633626947480767613720193686416436904105744370182256952341851373688970455913886022602371183628209812748418535784884286398157602682929374808039017713564584689360208260300600053<206> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2331442533 for P40 / February 27, 2011 2011 年 2 月 27 日)
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4. Related links 関連リンク