Table of contents 目次

  1. About 499...99 499...99 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
    4. Related sequences 関連する数列
  2. Prime numbers of the form 499...99 499...99 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 499...99 499...99 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 499...99 499...99 について

1.1. Classification 分類

Near-repdigit of the form ABB...BB ABB...BB の形のニアレプディジット (Near-repdigit)

1.2. Sequence 数列

49w = { 4, 49, 499, 4999, 49999, 499999, 4999999, 49999999, 499999999, 4999999999, … }

1.3. General term 一般項

5×10n-1 (0≤n)

1.4. Related sequences 関連する数列

2. Prime numbers of the form 499...99 499...99 の形の素数

2.1. Last updated 最終更新日

April 24, 2023 2023 年 4 月 24 日

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

  1. 5×102-1 = 499 is prime. は素数です。
  2. 5×103-1 = 4999 is prime. は素数です。
  3. 5×104-1 = 49999 is prime. は素数です。
  4. 5×106-1 = 4999999 is prime. は素数です。
  5. 5×1014-1 = 4(9)14<15> is prime. は素数です。
  6. 5×1054-1 = 4(9)54<55> is prime. は素数です。
  7. 5×10210-1 = 4(9)210<211> is prime. は素数です。
  8. 5×10390-1 = 4(9)390<391> is prime. は素数です。
  9. 5×10594-1 = 4(9)594<595> is prime. は素数です。
  10. 5×103460-1 = 4(9)3460<3461> is prime. は素数です。 (Harvey Dubner / Caldwell, Cruncher / December 31, 1989 1989 年 12 月 31 日)
  11. 5×105028-1 = 4(9)5028<5029> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1991 1991 年 12 月 31 日)
  12. 5×105219-1 = 4(9)5219<5220> is prime. は素数です。
  13. 5×105332-1 = 4(9)5332<5333> is prime. は素数です。
  14. 5×108072-1 = 4(9)8072<8073> is prime. は素数です。 (Harvey Dubner / Cruncher / October 1, 1994 1994 年 10 月 1 日)
  15. 5×1015796-1 = 4(9)15796<15797> is prime. は素数です。 (Harvey Dubner / Cruncher / June 16, 1999 1999 年 6 月 16 日)
  16. 5×1016131-1 = 4(9)16131<16132> is prime. は素数です。 (Harvey Dubner / Cruncher / June 16, 1999 1999 年 6 月 16 日)
  17. 5×1021456-1 = 4(9)21456<21457> is prime. は素数です。 (Eric J. Sorensen / Proth.exe / September 24, 2001 2001 年 9 月 24 日)
  18. 5×1029282-1 = 4(9)29282<29283> is prime. は素数です。 (Eric J. Sorensen / Proth.exe / October 7, 2001 2001 年 10 月 7 日)
  19. 5×1078790-1 = 4(9)78790<78791> is prime. は素数です。 (Eric J. Sorensen / Proth.exe / January 4, 2005 2005 年 1 月 4 日)
  20. 5×1085142-1 = 4(9)85142<85143> is prime. は素数です。 (Eric J. Sorensen / Proth.exe / October 9, 2005 2005 年 10 月 9 日)
  21. 5×10179972-1 = 4(9)179972<179973> is prime. は素数です。 (David Broadhurst / NewPGen, OpenPFGW / October 17, 2010 2010 年 10 月 17 日)
  22. 5×10211029-1 = 4(9)211029<211030> is prime. は素数です。 (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / November 4, 2010 2010 年 11 月 4 日)
  23. 5×10445773-1 = 4(9)445773<445774> is prime. は素数です。 (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / January 31, 2011 2011 年 1 月 31 日)
  24. 5×10464843-1 = 4(9)464843<464844> is prime. は素数です。 (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / February 13, 2011 2011 年 2 月 13 日)
  25. 5×10511056-1 = 4(9)511056<511057> is prime. は素数です。 (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / March 16, 2011 2011 年 3 月 16 日)

2.3. Range of search 捜索範囲

  1. n≤30000 / Completed 終了 / Ray Chandler / September 30, 2010 2010 年 9 月 30 日
  2. n≤100000 / Completed 終了 / Gary Barnes / December 1, 2010 2010 年 12 月 1 日
  3. n≤135000 / Completed 終了 / Gary Barnes / January 3, 2010 2010 年 1 月 3 日
  4. n≤140000 / Completed 終了 / Gary Barnes / January 14, 2011 2011 年 1 月 14 日
  5. n≤145000 / Completed 終了 / Gary Barnes / January 16, 2011 2011 年 1 月 16 日
  6. n≤150000 / Completed 終了 / Gary Barnes / January 18, 2011 2011 年 1 月 18 日
  7. n≤155000 / Completed 終了 / Gary Barnes / January 20, 2011 2011 年 1 月 20 日
  8. n≤160000 / Completed 終了 / Gary Barnes / January 24, 2011 2011 年 1 月 24 日
  9. n≤165000 / Completed 終了 / Gary Barnes / January 25, 2011 2011 年 1 月 25 日
  10. n≤170000 / Completed 終了 / Gary Barnes / January 28, 2011 2011 年 1 月 28 日
  11. n≤175000 / Completed 終了 / Gary Barnes / January 31, 2011 2011 年 1 月 31 日
  12. n≤180000 / Completed 終了 / Gary Barnes / February 3, 2011 2011 年 2 月 3 日
  13. n≤185000 / Completed 終了 / Gary Barnes / February 7, 2011 2011 年 2 月 7 日
  14. n≤190000 / Completed 終了 / Gary Barnes / February 11, 2011 2011 年 2 月 11 日
  15. n≤195000 / Completed 終了 / Gary Barnes / February 17, 2011 2011 年 2 月 17 日
  16. n≤200000 / Completed 終了 / Gary Barnes / February 20, 2011 2011 年 2 月 20 日
  17. n≤205000 / Completed 終了 / Gary Barnes / February 27, 2011 2011 年 2 月 27 日
  18. n≤210000 / Completed 終了 / Gary Barnes / February 28, 2011 2011 年 2 月 28 日
  19. n≤215000 / Completed 終了 / Gary Barnes / March 5, 2011 2011 年 3 月 5 日
  20. n≤220000 / Completed 終了 / Gary Barnes / March 9, 2011 2011 年 3 月 9 日
  21. n≤225000 / Completed 終了 / Gary Barnes / March 15, 2011 2011 年 3 月 15 日
  22. n≤230000 / Completed 終了 / Gary Barnes / April 17, 2011 2011 年 4 月 17 日
  23. 1000001≤n≤1010000 / Completed 終了 / Predrag Kurtovic / September 5, 2016 2016 年 9 月 5 日
  24. 1010001≤n≤1015000 / Completed 終了 / Predrag Kurtovic / June 12, 2017 2017 年 6 月 12 日
  25. 1015001≤n≤1020000 / Completed 終了 / Predrag Kurtovic / November 8, 2017 2017 年 11 月 8 日
  26. 1020001≤n≤1030000 / Completed 終了 / Predrag Kurtovic / January 29, 2019 2019 年 1 月 29 日
  27. 1030001≤n≤1040000 / Completed 終了 / Predrag Kurtovic / January 10, 2021 2021 年 1 月 10 日
  28. 1040001≤n≤1050000 / Completed 終了 / Predrag Kurtovic / October 5, 2021 2021 年 10 月 5 日

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

Cofactors are written verbosely to clarify that they are integers. 補因子はそれらが整数であることを明確にするために冗長に書かれています。

  1. 5×106k+1-1 = 7×(5×101-17+45×10×106-19×7×k-1Σm=0106m)
  2. 5×1015k+5-1 = 31×(5×105-131+45×105×1015-19×31×k-1Σm=01015m)
  3. 5×1016k+9-1 = 17×(5×109-117+45×109×1016-19×17×k-1Σm=01016m)
  4. 5×1018k+16-1 = 19×(5×1016-119+45×1016×1018-19×19×k-1Σm=01018m)
  5. 5×1022k+7-1 = 23×(5×107-123+45×107×1022-19×23×k-1Σm=01022m)
  6. 5×1028k+10-1 = 29×(5×1010-129+45×1010×1028-19×29×k-1Σm=01028m)
  7. 5×1035k+28-1 = 71×(5×1028-171+45×1028×1035-19×71×k-1Σm=01035m)
  8. 5×1042k+5-1 = 127×(5×105-1127+45×105×1042-19×127×k-1Σm=01042m)
  9. 5×1044k+35-1 = 89×(5×1035-189+45×1035×1044-19×89×k-1Σm=01044m)
  10. 5×1046k+29-1 = 47×(5×1029-147+45×1029×1046-19×47×k-1Σm=01046m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 27.85%. 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 27.85% です。

3. Factor table of 499...99 499...99 の素因数分解表

3.1. Last updated 最終更新日

February 8, 2024 2024 年 2 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=223, 224, 225, 229, 230, 231, 233, 234, 237, 238, 239, 241, 242, 248, 249, 254, 255, 256, 259, 260, 268, 269, 276, 282, 285, 287, 291, 292, 294, 296, 298, 299, 300 (33/300)

3.4. Factor table 素因数分解表

5×100-1 = 4 = 22
5×101-1 = 49 = 72
5×102-1 = 499 = definitely prime number 素数
5×103-1 = 4999 = definitely prime number 素数
5×104-1 = 49999 = definitely prime number 素数
5×105-1 = 499999 = 31 × 1272
5×106-1 = 4999999 = definitely prime number 素数
5×107-1 = 49999999 = 7 × 23 × 310559
5×108-1 = 499999999 = 691 × 723589
5×109-1 = 4999999999<10> = 17 × 14033 × 20959
5×1010-1 = 49999999999<11> = 29 × 1724137931<10>
5×1011-1 = 499999999999<12> = 2969 × 168406871
5×1012-1 = 4999999999999<13> = 491 × 10183299389<11>
5×1013-1 = 49999999999999<14> = 7 × 7142857142857<13>
5×1014-1 = 499999999999999<15> = definitely prime number 素数
5×1015-1 = 4999999999999999<16> = 17737 × 281896600327<12>
5×1016-1 = 49999999999999999<17> = 19 × 2631578947368421<16>
5×1017-1 = 499999999999999999<18> = 223 × 208513 × 10753058401<11>
5×1018-1 = 4999999999999999999<19> = 1871 × 3061 × 873037477229<12>
5×1019-1 = 49999999999999999999<20> = 7 × 782209 × 9131647862473<13>
5×1020-1 = 499999999999999999999<21> = 31 × 8999 × 1792313841322871<16>
5×1021-1 = 4999999999999999999999<22> = 1049 × 2137 × 2230437170146223<16>
5×1022-1 = 49999999999999999999999<23> = 1699 × 2069 × 3121 × 1382819 × 3295771
5×1023-1 = 499999999999999999999999<24> = 41717706103<11> × 11985318626233<14>
5×1024-1 = 4999999999999999999999999<25> = 59 × 88369891 × 958989105371471<15>
5×1025-1 = 49999999999999999999999999<26> = 7 × 17 × 420168067226890756302521<24>
5×1026-1 = 499999999999999999999999999<27> = 229 × 367021 × 409453351 × 14529115561<11>
5×1027-1 = 4999999999999999999999999999<28> = 4728835511159<13> × 1057342761912761<16>
5×1028-1 = 49999999999999999999999999999<29> = 71 × 76863049 × 9162079325173218881<19>
5×1029-1 = 499999999999999999999999999999<30> = 23 × 47 × 457 × 3691153 × 274199124029771599<18>
5×1030-1 = 4999999999999999999999999999999<31> = 761 × 1295159 × 1798241 × 44167979 × 63871459
5×1031-1 = 49999999999999999999999999999999<32> = 7 × 7142857142857142857142857142857<31>
5×1032-1 = 499999999999999999999999999999999<33> = 5449 × 116201 × 46344148759<11> × 17039169430889<14>
5×1033-1 = 4999999999999999999999999999999999<34> = 38431 × 131377567 × 990300741539880346687<21>
5×1034-1 = 49999999999999999999999999999999999<35> = 19 × 151 × 3389 × 3539 × 1453072637071271903252101<25>
5×1035-1 = 499999999999999999999999999999999999<36> = 31 × 89 × 5393 × 46103 × 91873 × 7933609111971493583<19>
5×1036-1 = 4999999999999999999999999999999999999<37> = 5821859 × 14350319 × 59847603710232662550619<23>
5×1037-1 = 49999999999999999999999999999999999999<38> = 7 × 277294097 × 25759138835390148450014993081<29>
5×1038-1 = 499999999999999999999999999999999999999<39> = 29 × 251 × 11366466029<11> × 2227468931749<13> × 2713071075761<13>
5×1039-1 = 4999999999999999999999999999999999999999<40> = 94601951941577<14> × 52853032071556332079876487<26>
5×1040-1 = 49999999999999999999999999999999999999999<41> = 51031 × 979796594227038466814289353530207129<36>
5×1041-1 = 499999999999999999999999999999999999999999<42> = 172 × 103993 × 4049537 × 2747806793519<13> × 1495121512283929<16>
5×1042-1 = 4999999999999999999999999999999999999999999<43> = 281988929 × 17731192560400128332697770556800831<35>
5×1043-1 = 49999999999999999999999999999999999999999999<44> = 72 × 15607 × 66981539719<11> × 83462160791<11> × 11695256285559017<17>
5×1044-1 = 499999999999999999999999999999999999999999999<45> = 124179401 × 544903140421<12> × 7389263145045437512323419<25>
5×1045-1 = 4999999999999999999999999999999999999999999999<46> = 29383 × 90641 × 4964564212417<13> × 378153434087985921176249<24>
5×1046-1 = 49999999999999999999999999999999999999999999999<47> = 61 × 819672131147540983606557377049180327868852459<45>
5×1047-1 = 499999999999999999999999999999999999999999999999<48> = 127 × 2113 × 1863231364891504037622367719889249527670849<43>
5×1048-1 = 4999999999999999999999999999999999999999999999999<49> = 401 × 419 × 8681 × 403839385653823501<18> × 8488543527639500097041<22>
5×1049-1 = 49999999999999999999999999999999999999999999999999<50> = 7 × 29873 × 3277033 × 42512082058217<14> × 1716326607809847779992969<25>
5×1050-1 = 4(9)50<51> = 31 × 191 × 140330365181<12> × 1690219812601<13> × 356024675868920968979299<24>
5×1051-1 = 4(9)51<52> = 23 × 113 × 887 × 212476691929898164831<21> × 10207721412314026811175233<26>
5×1052-1 = 4(9)52<53> = 19 × 2631578947368421052631578947368421052631578947368421<52>
5×1053-1 = 4(9)53<54> = 4171219943533847<16> × 119869008771664354615470177157617001817<39>
5×1054-1 = 4(9)54<55> = definitely prime number 素数
5×1055-1 = 4(9)55<56> = 7 × 6628103 × 359638647233<12> × 2996514338887868420109999937680284143<37>
5×1056-1 = 4(9)56<57> = 1306849 × 21861761939<11> × 17500861733896477551069397730000965327109<41>
5×1057-1 = 4(9)57<58> = 17 × 6977 × 39799 × 1059205433557112844529660590916081636064965120489<49>
5×1058-1 = 4(9)58<59> = 1381 × 11161 × 29745719 × 197012659 × 14201186189899<14> × 38978937129668780992541<23>
5×1059-1 = 4(9)59<60> = 12119 × 645013662506162113114235303<27> × 63963807121278519686890735807<29>
5×1060-1 = 4(9)60<61> = 46022462334366034383091<23> × 108642600729913241687795877946404353989<39>
5×1061-1 = 4(9)61<62> = 7 × 2999 × 36497 × 66841 × 1347794196963254122631<22> × 724388938827042065050019489<27>
5×1062-1 = 4(9)62<63> = 286708827469<12> × 1743929562315488233203353793595015722358410772661371<52>
5×1063-1 = 4(9)63<64> = 71 × 18191 × 3416551 × 1133097219382511529197024183271791397387679431115009<52>
5×1064-1 = 4(9)64<65> = 226769 × 1806640527163085400901<22> × 122043476729296339368106595283713408771<39>
5×1065-1 = 4(9)65<66> = 31 × 647 × 2017 × 136601 × 279758231 × 391413561881279890439<21> × 826276708121582603689519<24>
5×1066-1 = 4(9)66<67> = 292 × 509 × 587864447363206252128041<24> × 19869138190551905570637035479070888731<38>
5×1067-1 = 4(9)67<68> = 7 × 326369 × 140272480759<12> × 1233569997284703122617<22> × 126481436050474351353809584151<30>
5×1068-1 = 4(9)68<69> = 539018761 × 927611497366786459590411176801321021180559613211681884297159<60>
5×1069-1 = 4(9)69<70> = 10223 × 21841 × 222700765249<12> × 100553551744179667782063878013845536795815861602657<51>
5×1070-1 = 4(9)70<71> = 19 × 3701 × 20884099 × 4020195440200721<16> × 8469044373252048293813826925259521000805899<43>
5×1071-1 = 4(9)71<72> = 39226337 × 12746538123098264311551700583207654591862604963598818824199669727<65>
5×1072-1 = 4(9)72<73> = 179 × 379 × 142268654306145251<18> × 518046256518744534201143852172477041478507420743989<51>
5×1073-1 = 4(9)73<74> = 7 × 17 × 232 × 659538071 × 88794612455729<14> × 553545757991183<15> × 24501200153789689921545276275617<32>
5×1074-1 = 4(9)74<75> = 868742401 × 575544602662947494374687485755630799468713856410468907226734982399<66>
5×1075-1 = 4(9)75<76> = 47 × 1103 × 3967 × 20809 × 179497 × 70705384718453791<17> × 92060544483851155170132315922059142943119<41>
5×1076-1 = 4(9)76<77> = 1491079 × 27070291141<11> × 2436458076398993106511<22> × 508413976509188420071335762413852943931<39>
5×1077-1 = 4(9)77<78> = 1721 × 13457 × 3142611977<10> × 1152796297057<13> × 5959331539129246946854374243410458282053927233903<49>
5×1078-1 = 4(9)78<79> = 6869 × 185749 × 10133387274526757029763294405551<32> × 386718868974885884183034458894767921529<39>
5×1079-1 = 4(9)79<80> = 7 × 89 × 257 × 3663911 × 144143696369<12> × 983172155462527<15> × 57384473092865601833<20> × 10480555334574514749761<23>
5×1080-1 = 4(9)80<81> = 312 × 9471311 × 72501946921<11> × 757681791255414060511091973700879622125929902613500513730089<60>
5×1081-1 = 4(9)81<82> = 2220122479<10> × 2252128000727296811447671486776563555528055170869696869548249819779424881<73>
5×1082-1 = 4(9)82<83> = 59 × 131 × 74084489 × 4262242939<10> × 3999697664940175951<19> × 5122170645502040610147144916761278538394811<43>
5×1083-1 = 4(9)83<84> = 311 × 89578207 × 53670294504958910171671<23> × 334405392090798370190636746133681976286074293107697<51>
5×1084-1 = 4(9)84<85> = 21096806531<11> × 910157530676614206199<21> × 260397444216612572991415700896842524291999850746407571<54> (Tetsuya Kobayashi / GMP-ECM 5.0.1 B1=250000 / April 30, 2003 2003 年 4 月 30 日)
5×1085-1 = 4(9)85<86> = 72 × 97 × 167 × 71993 × 156967 × 468889 × 11888225796280073236289818089617168424724309992639798189226237711<65>
5×1086-1 = 4(9)86<87> = 320219 × 821651 × 1804199 × 16429609614080419<17> × 64109713672026372440234786403128975420662601832221891<53>
5×1087-1 = 4(9)87<88> = 5471 × 281986659391<12> × 80985338346257<14> × 3960651466544880631<19> × 14819506360555096801<20> × 681817214224663305577<21>
5×1088-1 = 4(9)88<89> = 19 × 251 × 788222383415680615531<21> × 13301294782996692650772779830245783046918888799194961081470806941<65>
5×1089-1 = 4(9)89<90> = 17 × 127 × 22955087 × 10088774591510569752491188790492301084872447142512973564801027984016307522045503<80>
5×1090-1 = 4(9)90<91> = 3600156366041<13> × 1388828565104346367390732883221933908575097904441526411721945028739732315788439<79>
5×1091-1 = 4(9)91<92> = 7 × 124178543 × 56595520855166896490633<23> × 1016350121138100285575150664078603665704389785081622082756303<61>
5×1092-1 = 4(9)92<93> = 109 × 4451 × 5939 × 166993864666176028827919<24> × 1039135235455188198892946892178092736562703887865487222957021<61> (Tetsuya Kobayashi / GMP-ECM 5.0.1 / May 2, 2003 2003 年 5 月 2 日)
5×1093-1 = 4(9)93<94> = 166538826833<12> × 1406177828502620908247<22> × 21350805158152830860520784562872824898695271244778334287154249<62>
5×1094-1 = 4(9)94<95> = 29 × 2212770528161<13> × 779176109357976501851734459821169737249971158403291789059073820632445599196078571<81>
5×1095-1 = 4(9)95<96> = 23 × 31 × 4127 × 5591 × 15133469089<11> × 3436322642497<13> × 126327038939383169511047<24> × 4626235842137982052517224390030337830489<40>
5×1096-1 = 4(9)96<97> = 199 × 409 × 2549 × 4301920031<10> × 5602236664415060835237041259349510711939653660542440787058692336479570758117331<79>
5×1097-1 = 4(9)97<98> = 7 × 224143771996732776950082953712018457<36> × 31867301416526801551593357003400355492602350106995416964769201<62>
5×1098-1 = 4(9)98<99> = 71 × 21061 × 32369 × 336132856559<12> × 15497820401699<14> × 140580007773556529<18> × 2975610929009003659679<22> × 4740477468725048309861911<25>
5×1099-1 = 4(9)99<100> = 220217 × 444720257 × 51054291106366982498617178218209509431006624318394826526089092486656912521526928471671<86>
5×10100-1 = 4(9)100<101> = 359 × 71761 × 51118560947729578842221<23> × 37967189886147837365372595097662947484177171817130693531332288520596381<71> (Tetsuya Kobayashi / GMP-ECM 5.0.1 / May 1, 2003 2003 年 5 月 1 日)
5×10101-1 = 4(9)101<102> = 66503233 × 7518431472346615088622834321453214161783683509040831142750608831302983420369954044189099799103<94>
5×10102-1 = 4(9)102<103> = 77445861443580871<17> × 2048606644769912133818855399<28> × 141174718795035969912255984139<30> × 223231913053410135365883183629<30>
5×10103-1 = 4(9)103<104> = 7 × 104012801 × 1194344807225389247<19> × 57498358564889674751215812621408585787653430022209464428054840226827603587831<77>
5×10104-1 = 4(9)104<105> = 389 × 6679 × 212391381165121686295741<24> × 906091529427786757083878431734364297770378703199281665650555796735419488169<75>
5×10105-1 = 4(9)105<106> = 17 × 226783 × 773731739146650359<18> × 1676178147958646233562725748630699804202114929314675216287886035119674866069804151<82>
5×10106-1 = 4(9)106<107> = 19 × 61 × 448580653183815696347596509441422230841080789699<48> × 96171420178862927652971517159689674091160642927176945539<56> (Makoto Kamada / SNFS / 7:01:13:46)
5×10107-1 = 4(9)107<108> = 28559 × 17507615812878602191953499772400994432578171504604502958787072376483770440141461535768059105710984278161<104>
5×10108-1 = 4(9)108<109> = 269 × 9199 × 37554191 × 226966348667797098201473126585921<33> × 237059423406092043532584485243978378078675115458049696864598139<63> (Naoki Yamamoto)
5×10109-1 = 4(9)109<110> = 7 × 151 × 40659161 × 399165182679651943<18> × 736887192641191481<18> × 3955332002006630984264161126350907881288913862573770427420444089<64>
5×10110-1 = 4(9)110<111> = 31 × 7229 × 1269354537069049<16> × 196597424979150079<18> × 8940654674327449305288389922259782922968356685248805705937331644042476131<73>
5×10111-1 = 4(9)111<112> = 380966671 × 464148137 × 10087754249<11> × 74912161677127<14> × 4597549596809249<16> × 11259529294618699281913727<26> × 722824606755234863808146777353<30>
5×10112-1 = 4(9)112<113> = 541 × 47555750069<11> × 17580027457273324381682122351<29> × 110547812752997689624768501026869827298090082938184622995654239202672881<72> (Tetsuya Kobayashi / GMP-ECM 5.0.3)
5×10113-1 = 4(9)113<114> = 839 × 1223 × 2597055515591<13> × 1504561409656701841<19> × 124706885962490142186110724170071181693577935888718649611555069179218478742857<78>
5×10114-1 = 4(9)114<115> = 126583211 × 1447145884664060547607987361879<31> × 58295675470326978906201157594508111<35> × 468214914404256693353199842140909817566661<42> (Naoki Yamamoto)
5×10115-1 = 4(9)115<116> = 7 × 24223 × 844200728407<12> × 257974230067681<15> × 926611401031357397094287<24> × 1461249407848068148010004900632985798913488360897501123117071<61>
5×10116-1 = 4(9)116<117> = 149 × 3610913401<10> × 6905844119<10> × 134570507976557634605170316499390831476235505207831538496233020505472452668028816354301004899229<96>
5×10117-1 = 4(9)117<118> = 23 × 2067841977583213889<19> × 773956372891384392141906610342793159273<39> × 135833953232315983621727763569180848191814905661946744078129<60> (Naoki Yamamoto)
5×10118-1 = 4(9)118<119> = 2029 × 24419 × 4779067533081171620075089<25> × 2786618623875381039505630019<28> × 75777344064930131478467378162643396901573118106627819834739<59>
5×10119-1 = 4(9)119<120> = 1823 × 423744194695234481<18> × 2359021240961465955909271607<28> × 274377012411930332896579465900592383987866673386157426062973517910681239<72>
5×10120-1 = 4(9)120<121> = 1072520549<10> × 428998469609<12> × 132187016174291209658899<24> × 513994800908882164570571736671<30> × 159941481343857208967274224370322882563454005191<48>
5×10121-1 = 4(9)121<122> = 7 × 17 × 47 × 8939746111210441623457893795816198819953513320221705703558018952261755766136241730734847130341498301448238870016091543<118>
5×10122-1 = 4(9)122<123> = 29 × 1361 × 151969 × 3820259 × 65730931117935949<17> × 295580112727441787209<21> × 1123106842576913778431910010456283868933594020826855540064402870654661<70>
5×10123-1 = 4(9)123<124> = 89 × 2111 × 8215978320845452759352519383001<31> × 3239160589249899026971792199328906772388800723424699494389476245714793002129219351491281<88> (Tetsuya Kobayashi / GMP-ECM 5.0.3 (B1=1000000))
5×10124-1 = 4(9)124<125> = 19 × 13355127649<11> × 31051187578097616642241<23> × 6345855011381784087829871089920571071796570193875981656725271537907550424647305775545196869<91>
5×10125-1 = 4(9)125<126> = 31 × 992445257 × 36167938192618912257635160348826241<35> × 541041326367575421678108269681570849<36> × 830515149780762684023194221858216749394061433<45> (Sander Hoogendoorn / GGNFS-0.42.0 for P35) (Makoto Kamada / PPSIQS 1.1 / 1:35:00:76)
5×10126-1 = 4(9)126<127> = 285484979731787951<18> × 17514056272583870854330138580990379918626129638284884533063763026487208290203482536297575718330574369082710449<110>
5×10127-1 = 4(9)127<128> = 72 × 2193007 × 465300914801141137465124184207681368038292180740035606501083876603946926177022634925935215055522078188737646342139689793<120>
5×10128-1 = 4(9)128<129> = 2132863679<10> × 80163415599119<14> × 358766816800741<15> × 42588483156191111202485499558026020951227589<44> × 191393089402690967137916593562072406383348202151<48> (Naoki Yamamoto)
5×10129-1 = 4(9)129<130> = 28806180210361<14> × 46464233742069111351508303<26> × 3735644598134561931083031008165112883162540399392867487389560821947392229292244653540388953<91> (Tetsuya Kobayashi / GMP-ECM 5.0.3)
5×10130-1 = 4(9)130<131> = 739 × 1129 × 1779149 × 37524595431275311<17> × 7628309663740789043344274685157484199841<40> × 117672497216416907975811138393270288338026728779873725975710671<63> (Sander Hoogendoorn / GGNFS-0.42.0)
5×10131-1 = 4(9)131<132> = 127 × 593 × 919 × 43461137 × 15053075311<11> × 123330985375540225457<21> × 6765385965330567580673<22> × 13234422065464900721853289901933749428169475457721487899708932793<65>
5×10132-1 = 4(9)132<133> = 181 × 50261 × 288475492849<12> × 1905247411853381893815328568819284588489745220990160150662429364473877215513217076215366687311332715324899825072711<115>
5×10133-1 = 4(9)133<134> = 7 × 71 × 219487417057<12> × 2348810983951<13> × 15643468407459141953163921151000061497<38> × 12474492012328826373816556204599871102049686859053368900342040470592073<71> (Sander Hoogendoorn / GGNFS 0.53.0 with getdeps 0.50.2-k1)
5×10134-1 = 4(9)134<135> = 1932968767902669019<19> × 399681339598326181051<21> × 685338713864844244229<21> × 4617939435919416571588938626659<31> × 204492694288501725832781182620621901105234361<45>
5×10135-1 = 4(9)135<136> = 269003202410838504214036520941412612134351136344950318928159<60> × 18587139317262429780586757996354609670472835010983311369908899791500395369761<77> (Sander Hoogendoorn)
5×10136-1 = 4(9)136<137> = 49739 × 37933257899<11> × 192354257809333079137411266279438005089<39> × 247427558723526151962343402114292522351<39> × 556804757026412458852371557261880118927562681<45> (Tetsuya Kobayashi / GMP-ECM 5.0.3 (B1=1000000) for P39(2474...)) (Makoto Kamada / PPSIQS 1.1 / 1:03:34:68)
5×10137-1 = 4(9)137<138> = 17 × 746287 × 4644161 × 2112435529676231<16> × 31897267094030675863<20> × 125942120413467224888500799828741123112891687548568287882198803177520458208587047174902657<90>
5×10138-1 = 4(9)138<139> = 251 × 30848894051<11> × 858292490077141133131811<24> × 4998450918195148039242942777839<31> × 150517133684174871077229116828872221166329793521275015917468006604287531<72>
5×10139-1 = 4(9)139<140> = 7 × 23 × 2473 × 193513 × 612751 × 520906705509951127<18> × 2033133467853503882944692120674142232919355300389999380443264663317076883841236293065012518784554572990983<106>
5×10140-1 = 4(9)140<141> = 31 × 59 × 193451811779<12> × 4608628097463739<16> × 414707186931967381<18> × 739384381254583343700514662475642927587293336383863496575684033762658639611948623521559798071<93>
5×10141-1 = 4(9)141<142> = 863 × 864112969 × 33102413419941380298625729200482713<35> × 202548498000084611654776402535431487378132205253772216085513563043908316903499360835198098115009<96> (Greg Childers / GGNFS)
5×10142-1 = 4(9)142<143> = 19 × 33738391 × 69976289 × 727879169 × 14451133963291796815528100748696733275771551<44> × 105969262443706424717542949006868182672629853917824633425083022550272421341<75> (Greg Childers / GGNFS)
5×10143-1 = 4(9)143<144> = 25475602727<11> × 121025048944398409<18> × 162169907734099351982810784387864555084768717577684814872172611542454903077069853784159799137292780392149514685685793<117>
5×10144-1 = 4(9)144<145> = 431 × 184589806882759<15> × 62847067615245909702116215011262763058542381013287871463053198226335816003644454302833001096420995430316196612233370219895833031<128>
5×10145-1 = 4(9)145<146> = 7 × 191 × 200407 × 30320577358085873<17> × 3742689245540972587559<22> × 10770666850886758816127596408319<32> × 152672874066731926396057308274042971603911517666371368472643836198617<69> (Greg Childers / GGNFS)
5×10146-1 = 4(9)146<147> = 1324743175841<13> × 41231655271646690609789<23> × 491797844488087910675065491701111<33> × 18613194785067937897308160940271109215879924182776436506899598937897470234894541<80> (Tetsuya Kobayashi / GMP-ECM 5.0.3 (B1=1000000))
5×10147-1 = 4(9)147<148> = 30241 × 165338447802652028702754538540392182798187890612082933765417810257597301676531860718891571045931020799576733573625210806520948381336596012036639<144>
5×10148-1 = 4(9)148<149> = 659 × 75872534142640364188163884673748103186646433990895295902883156297420333839150227617602427921092564491654021244309559939301972685887708649468892261<146>
5×10149-1 = 4(9)149<150> = 439 × 6361 × 9892593989592316723951<22> × 12991330986777786451229660905897078106018495159<47> × 1393208949869384358841491740657456164913361005125028453793652095448657424009<76> (Greg Childers / GGNFS)
5×10150-1 = 4(9)150<151> = 29 × 1439 × 4591 × 8627111 × 3025091629186196107796613330751766546521832211595667959252285632901129362739800679669696793905950113922940539746028462910563249258284429<136>
5×10151-1 = 4(9)151<152> = 7 × 937 × 1896379496319300094129<22> × 4019824773606285815131597580589717782737580200683987654218740047905803189496129281298225033541766939719103076480608786277761009<127>
5×10152-1 = 4(9)152<153> = 6855481 × 2245341102733892629<19> × 744672514925099317753393598897750509322858911004792161<54> × 43619875480449736340301463870436173570992711432762799275899219166322466491<74> (Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 / 47.42 hours on Pentium 4 3.20 GHz, 1 Gig RAM, Windows XP and Cygwin / January 18, 2007 2007 年 1 月 18 日)
5×10153-1 = 4(9)153<154> = 17 × 33872102210024327<17> × 8683182556404204167336062747655902186710139922632160127541164235580790980481733112926689278161490483633528934268472110468455427818863161<136>
5×10154-1 = 4(9)154<155> = 571 × 4549 × 394729 × 6600156768178848839<19> × 7388642841687726062777727140214781312035515139538648213156236783124120901569415373369738710314469886334325451377592665197751<124>
5×10155-1 = 4(9)155<156> = 31 × 263 × 7802657217359<13> × 73023542139226173045665561<26> × 107633419637891693872637007351985902969706385789274068012272478209234741756036503405781750665502424552630242851617<114>
5×10156-1 = 4(9)156<157> = 325933631 × 418725471349<12> × 64649255422764285424382191141<29> × 1196044320747080988848275421315051<34> × 473806101133225839977941970810800179066086580068330368731246322000830542731<75> (Tyler Cadigan / GGNFS-0.77.1-20050930-pentium4 gnfs / 27.31 hours on P4 3.2 gig, 1024 Mb RAM for P34 x P75 / October 12, 2005 2005 年 10 月 12 日)
5×10157-1 = 4(9)157<158> = 7 × 1784911 × 8397428359<10> × 154950203473026832889059234829083441818646269399640511<54> × 3075508559189988737150043030934655780723081191090507472552844326729132490697996382741663<88> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 36.22 hours on Cygwin on AMD XP 2700+ / April 16, 2007 2007 年 4 月 16 日)
5×10158-1 = 4(9)158<159> = 929 × 2039 × 195480696444471195235091<24> × 3914379888823857856496565940348441055481401908952110819<55> × 344961172633478712235231612125560933379158026766703661954210221883077707201<75> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 24.89 hours on Core 2 Quad Q6600 / July 22, 2007 2007 年 7 月 22 日)
5×10159-1 = 4(9)159<160> = 5303 × 3190556186353927<16> × 18565652713807034159<20> × 15917386355105128332287726809575610846672449603649620305544782943758902542591857243762550101306322001143522107390161938481<122>
5×10160-1 = 4(9)160<161> = 19 × 436091 × 2329189 × 1033904918067164428884577564259<31> × 6893933938446466919399636517410130127156761488611<49> × 363485282102468445025331961873781689545727542437808306501301663929371<69> (Wataru Sakai / GMP-ECM 6.0 B1=10000000, sigma=2061588207 for P31 / March 8, 2005 2005 年 3 月 8 日) (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs for P49 x P69 / 101.60 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 18, 2006 2006 年 9 月 18 日)
5×10161-1 = 4(9)161<162> = 23 × 5039 × 5503 × 121219311137<12> × 205172085665013628136788854347422145538579372307983152097920947502671<69> × 31521596990625887572504276079879084677165618298704568194646451128941172807<74> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.26 / October 2, 2007 2007 年 10 月 2 日)
5×10162-1 = 4(9)162<163> = 7898189142101<13> × 456514351349672851<18> × 7739832354657573536230860093069953953660396661<46> × 179166366257503162309509372277349334970926729613420475526494728627218732934704149702509<87> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.32 / January 14, 2008 2008 年 1 月 14 日)
5×10163-1 = 4(9)163<164> = 7 × 113 × 4051162866465457<16> × 922191787468962700083112302737<30> × 80377700901754687749486798145765159<35> × 10600775268809505921573949265742014977<38> × 19857261721993282761679812592330289110528447<44> (Wataru Sakai / GMP-ECM 6.0 B1=10000000, sigma=3353644342 for P35 / March 16, 2005 2005 年 3 月 16 日) (Wataru Sakai / GMP-ECM 6.0 B1=10000000, sigma=3237705988 for P30, ppsiqs for P38 x P44 / March 17, 2005 2005 年 3 月 17 日)
5×10164-1 = 4(9)164<165> = 121229 × 93065452014541<14> × 4609272099677821<16> × 6199401341721886342501<22> × 19306339505367483920172035659730245319<38> × 80332808754804132639262177760295673590550769997275924317754987315974609<71> (Wataru Sakai / GMP-ECM 6.0 / April 8, 2005 2005 年 4 月 8 日)
5×10165-1 = 4(9)165<166> = 428440364567<12> × 4418255297469253568147847349351285035723609901981851222353873612047<67> × 2641367423527036890767831864312306241956122491114136519637229891724953923688971860336151<88> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.28 / October 15, 2007 2007 年 10 月 15 日)
5×10166-1 = 4(9)166<167> = 612 × 7951 × 18959 × 41274509 × 84427642127312153021137396271<29> × 1036244557985917323855656628571<31> × 31378746637656538548025658341102831<35> × 786699225732513079105689913385630462760166633060831769<54> (Shusuke Kubota / GMP-ECM 5.0.3 B1=250000, sigma=1074148556 for P31) (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=2124137356 for P35, msieve 0.88 for P29 x P54)
5×10167-1 = 4(9)167<168> = 47 × 89 × 5322353 × 22458381991549592782890679647633496941192335844530446385788776347501741550840110197299316241862298094625585133811737525413646228785066584062270274179126162601<158>
5×10168-1 = 4(9)168<169> = 71 × 461 × 1609 × 14951 × 80777981 × 22639721157902129095414403005942496800349<41> × 457434303099638694586122437203847366912844131<45> × 7590871641081854629092704253048698545019692817001067700599918729<64> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.36 / 55.74 hours on Cygwin on AMD 64 3200+ / July 18, 2008 2008 年 7 月 18 日)
5×10169-1 = 4(9)169<170> = 72 × 17 × 51971109847877751141565924226072367623<38> × 6247449254103117689987713647000874500741834590985633042232135777<64> × 184867374942010724757709190165050993402607186564005758034404013993<66> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 80.00 hours on Cygwin on AMD 64 3200+ / May 22, 2007 2007 年 5 月 22 日)
5×10170-1 = 4(9)170<171> = 31 × 4688909 × 5962171 × 414098898368494463344506663169333769<36> × 1393246636581073462780644946707410311348854022175587735092066569086144683145170283932792460440716222911271989247205306919<121> (Robert Backstrom / GMP-ECM 6.2.1 B1=1114000, sigma=3235219842 for P36 / October 2, 2008 2008 年 10 月 2 日)
5×10171-1 = 4(9)171<172> = 1097 × 15569 × 218008919017<12> × 9027242246182409329<19> × 148755591678074552338521301344553612216094823722617113203733880165737743025480237399253007757569877580499575993572313758682163468875951<135>
5×10172-1 = 4(9)172<173> = 10889 × 2882359 × 23331915524945545696221472599200406173115587461<47> × 68278432084467642690581024494631409446426792252293530420303471343294308319297030303253720850691295975733917647872509<116> (Ignacio Santos / GGNFS, Msieve snfs / 56.01 hours / September 17, 2009 2009 年 9 月 17 日)
5×10173-1 = 4(9)173<174> = 127 × 3911 × 18127 × 60115481 × 23178928080286249351<20> × 2847970263141744131023830845478132413777645258337832393628729170631<67> × 13993856238980368759578357212092380131077296745377065063456859221722961<71> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 37.09 hours on Core 2 Quad Q6700 / October 11, 2009 2009 年 10 月 11 日)
5×10174-1 = 4(9)174<175> = 100836539 × 386045671789<12> × 202149331951309<15> × 28345499727878470190919484864294064341<38> × 463029342608148463454164159741210468863485451451681<51> × 48411489356292646627148450479697213943551789779252721<53> (Jo Yeong Uk / GMP-ECM v6.2.3 B1=3000000, sigma=8051102569 for P38, GGNFS, Msieve v1.39 gnfs for P51 x P53 / 4.42 hours on Core 2 Quad Q6700 / October 10, 2009 2009 年 10 月 10 日)
5×10175-1 = 4(9)175<176> = 7 × 107183 × 2543334728950591<16> × 1003880437516672343<19> × 6033965706180633947575226973035593<34> × 4325713036344580776461295797750335517660863417205395531955960411517789548035861791579322805691565162231<103> (Wataru Sakai / GMP-ECM 6.0 B1=10000000, sigma=3401853249 for P34 / April 5, 2005 2005 年 4 月 5 日)
5×10176-1 = 4(9)176<177> = 48409 × 48550259 × 1685407140856189648612097538079896782968048556689<49> × 126225619910469676004414039354831078351797442441561563713439568704176968850333129983096588258532811794520832130928061<117> (matsui / GGNFS-0.77.1-20060513-prescott snfs / 224.48 hours / May 30, 2008 2008 年 5 月 30 日)
5×10177-1 = 4(9)177<178> = 30973583 × 39989645019285243151<20> × 4068269709359954401976297716690750943446114169<46> × 992250373611379227883163588164400121551512275167316952271377534693843762018044616947203837967745867950487<105> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 58.68 hours on Core 2 Quad Q6700 / December 20, 2009 2009 年 12 月 20 日)
5×10178-1 = 4(9)178<179> = 19 × 29 × 3121 × 45215056267958609<17> × 643045289414757855416211124926711766665239833362229024358393704927082787709265501601066868796983284161023741067316317462443984817217172699138594183840971241<156>
5×10179-1 = 4(9)179<180> = 100633529 × 10276894318800611063<20> × 551421612914557051308292624692847<33> × 876761814633993523106354211564896283956156882713530327635666576447814027168039294731780218758528595761801494512642521871<120> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=250000, sigma=4222987752 for P33 / October 10, 2009 2009 年 10 月 10 日)
5×10180-1 = 4(9)180<181> = 10621939 × 371220517601500959349955067754789808321<39> × 1166301555538974517603112159803243199069<40> × 455836425176168552226557086859741685930538511<45> × 2385142595979479983692619755161942793993731666526119<52> (Wataru Sakai / GMP-ECM 6.0 B1=10000000, sigma=4237437119 for P39 / March 11, 2005 2005 年 3 月 11 日) (Jo Yeong Uk / GMP-ECM v6.2.3 B1=1000000, sigma=2748895193 for P40, GGNFS, Msieve v1.39 gnfs for P45 x P52 / 1.87 hours on Core 2 Quad Q6700 / October 13, 2009 2009 年 10 月 13 日)
5×10181-1 = 4(9)181<182> = 7 × 972 × 193 × 457 × 422822039 × 5656697469953<13> × 173579002511793813594159069431<30> × 1064331088086742281466450399965259429540937717843448019984241<61> × 19478723013143054838808802263731536889575609008494945550219489<62> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=50000, sigma=1211348993 for P30 / October 9, 2009 2009 年 10 月 9 日) (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 gnfs for P61 x P62 / 140.90 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / October 17, 2009 2009 年 10 月 17 日)
5×10182-1 = 4(9)182<183> = 402045318839<12> × 7177564523816592869440879538846475176869730760304849<52> × 173267811176972637202721174591604786380093280093612986568064406694146885800020811068408853083028936835099405426401335209<120> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 92.44 hours on Core 2 Quad Q6700 / December 31, 2009 2009 年 12 月 31 日)
5×10183-1 = 4(9)183<184> = 23 × 11633 × 945200151001218657635011445058228730913844677283075507271374283027271720740913<78> × 19770909942771694388069711525503787363511760112454424254375327438641837630246346547998813862502042297<101> (Wataru Sakai / Msieve / 197.96 hours / June 9, 2009 2009 年 6 月 9 日)
5×10184-1 = 4(9)184<185> = 151 × 1811 × 26149492819353460891<20> × 19904026613441188764553765519<29> × 351293725658528142025984363908540515455299471247490008661682391281288234075835346606964794661872221262643846492958379267355968427671<132> (Wataru Sakai / GMP-ECM 6.0 B1=10000000, sigma=1219650535 for P29 / March 8, 2005 2005 年 3 月 8 日)
5×10185-1 = 4(9)185<186> = 17 × 31 × 87631 × 30963646453769<14> × 13467097731105253924325838530156698063<38> × 25964233709024130179916331896236768142386809082711053887820914535009226635473159313679197722834392092837158149045577065290385641<128> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=575025177 for P38 / December 10, 2009 2009 年 12 月 10 日)
5×10186-1 = 4(9)186<187> = 4409 × 4721179 × 20792509 × 34924527393985951<17> × 149270640821931973883035346612051055146889903083133923624440501<63> × 2215989027031415584734612311830420673337291212196945273240676509436087130063218466088577451<91> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 108.57 hours on Core 2 Quad Q6700 / January 5, 2010 2010 年 1 月 5 日)
5×10187-1 = 4(9)187<188> = 7 × 829170787446038508271<21> × 111277774907745473529586539271137126937277242947428985065596817713<66> × 77414005374893008635864387538323623490032732987347761112605716671322732461197155133915811344002291959<101> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 129.49 hours on Core 2 Quad Q6700 / January 9, 2010 2010 年 1 月 9 日)
5×10188-1 = 4(9)188<189> = 251 × 3921791 × 56931191 × 6521172061<10> × 1368156911680849504233600593059771759024687800841838200499789414954100306830539820993823551578434669722369230735281546672545988514586369202111503378005917499098089<163>
5×10189-1 = 4(9)189<190> = 414457 × 548526529 × 218359541786865057171137<24> × 362114869786328767678706254340330776690101808781230007<54> × 278146984110733504640917712329377431369886449408844968830703171101286957984960895130897298993079937<99> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 133.54 hours on Core 2 Quad Q6700 / January 14, 2010 2010 年 1 月 14 日)
5×10190-1 = 4(9)190<191> = 99540974625765465275232034702200919<35> × 502305710668196126484659145583463988849571937897513433848127456075026044866256022945692253079700553166877184985681787449184093822883155280824677517509895321<156> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=3894616504 for P35 / May 12, 2007 2007 年 5 月 12 日)
5×10191-1 = 4(9)191<192> = 11765209 × 3480081817753<13> × 106144520413782227988033709274285099503713060989987541951119<60> × 115049126121589055199022162558728951136501798027571833624874769803489031614030807294626008542866906186262107663073<114> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 160.37 hours on Core 2 Quad Q6700 / January 23, 2010 2010 年 1 月 23 日)
5×10192-1 = 4(9)192<193> = 72560301641228201<17> × 68908203065669709860463879359910395252682671905169603284513010578443315246043750346398006233271822191756386346690807589820929022083022657541265004710710306522773447649333988199<176>
5×10193-1 = 4(9)193<194> = 7 × 8839 × 107516249752971035684650211176390698878497<42> × 24173803155985955692016681563323357514896673933228266043927201<62> × 310920775016922058394050530166095476535227621922355453952479835190354825775506258573679<87> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3184635571 for P42 / February 17, 2009 2009 年 2 月 17 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 198.25 hours on Core 2 Quad Q6700 / January 29, 2010 2010 年 1 月 29 日)
5×10194-1 = 4(9)194<195> = 2063673432680440504344308255721789938709506185655504408686729651476059482949<76> × 242286396714700023343462981244314581366417767442682354276028410445885393174798778445278457127741012032445076995991310451<120> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2170.77 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / September 20, 2007 2007 年 9 月 20 日)
5×10195-1 = 4(9)195<196> = 199 × 763037308894072031327<21> × 32928439865044083099237880745307554207094208046670251449773784849353921824251947711262778330304269115848753348658742636216921378609898406441929321575786489924920023751315863<173>
5×10196-1 = 4(9)196<197> = 19 × 16981 × 49811 × 1697118101741918215208512034099<31> × 1833225185034239750757162601262933487008785125955739998834505594511896594577580588571645784267706977995671427911855205353218635320637341730698774065206061769<157> (Wataru Sakai / GMP-ECM 6.0 B1=10000000, sigma=2499077748 for P31 / April 17, 2005 2005 年 4 月 17 日)
5×10197-1 = 4(9)197<198> = 6526969 × 317598963369528079750990794635037797243393<42> × 241201152213646957316475021456496581554806604208884919421444257764720088176608878043853450754138121069950925545626957019712893914235709811564144209847<150> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=11000000, sigma=5407462151 for P42 / January 24, 2010 2010 年 1 月 24 日)
5×10198-1 = 4(9)198<199> = 59 × 719 × 2081 × 3001 × 94111 × 2003879 × 397770851 × 3669695664592673615978065665298668275956953672441671<52> × 68560841789797206872933304052381552430659655586189485404223202781305551694444522299196431882818449926154085718257351<116> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=11000000, sigma=3155546428 for P52 / January 19, 2010 2010 年 1 月 19 日)
5×10199-1 = 4(9)199<200> = 7 × 233 × 29033 × 110474303778793<15> × 4139828065935440294061146400286899184110194422807<49> × 2394322967500650161225019678510910790744709336941257<52> × 964268145009238051063451368642139776954588774704684668839609708242943445219359<78> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=3000000, sigma=6195808489 for P49 / December 22, 2009 2009 年 12 月 22 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P52 x P78 / 104.78 hours on Core 2 Quad Q6700 / December 28, 2009 2009 年 12 月 28 日)
5×10200-1 = 4(9)200<201> = 31 × 109 × 27509 × 25738900941728998684305569489<29> × 208985912004232692112989418962913512143454946422920593821299571281505741429255867900662632079343171630051175697271076302567705286976144762874932292328157121848234881<165> (Wataru Sakai / GMP-ECM 6.0 B1=10000000, sigma=247942321 for P29 / March 28, 2005 2005 年 3 月 28 日)
5×10201-1 = 4(9)201<202> = 17 × 1511 × 7727 × 205063 × 1257156212981593<16> × 176867586029104464937617854753<30> × 182196639933150089145482211714113<33> × 4171804209352072500638887160821389196590907292233<49> × 726869797784362812569971191501943992622966056149515373889530897<63> (Dmitry Domanov / ECMNET/GMP-ECM 6.2.3 B1=11000000, sigma=4184393397 for P30 / March 14, 2010 2010 年 3 月 14 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2358317610, Msieve 1.40 gnfs for P33 x P49 x P63 / March 15, 2010 2010 年 3 月 15 日)
5×10202-1 = 4(9)202<203> = 165469 × 60250033321<11> × 8661365851031940612715942013919458904705195432371383278224633626971329331164714839249<85> × 579041495320712778615169255821394165248896700888060879315604241064691597839075058923520848613019665699<102> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P85 x P102 / November 1, 2019 2019 年 11 月 1 日)
5×10203-1 = 4(9)203<204> = 71 × 89833 × 78500779957629215047583<23> × 2554622678263833197592677847961<31> × 390908413013978675146771484752199003167231189156775159156205850793919698840431642638279029672333023682560763345367200793430440317854489182418711<144> (Serge Batalov / GMP-ECM B1=2000000, sigma=538880341 for P31 / February 15, 2010 2010 年 2 月 15 日)
5×10204-1 = 4(9)204<205> = 569 × 22764149 × 73608485739931<14> × 63529434660685481712826065940753124136218774931706660112279<59> × 82547408615885665856592926150814026874539609045397055599612719249737327619468454230616936839903083048490196933791967820871<122> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P59 x P122 / December 24, 2019 2019 年 12 月 24 日)
5×10205-1 = 4(9)205<206> = 7 × 23 × 479 × 4679 × 29999777 × 13984521033513361<17> × 143180538629301487<18> × 1770149894561865592969<22> × 1303154509926688287584412808142144845918099266425590026454809110799644993854207766722918558198054754923778128078276801429916348227039489<136>
5×10206-1 = 4(9)206<207> = 29 × 41006152481744188673570493536228027728945855165177610503773899582571449282291<77> × 420458352390428142168860231001144457925753534637387296224061124677353255986020251179755458703468680200706467524489936297238404041<129> (Ignacio Santos / GGNFS, Msieve snfs / April 13, 2010 2010 年 4 月 13 日)
5×10207-1 = 4(9)207<208> = 5081 × 6992753 × 666095582772319873602857<24> × 10321173170665285965397933597759628491490741694395073646315859557433<68> × 20469489079509010463842786717858580632039543792945477535870772969766526704942611906341103638209973787508903<107> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P68 x P107 / January 22, 2020 2020 年 1 月 22 日)
5×10208-1 = 4(9)208<209> = 1171 × 122948605195431779<18> × 3210887022642510929<19> × 5444512418059213485770287129621<31> × 33761778333577836984095743612600055368309<41> × 588410171277877085168215275935150219768724737738366019195693655037268780693134405011863923995596031<99> (Dmitry Domanov / ECMNET/GMP-ECM 6.2.3 B1=11000000, sigma=1860206752 for P31 / March 15, 2010 2010 年 3 月 15 日) (Ignacio Santos / GMP-ECM 6.2.3 B1=11000000, sigma=236103015 for P41 / March 23, 2010 2010 年 3 月 23 日)
5×10209-1 = 4(9)209<210> = 74233923525755882623876843773148868376704546444139853177420627156639777259999<77> × 6735465084591981075391067251840787634425730351218289307321272035738372690381401228815484151781099392987616594380626862745747377260001<133> (Sinkiti Sibata / Msieve 1.42 snfs / March 17, 2010 2010 年 3 月 17 日)
5×10210-1 = 4(9)210<211> = definitely prime number 素数
5×10211-1 = 4(9)211<212> = 72 × 89 × 4951 × 16567 × 745249 × 254973001 × 1370131540133423<16> × 536894874227096365886010857939423097275369811278452647514684222356755817288692978987960826527830027048876118207636637678232478624001591899726142021546537386927893359109201<171>
5×10212-1 = 4(9)212<213> = 131 × 7019 × 35251 × 917159 × 1138268503511<13> × 42384437418779<14> × 348623172528105278132712210097948288725590685696958270579947595714045828665083405289482366221058412141513235927105087448908105217196210958991533444611175080207845911061471<171>
5×10213-1 = 4(9)213<214> = 47 × 230807 × 21470669413327<14> × 53438730700991<14> × 62997301299238279<17> × 15860760643458946874022600554360703213481516897168621728357230159<65> × 402045767566307434874377773748286737555448607088803303487745034221811130246501832307787215605404303<99> (Eric Jeancolas / factordb for P65 x P99 / February 7, 2023 2023 年 2 月 7 日)
5×10214-1 = 4(9)214<215> = 19 × 9752788909634205994619077221096785938960657926162541908530453339026816786573399<79> × 269828350818588838486696965972521625094679526174992740456312339175621830637920213766353561475619315428814153401271388702815978467270179<135> (Robert Backstrom / Msieve 1.44 snfs / October 16, 2010 2010 年 10 月 16 日)
5×10215-1 = 4(9)215<216> = 31 × 127 × 466054697 × 272500748985066019012789891492208280711772884530143604633878517182064834319308203605063466497631046611203432103989092871256565914789339319429089872301805903210724528694310621204799013041076458705607749191<204>
5×10216-1 = 4(9)216<217> = 631 × 728561 × 316199580957499<15> × 116574985803146511559428829879757700017147911926744450502111<60> × 295058455088200703710024912208089384052846390323806219151342388557461299394078344840807339700656777850221803274170568847291108200084501<135> (Eric Jeancolas / factordb for P60 x P135 / February 7, 2023 2023 年 2 月 7 日)
5×10217-1 = 4(9)217<218> = 7 × 17 × 29979151613498035542461348082989786726503784244119182673178067671784924775137379879<83> × 14015342149899637914483845929363307316765291907978376298070367648161549469669907884526761546482631026407992131079476454286243492845599<134> (Erik Branger / GGNFS, Msieve snfs / March 8, 2011 2011 年 3 月 8 日)
5×10218-1 = 4(9)218<219> = 1579 × 15145902419<11> × 1061321782144572375191<22> × 19699066317537463189229620541624685180941055270533636007069702376055460044362469807027640760931975633841454321050993440254800666541466274977261552236810041503286227089784685583148483689<185>
5×10219-1 = 4(9)219<220> = 1041857 × 358543609 × 50967138535849511<17> × 262621122421314956487628953246670825239201859589415637462256758501998489250926395753657659320971330539960216544939753930473703014962002059415187864299102198081823757616914878419627055692593<189>
5×10220-1 = 4(9)220<221> = 104236478505302923265970629<27> × 479678522499743711150503738794160722423759353741289350123608605948542585858175629283429721040009521239042312881825027225078698973495145765184978506840959046871795329427929569172390731888040524531<195>
5×10221-1 = 4(9)221<222> = 1074381187231903<16> × 465384172714554442579770043108939497553681199835462745043912131566467614397404243470244945499515514509680123092719093204327640678090919646593440826133938337564227376687900789409434943161922481034583390262433<207>
5×10222-1 = 4(9)222<223> = 1151 × 3061 × 16376359 × 22966405098500429487826467596467086275956617380822614148312137846496943681046775281<83> × 3773296909184394250574158477898778491609230279536702956242016369841470285379967796154781688717210749960693477326466415885967371<127> (anonymous / Msieve 1.53 snfs for P83 x P127 / January 16, 2019 2019 年 1 月 16 日)
5×10223-1 = 4(9)223<224> = 7 × 315223 × 21118070929959317211626114099727311791<38> × [1073000247561339300781980328244866992740839568567052581454393772037678240087127436460526365491700195594995855785448223892375425434892528225565869520524190025763099217582798520423249<181>] (Lionel Debroux / GMP-ECM 6.2.3 B1=3000000, sigma=2793598215 for P38 / February 17, 2010 2010 年 2 月 17 日) Free to factor
5×10224-1 = 4(9)224<225> = 4259 × 36418777663409<14> × 851656886812221489761650074771849972581<39> × [3785056235539252957419901760913803349237596296285105697481640266338746205559778137253554308273021639716792707801903916220178510661762642974436979058492175269675845403809<169>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2506630945 for P39 / March 13, 2011 2011 年 3 月 13 日) Free to factor
5×10225-1 = 4(9)225<226> = 195137 × 28838803609280510349219982031<29> × 247261790284811252546669307192809454199807<42> × [3593321959467375351300115139099431792086576064520801154758481614174516732808784673224354794102131804610101836595616424592156197257336371016290003269231<151>] (Florian Baur / GMP-ECM 7.0.4+ds-6 B1=11000000, sigma=2967173348 for P42 / August 9, 2022 2022 年 8 月 9 日) Free to factor
5×10226-1 = 4(9)226<227> = 61 × 365606179451<12> × 1666225236661644544904272171<28> × 182501490957644244995946501154690449123644111<45> × 7372699226473994608203901243870940633170357396747605658175157027007000543354235955835658215954508299101514672607947410659222198418546528316189<142> (Florian Baur / GMP-ECM 7.0.4+ds-6 B1=11000000, sigma=18425149 for P45 x P142 / August 9, 2022 2022 年 8 月 9 日)
5×10227-1 = 4(9)227<228> = 23 × 12007 × 9218551 × 568514560698751<15> × 2762300186607512018745405648791<31> × 447336377102339125698176114896399<33> × 8626344382618303838988675128545481723242783<43> × 32409439607461008824778680821663857325194089577362379029205157792407692648940641787492915621697<95> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1838114820 for P31 / February 7, 2010 2010 年 2 月 7 日) (Serge Batalov / GMP-ECM B1=2000000, sigma=791304540 for P33 / February 15, 2010 2010 年 2 月 15 日) (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=1637473757 for P43 / February 21, 2010 2010 年 2 月 21 日)
5×10228-1 = 4(9)228<229> = 1340580408611<13> × 163865367925725876653408771<27> × 196771474856642454715714431281<30> × 115671886301237154045217332503961058597471229722296706604301921699391422012991931418877907494815298985253131032110050166584474805777069650940596817728283516659159<162> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1379537045 for P30 / February 8, 2010 2010 年 2 月 8 日)
5×10229-1 = 4(9)229<230> = 7 × 19031 × 617130353165359384117028441089<30> × [608181839209934649515819756829809452926459803673257356692998348015455689664863948500202411423137819449976464099365727358114578914127059890163124787808139712240262938520595711065046434206508822623<195>] (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1265248697 for P30 / February 8, 2010 2010 年 2 月 8 日) Free to factor
5×10230-1 = 4(9)230<231> = 31 × 33161 × 2240959160559829<16> × [217043482878650632536824945920947140964320293604342932570231621045970937147714464148791612854695096924586326581127223240696128763463733573403584521840841009016730005031781293925347452307196039893152316930129141<210>] Free to factor
5×10231-1 = 4(9)231<232> = 3257 × 9769 × 684212423 × 43498735127<11> × 130950721636235041<18> × 3530686834348838827583225023<28> × [11420035611435368713073157578488543996684157602114775891980190118537431724099209657460973221210875152918670707182595360344940508299307862077981278627259445037601<161>] Free to factor
5×10232-1 = 4(9)232<233> = 19 × 6581 × 3009689 × 6250366411<10> × 17394881711<11> × 44380274847738689<17> × 2015596685486421645229<22> × 13660994338238836878728198179342245688487783250877917208370170381080458800916140403572832907730734631564765413551089905458912497798505376145989160963163024172512569<164>
5×10233-1 = 4(9)233<234> = 17 × 546671 × 2632999 × 2748457 × [7434562317926460457414657297383108075633931846066533669822849922943734905143354593366058129468311477576588226576688000445143454682976782952722417866417513393949416463993266778820715598162010144529264005675190843999<214>] Free to factor
5×10234-1 = 4(9)234<235> = 29 × 44527411 × 14115458699<11> × 484669626405859<15> × [565983489748107913303715073226094944654039616427992999879187456268460762643161884792381911850258280633415421328015436285931144046809495556482183304473172587111998577082136008997000933332492391342292681<201>] Free to factor
5×10235-1 = 4(9)235<236> = 7 × 1753 × 17694626857<11> × 163170119443523039<18> × 82927363425588896639<20> × 7552440481095804050451623<25> × 2253319831514374981330475963437255461725177229400990870788877589876743701764481205650646188852571088395188717849993658138288232054745509795046948753349854812399<160>
5×10236-1 = 4(9)236<237> = 16111 × 2014225849529<13> × 1404690170350389089<19> × 290126885897063828909<21> × 31772053217490941549591<23> × 2217852821233428058656061829389<31> × 6470258543437344169265993338041712737160819241716314457256782291<64> × 82922270089712866414156353901693856106990556211017845529500725869<65> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2876774110 for P31 / February 8, 2010 2010 年 2 月 8 日) (Markus Tervooren / Msieve 1.45 for P64 x P65 / May 11, 2010 2010 年 5 月 11 日)
5×10237-1 = 4(9)237<238> = 2369983081<10> × 61934141918706589438223<23> × [34063920753524954385843233629928351135158593822066367754903503249220845561624412734170904679678674619032576035585555670796107096404320374580342215037705355317492753721909171142699851760177657250117264960873<206>] Free to factor
5×10238-1 = 4(9)238<239> = 71 × 251 × 311 × 691 × 102611 × 131939 × 3770643185594884855062872657981351658981041<43> × [255750771392109959999408101486188660978546255114160333316743868786983121417413844120867172568236824691164917643963749253355746418074108029648896302647544320710165617356592364871<177>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3766316928 for P43 / October 26, 2011 2011 年 10 月 26 日) Free to factor
5×10239-1 = 4(9)239<240> = 223 × 24155081 × 1845143116807<13> × 5894766588948488081<19> × 25616050232745547195235941872673<32> × [333156128119418852911979742735163554111726301465071133691010432496864876386752207400220263894483613510408835338957772125123778523865612598997627728000470222847119405903<168>] (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=1220104373 for P32 / September 20, 2010 2010 年 9 月 20 日) Free to factor
5×10240-1 = 4(9)240<241> = 191 × 3461 × 2690920046364699064192261715761<31> × 2810827823046578732309945858361301765321017194641362074991732793795156529399851864763623962944446216182530402258382409509009244368928634311692449977438787477729329410297310626971000350274958564005706519709<205> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=570533954 for P31 / February 17, 2010 2010 年 2 月 17 日)
5×10241-1 = 4(9)241<242> = 7 × 4198123253828837668608670247<28> × 24771111459882069751848520790069279<35> × [68686484008661172948703761740333261688094379389728492345659030929957397079798283183390414804461724983518887704730869036988083558574125907542353477804544085656528550127345216310289<179>] (Ignacio Santos / GMP-ECM 6.3 for P35 / September 20, 2010 2010 年 9 月 20 日) Free to factor
5×10242-1 = 4(9)242<243> = 2381 × 709861 × 20928644453908721<17> × [14135012352185399391201858831031956491118505741931977729656952923697966221455827334594091137507029017917779233763652964856106695837450811042854476838629949106203832598248165426761434128936422158348957648223278692138959<218>] Free to factor
5×10243-1 = 4(9)243<244> = 2481097 × 28969103167<11> × 69565067411115205532160326203300300351007177055315996670169689596295319902383800027691004457968624517330033227032820302187475916752155656654703180784650580344083762664065740897032660720373528385919348940864588008720057937974201<227>
5×10244-1 = 4(9)244<245> = 37649 × 28630487916322577729<20> × 46386094640337558724297348481235051522251886841023697086700864897337006721011304628631801859319973246680185588179139834652701219250866731370748745779748163468437172214512998590201970890931079632585211864058431422533712719<221>
5×10245-1 = 4(9)245<246> = 31 × 44563313 × 578324671 × 4435525939519<13> × 84498517658721721<17> × 4241041226322921615926912669770783<34> × 393724475204028496018935860671451568581958325965950982099035563957567744768092731389339581853971895514087327446403251929667323634729236081636073754954618533633998119<165> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3327840844 for P34 / February 9, 2010 2010 年 2 月 9 日)
5×10246-1 = 4(9)246<247> = 58930429401730153100681299441519307165466512611<47> × 84845809724461362218165130586126185531399732821311034367560252283968350458879284749501409247653423973356433519951891027006864486811560455329257878845231262477127557316889330342370345671140710102771509<200> (Dmitry Domanov / ECMNET/GMP-ECM 6.2.3 B1=11000000, sigma=2749045811 for P47 / February 22, 2010 2010 年 2 月 22 日)
5×10247-1 = 4(9)247<248> = 7 × 26423 × 151871 × 146005927 × 227709743 × 6444224421774218716692167479927125409<37> × 6797785463025725173887190631272412879<37> × 1222150746025799862132186343332481842357590604908111367945092773137682768169311767654192798992307347389925681556198396431678919601432890642165514999<148> (Ignacio Santos / GMP-ECM 6.3 B1=11000000, sigma=2762950941 for P37(6797...) / September 21, 2010 2010 年 9 月 21 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1739591430 for P37(6444...) / March 17, 2011 2011 年 3 月 17 日)
5×10248-1 = 4(9)248<249> = 401 × [1246882793017456359102244389027431421446384039900249376558603491271820448877805486284289276807980049875311720698254364089775561097256857855361596009975062344139650872817955112219451371571072319201995012468827930174563591022443890274314214463840399<247>] Free to factor
5×10249-1 = 4(9)249<250> = 17 × 23 × 383 × 3823 × 47911 × 209471 × 398681 × 43619353 × 212722367281<12> × [235241054550401971978237896515155994787634316184247420487095416376554003673041959185633873329023669439790681116334334380256794250219808534119974411608929919161930199234920382928138825441136188796489687584577<207>] Free to factor
5×10250-1 = 4(9)250<251> = 192 × 179 × 773766229746668936380940590228880050759064671381482226589702719014531329794642442625234064284498367353255234528544236215354617063092898373543385072501895727262879338894133304446060756124359708444884631455144771661585601757996873984431823457497021<246>
5×10251-1 = 4(9)251<252> = 167 × 2216992578722370619028849<25> × 31659415979788077458312286878799382781668758983<47> × 42656615536852743284362884719890969938267657730814498638741442838185624334434215076459259854096941166380573364544168307701010064040405860765539263074481103760218989750064898409791<179> (bbmz / GMP-ECM B1=110000000, sigma=1819184575 for P47 / January 21, 2012 2012 年 1 月 21 日)
5×10252-1 = 4(9)252<253> = 1337782429<10> × 6563250056485602277363426735241<31> × 569463071090041234434700106028665339438468947321698050512940662775358034080081422533581465052956809089036696292265014929059901900620994821496488399320686094168717959659764387351497456632454316362832614142540061491<213> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=507066655 for P31 / February 17, 2010 2010 年 2 月 17 日)
5×10253-1 = 4(9)253<254> = 73 × 4728697 × 1154281424229612803825531588437765022029216434433<49> × 26706851461694992127836629096338493624748434732844941827709174443517046457820604063648797470783052696098718135400781983910932873170423876153548653062432886051276341246406047118330034278230852943393<197> (nenym / GMP-ECM B1=110000000, sigma=4209279447 for P49 / September 21, 2010 2010 年 9 月 21 日)
5×10254-1 = 4(9)254<255> = 229 × 1229 × 10844591 × 64855976721872521<17> × [2525919220410231504278491100257123244022059151503034160323813553029886948358968630391852582830424999753431035915490369293371145199981384532416163468542213712873035342731787414939535744817102023638894712441932672022546824858249<226>] Free to factor
5×10255-1 = 4(9)255<256> = 89 × 26849 × 219961943 × 9770982045647<13> × 1498647331439513<16> × 275885153232944813826786649<27> × [2354714976365288705472274129562633774669198188902243051885189973400058103599557704805299423434433936023944272309143875527903737738750784695400329532205728896988908237899739892778425959167<187>] Free to factor
5×10256-1 = 4(9)256<257> = 59 × 625185061 × 1167899069<10> × 29445498686223281<17> × 4474563115550753206715869546223274629<37> × [8809160775479929615183643508450521035541361498928406361400894340271692298221341657341488745556272737178013020673266531850189162081828314596703563026652702798613429966585795963190105321<184>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3335501762 for P37 / March 14, 2011 2011 年 3 月 14 日) Free to factor
5×10257-1 = 4(9)257<258> = 127 × 433 × 48370681 × 45114468734558281<17> × 4166585879961257089590085238545323493945240375224651580102858546965890934553249490032223610688238968493876029101558692273721551474607836275815951737599573006846624153586331810494100920323312683422569575168417463334381313236983249<229>
5×10258-1 = 4(9)258<259> = 10430222161<11> × 11721584125896675342500506911851<32> × 40896876179314256708197688730526378700307486382117075718756240561425595787321194706560407846097028792484350330966187710540072020452048475447430346837444745243006926659151784597045151359550780184019874821304763207220909<218> (Wataru Sakai / GMP-ECM 6.2.1 B1=1000000, sigma=368619935 for P32 / February 17, 2010 2010 年 2 月 17 日)
5×10259-1 = 4(9)259<260> = 7 × 47 × 151 × 577 × [1744300663291258824460663107060674417106175197628393000567979181980899698420881120921096803698112767851757328844945381236620559799807310594327541220179479467889221418491115038268386682013256475724933972114842104334088278289076878760952071397156573625553<253>] Free to factor
5×10260-1 = 4(9)260<261> = 31 × 16979535342200421701<20> × [949910108433763141626427011905933734472127348340534238738503562146273666055673483535052585766945749303806624296849358099441833063032017616444226302571950064914070462390153540702140200578026064523609498028624377527702737392750248075760726829<240>] Free to factor
5×10261-1 = 4(9)261<262> = 113698069763224668441418917753548078179029210350369741917532633596794622588331183893056759545165527874097256881474110329<120> × 43976120354659146612026798097328326960551803227692600806060100248339479031211430178642452342456158830386446137151012230371188980878145277266231<143> (NFS@home + Dmitry Domanov / Msieve 1.54 for P120 x P143 / February 6, 2024 2024 年 2 月 6 日)
5×10262-1 = 4(9)262<263> = 29 × 1999681 × 5820941762021<13> × 87584239840995775349261<23> × 1691188695639121550118220217310676421587979009916735332822758410018390592123314711576805503191567204931703662792274146619302149212808157016389739928565896981689051090304832978954381452830015892761314364978264319249360171<220>
5×10263-1 = 4(9)263<264> = 10151 × 22031 × 391057 × 17991383 × 149926129 × 1315127760503<13> × 43744754891442721<17> × 36842669678661212801427552231032956648902983656429087349041112457470298317561874413350788728201550524766474673976319353976171342183136133731560335954462546954963851137936238593410087438710546547389175356567<206>
5×10264-1 = 4(9)264<265> = 149 × 2277637025924092069<19> × 1893000465084033824221<22> × 71574751298739459826382893837067971700745341219<47> × 96047343930453556960582240885311715778109782279501<50> × 1132148235176188484312968821564706450614614389182354920791227378154757269713912545811549780696328878080522672041019997412052021<127> ([TiDC] Chulma / GMP-ECM B1=110000000, sigma=1672675337 for P47 / January 23, 2012 2012 年 1 月 23 日) (Serge Batalov / GMP-ECM B1=260000000, sigma=1213924942 for P50 / March 19, 2014 2014 年 3 月 19 日)
5×10265-1 = 4(9)265<266> = 7 × 17 × 2617 × 17764399519<11> × 65600930071<11> × 5374453002137<13> × 25634480599005581681335977752906661895572766130898459888067482679900312682327167809244759997298396635686472128867649348430205220934853493034568531563215375398327451986503468738627800221153229099562312065503094318853044421842401<227>
5×10266-1 = 4(9)266<267> = 16251683414697871322752974461<29> × 42055974349658795815118333165599264049<38> × 731549893787415269659021683715554821546414013514632748597895148643048786057012063701382541053119583906922523242736160772867039965193039229900936054692314510169570118435036921197085612238977098165649691<201> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1625519868 for P38 / March 17, 2011 2011 年 3 月 17 日)
5×10267-1 = 4(9)267<268> = 21839 × 590004575761<12> × 2083147957065396209<19> × 2266104046057163358559<22> × 672294556863575979753546898422059650697<39> × 15771087553948236103510972548373095484103<41> × 7752837390306113959911758321417063934755121337603800321290560565278365777380019820546583225941042401278918964800953107870054765933361<133> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3202207193 for P41 / March 17, 2011 2011 年 3 月 17 日) (Dmitry Domanov / GMP-ECM B1=110000000, sigma=2151041565 for P39 / April 22, 2011 2011 年 4 月 22 日)
5×10268-1 = 4(9)268<269> = 19 × 6011 × 53270891 × 112894129976039<15> × 210145795799035979<18> × [346407788319196507661931854212894390937512642183121779541855467777404480281636620010015302301667363952733637144680786081305178170643735660905940187401559311071916945046217948526336345541445900240335045432023801553820964136241<225>] Free to factor
5×10269-1 = 4(9)269<270> = 392663 × 5016472508694540713<19> × 2390737653041124668089088194573501849<37> × [106174363441448918421035747285627000272328792644690333909138640563165093998942953645853955007045389438717524367018500237929064967925996027858636171603269215999801862457663548255652172162930724469243323464693529<210>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1816128360 for P37 / March 18, 2011 2011 年 3 月 18 日) Free to factor
5×10270-1 = 4(9)270<271> = 3655682986470754331<19> × 770928260351424785483879849<27> × 487514667647903094609528994762081665781<39> × 7396926050492286873060112876261428802945111<43> × 149315652768829739360005948083913547878672243509709<51> × 3294907370558216673526162561914992715933546258236037329206290742504811395611483694479908763859<94> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=41123723 for P39 / October 10, 2011 2011 年 10 月 10 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2624574968 for P43 / October 11, 2011 2011 年 10 月 11 日) (Erik Branger / GGNFS, Msieve gnfs for P51 x P94 / January 26, 2015 2015 年 1 月 26 日)
5×10271-1 = 4(9)271<272> = 7 × 23 × 991 × 1319 × 2922174137493887033<19> × 36561763732465014847<20> × 6175306400072659261608475344391841<34> × 360108967870077375980692896957073543446306509717513838764846211587186808799161075713705185030937913870605615181802810440810529939205295274191681148674933514779907615384709673895926536133217681<192> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1801153034 for P34 / February 11, 2010 2010 年 2 月 11 日)
5×10272-1 = 4(9)272<273> = 6972499417926424301<19> × 71710296413147170689960249183255813878918021245212428754456348503792277434673300529640577005940651578262406474163740082474786750426430811505384796151394376300084382604526126646585465563933454256203257109599185014649144234218010805545600385937181102934299<254>
5×10273-1 = 4(9)273<274> = 71 × 313 × 1087 × 152956107333614214551<21> × 1051802224850632142950906676913209640881<40> × 49919715636137073264992265468097820243197943<44> × 25772987530263947503222317540276912362903471787800921773288351341811875974270088531611770346163020333286289776690368408425082316260411114225257904951399589653274703<164> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=809287384 for P40 / March 18, 2011 2011 年 3 月 18 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=813137993 for P44 / October 2, 2011 2011 年 10 月 2 日)
5×10274-1 = 4(9)274<275> = 1454962901318821<16> × 7357489449952379<16> × 169692615346047179<18> × 20141793389121620640509<23> × 6020265276831740730403081827065454159708760111<46> × 4266285792149754766935132203741387094349195849924369479915177172719847645891049<79> × 53206143732147572645990093260185277167202411942060583110206878600239864394333809<80> (Beyond / GMP-ECM B1=110000000, sigma=1157590612 for P46 / January 24, 2012 2012 年 1 月 24 日) (Youcef Lemsafer / Msieve 1.53 gnfs for P79 x P80 / June 12, 2014 2014 年 6 月 12 日)
5×10275-1 = 4(9)275<276> = 31 × 113 × 601 × 1322743 × 349231409 × 22396717171947201851065687<26> × 22955262385055455939698793639996065383027038959926118812774998305413387634543367894871997807892466963794510940332192180285800172086964451935029523926296465620335331165346443177060915733019479704763731420449564512320162878482200057<230>
5×10276-1 = 4(9)276<277> = 2441 × 7829 × [261635054785595566939354930400104360990652878359740769894637993627511951620120133398295573202898141967262233518809912138239172010867901559705982897753700840931694988574135522458255996191430834497042451177198149151760837931264180292925560797733654363034022656235242147691<270>] Free to factor
5×10277-1 = 4(9)277<278> = 7 × 97 × 108377 × 5510369 × 849480001 × 25885045568128183<17> × 5607642647938336538244722383459860777136130451913061134682641197423558504108771645453514963770311082218105894721907865191439314412495047917324188445954860227702231175467397010192803525817771457044676619456667841035990092674202458386636439<238>
5×10278-1 = 4(9)278<279> = 7570996600571<13> × 47303422964191<14> × 3093782708661875749<19> × 451268040378903319742284123605402309946881914184865502350886743922649175456857570947568757549410830507108358483010062539644117663070737646364697690581218490093151322325912084803534047112671618792274457791829103853101243632733722672791<234>
5×10279-1 = 4(9)279<280> = 359 × 24051357191<11> × 1996535065173031<16> × 2746233211781468298647<22> × 105614028981077457561258494073628546270634879343184858611112448071056287493146293861695164701401739685603235042017457993522736952968869830505504280946693229254012630406701684740681388062306347274074873308009559947542649543608733903<231>
5×10280-1 = 4(9)280<281> = 5562137660941<13> × 8989349607636467958114881257975534668130637722707688234910040930369503203651794818282807670746480226781651086751144222375678002680805098857866527879992743161435315623793706680393473399532823056925134338266890105645255894401544567914945593344418627111595449417192001339<268>
5×10281-1 = 4(9)281<282> = 17 × 599 × 29753 × 1148599 × 11989897 × 1334578681<10> × 89791541870972540959884177525142025759683629929335664300674571758745328774682405780212925085494518194767690111237605899855528846049841211344871145605734017063971758625479786796756495126676415539664471448461313620829451891196971351172363909258601330807<251>
5×10282-1 = 4(9)282<283> = 11519 × 312799 × [1387681728748897201350993311087927457847466885293665735443322533401465212783601288536975898550292256165810666079844557310255017571199335803569816853440722196020123750786670180539538266184171690837518408198304201805273960510576188403256972167262848365491086252642566132181279<274>] Free to factor
5×10283-1 = 4(9)283<284> = 7 × 28111 × 5056830553<10> × 9438157197325872778158911<25> × 1407506020517889111185547719235950858417521<43> × 3782507520783930397067686485988603301582352341211720698729449666269870878899160010706235569931685067079837571419760406023457198600196381481320525644660307866064840118204968723024251167192704671460462609<202> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1645586100 for P43 / October 2, 2011 2011 年 10 月 2 日)
5×10284-1 = 4(9)284<285> = 551382774466529<15> × 906811063301274517961490941336414678470284957556429626574000374455039067480670114092665601378513159089884143538650774750276824401714267897481767016638297654715545454169758474920431134930316453905203783308724084617058170061164204922250843915242147262050657171931832894431<270>
5×10285-1 = 4(9)285<286> = 86052234771785423833873722405105681185807<41> × [58104243466311308429323738270471415711610138047632125796034305485877692313509930236831658899486641092123757802339149626882666141226378538206898383668001045131822608655742136240968310105563653264429735447896249210458390856665332040664612189687057<245>] (Markus Tervooren / GMP-ECM B1=4556772, sigma=3899543000 for P41 / February 17, 2010 2010 年 2 月 17 日) Free to factor
5×10286-1 = 4(9)286<287> = 19 × 61 × 34657949 × 17028103236964031115409765778805014621<38> × 38079087783527363082009265754731462080091319<44> × 1571508106287635422498009940970694382056353151<46> × 1221558511240692253247188430906522327490175384156787453275634303400294821196820707032361139537324571942402853730476889968063160130160915545245992879161<151> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2932028298 for P46 / February 12, 2010 2010 年 2 月 12 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3551212317 for P38, B1=43000000, sigma=2615213188 for P44 / October 2, 2011 2011 年 10 月 2 日)
5×10287-1 = 4(9)287<288> = 6975277102185307193<19> × [71681740047768622391625856109412363514464273685802455528669287124971191342006780725963311052514116536365917333813063106894338445011865450497892830763493161524637739813074709314017841999379883295018865916580537172034930935453186079087228483955599802562301454494363069943<269>] Free to factor
5×10288-1 = 4(9)288<289> = 251 × 4111595641<10> × 11746172639889128403335067329<29> × 3189078141871089191241201614788049<34> × 5798443240784036861141900382091909<34> × 22305549934151822322965727735916523940259898005514074803898278947665467056291466137618909739843095721598102066758940059253690856242677462063999800406016029545852646169478031271655201<182> (Ignacio Santos / GMP-ECM 6.3 B1=3000000, sigma=715276067 for P34(5798...), B1=3000000, sigma=356507500 for P34(3189...) / September 25, 2010 2010 年 9 月 25 日)
5×10289-1 = 4(9)289<290> = 7 × 7919 × 901989789475583136398895964497681886241047751339454837371240957552360507279057601067955910739090433496292821965255353309400537585914527447549293741994840618404199664459798315083073259610701206862338318330236501722800497898363790521891292190572402720401205058358739379070228925008568903<285>
5×10290-1 = 4(9)290<291> = 29 × 31 × 10160856615691<14> × 2115956647996669<16> × 25868617789854959387487706075473256459990936925805658505905835166133484315163095546661118392020424359334459839676340578884505706945063405204953453562916841421803279161126777464925636944903163140567717685421035023510663212045922132377803986859557667312986473419<260>
5×10291-1 = 4(9)291<292> = [4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<292>] Free to factor
5×10292-1 = 4(9)292<293> = 1748981296129<13> × 787178876076979<15> × 139387412072686308492791<24> × 340594920207321036107737951<27> × [764979305599778402541510996781611053102539202085341523045371810158799195422535248328295541119036344002205967766204496470272707991493780248555040734934943771441807513047848685491388676609764521288718610960143849615229<216>] Free to factor
5×10293-1 = 4(9)293<294> = 23 × 1831 × 611701007 × 3058496458864340739258551<25> × 6346096131487310393303347255660986105742326359807046643577884809398791637178947483370686393951396530304637620820803445604466103263642321487766901592630861349876597998361355526872644422059674903211402440591091789830609832907289191836485320954836666064309239<256>
5×10294-1 = 4(9)294<295> = 199 × 296518324348641139<18> × [84735498879864290426552485547983392598222616336822368242684214105622908349537061975456183376931441201587879456887766185727011914126293864325846657998835196024004132871800228742157235424282933440537978194756662704394825955509785073100113014984874781355507222421682989712167059<275>] Free to factor
5×10295-1 = 4(9)295<296> = 72 × 2430359 × 209257729 × 2006420638761469652835453862826954278638695350140425856253194497502892405899200478024951637797133472997283475917249745879841366477076398451075674457920675030761189429808221992067212257516704985058769844442696074758008824355158605743856215633110456538614359595770030865232143110441<280>
5×10296-1 = 4(9)296<297> = 218249 × 2843589839<10> × 38591906359<11> × 83417596088855925173089<23> × [250263137856297603313811100078035555593427534262020030610568434186413456603463995858103458131388303743146577336782473688377946745484469670725035862267590796410198330877099015473344551075227633543700102946749711562440567124761714803394940701878665759<249>] Free to factor
5×10297-1 = 4(9)297<298> = 17 × 13049 × 1267991119<10> × 704582187583<12> × 128095237059977817736208549181569948642526887<45> × 196953180607662340838704808812030726709543318512843221210558739934257899726319378104177618567004283710160688940293166175756392571680571762295524719914492223622376559261739453349592195717778848695748524479998558013070785951789297<228> (Dmitry Domanov / GMP-ECM B1=110000000, sigma=2038989449 for P45 / October 4, 2011 2011 年 10 月 4 日)
5×10298-1 = 4(9)298<299> = 209579 × 116476252448176775864629<24> × 63725051961656089586609879745629<32> × [32142129996354455319938628022977334474065593314901453712967035593847058549219979536849702341418163018565730778560429630148895352922384817648012600802369857839827926364335178459117252087950453158417391558422016917222309866479256365334807741<239>] (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3875277313 for P32 / February 13, 2010 2010 年 2 月 13 日) Free to factor
5×10299-1 = 4(9)299<300> = 89 × 127 × 2132733466305406944552656449501978228207906169<46> × [20741477651634618509554333916716248310117115165561874059497125254379027379798724302391029290176171106591409645847649344395603795203243623261261097952977784729230037791598157191350396059712976936770526320385321476181393851481004431180911094128990124657<251>] (Markus Tervooren / GMP-ECM B1=43000000, sigma=3819258053 for P46 / March 8, 2010 2010 年 3 月 8 日) Free to factor
5×10300-1 = 4(9)300<301> = 409 × 20551 × 811981 × 1875493268248863759663828095058839<34> × [390618097401566377522933719307384801192602986300646859370367931148000202291598917893560038267689544235286095461048178254159919988406277938982466624986401532121365732240332988438096480652284716502695438905699801158632694525799968505694388335852184233045779<255>] (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1335094533 for P34 / February 14, 2010 2010 年 2 月 14 日) Free to factor
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