Table of contents 目次

  1. About 900...001 900...001 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 900...001 900...001 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 900...001 900...001 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 900...001 900...001 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

90w1 = { 91, 901, 9001, 90001, 900001, 9000001, 90000001, 900000001, 9000000001, 90000000001, … }

1.3. General term 一般項

9×10n+1 (1≤n)

2. Prime numbers of the form 900...001 900...001 の形の素数

2.1. Last updated 最終更新日

July 9, 2018 2018 年 7 月 9 日

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

  1. 9×103+1 = 9001 is prime. は素数です。
  2. 9×104+1 = 90001 is prime. は素数です。
  3. 9×105+1 = 900001 is prime. は素数です。
  4. 9×109+1 = 9000000001<10> is prime. は素数です。
  5. 9×1022+1 = 9(0)211<23> is prime. は素数です。
  6. 9×1027+1 = 9(0)261<28> is prime. は素数です。
  7. 9×1036+1 = 9(0)351<37> is prime. は素数です。
  8. 9×1057+1 = 9(0)561<58> is prime. は素数です。
  9. 9×1062+1 = 9(0)611<63> is prime. は素数です。
  10. 9×1078+1 = 9(0)771<79> is prime. は素数です。
  11. 9×10201+1 = 9(0)2001<202> is prime. は素数です。
  12. 9×10537+1 = 9(0)5361<538> is prime. は素数です。
  13. 9×10696+1 = 9(0)6951<697> is prime. は素数です。
  14. 9×10790+1 = 9(0)7891<791> is prime. は素数です。
  15. 9×10905+1 = 9(0)9041<906> is prime. は素数です。
  16. 9×101038+1 = 9(0)10371<1039> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1984 1984 年 12 月 31 日)
  17. 9×1066886+1 = 9(0)668851<66887> is prime. は素数です。 (Peter Benson / NewPGen, OpenPFGW, Proth.exe / December 31, 2004 2004 年 12 月 31 日)
  18. 9×1070500+1 = 9(0)704991<70501> is prime. は素数です。 (Peter Benson / NewPGen, OpenPFGW, Proth.exe / March 10, 2005 2005 年 3 月 10 日)
  19. 9×1091836+1 = 9(0)918351<91837> is prime. は素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  20. 9×10100613+1 = 9(0)1006121<100614> is prime. は素数です。 (Predrag Kurtovic / September 23, 2013 2013 年 9 月 23 日)
  21. 9×10127240+1 = 9(0)1272391<127241> is prime. は素数です。 (Bob Price / PFGW / January 22, 2015 2015 年 1 月 22 日)

2.3. Range of search 捜索範囲

  1. n≤100000 / Completed 終了 / Dmitry Domanov / March 8, 2010 2010 年 3 月 8 日
  2. n≤124000 / Completed 終了 / Predrag Kurtovic / September 23, 2013 2013 年 9 月 23 日
  3. n≤200000 / Completed 終了 / Bob Price / January 22, 2015 2015 年 1 月 22 日
  4. n≤250000 / Completed 終了 / Predrag Kurtovic / May 25, 2018 2018 年 5 月 25 日
  5. n≤300000 / Completed 終了 / Predrag Kurtovic / June 17, 2018 2018 年 6 月 17 日
  6. n≤350000 / Completed 終了 / Predrag Kurtovic / July 8, 2018 2018 年 7 月 8 日

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

  1. 9×106k+1+1 = 7×(9×101+17+81×10×106-19×7×k-1Σm=0106m)
  2. 9×106k+1+1 = 13×(9×101+113+81×10×106-19×13×k-1Σm=0106m)
  3. 9×1013k+2+1 = 53×(9×102+153+81×102×1013-19×53×k-1Σm=01013m)
  4. 9×1016k+2+1 = 17×(9×102+117+81×102×1016-19×17×k-1Σm=01016m)
  5. 9×1018k+17+1 = 19×(9×1017+119+81×1017×1018-19×19×k-1Σm=01018m)
  6. 9×1022k+15+1 = 23×(9×1015+123+81×1015×1022-19×23×k-1Σm=01022m)
  7. 9×1028k+16+1 = 29×(9×1016+129+81×1016×1028-19×29×k-1Σm=01028m)
  8. 9×1034k+13+1 = 103×(9×1013+1103+81×1013×1034-19×103×k-1Σm=01034m)
  9. 9×1043k+18+1 = 173×(9×1018+1173+81×1018×1043-19×173×k-1Σm=01043m)
  10. 9×1044k+23+1 = 89×(9×1023+189+81×1023×1044-19×89×k-1Σm=01044m)

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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 29.15%. 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 29.15% です。

3. Factor table of 900...001 900...001 の素因数分解表

3.1. Last updated 最終更新日

March 3, 2016 2016 年 3 月 3 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=206, 209, 210, 211, 217, 223, 224, 232, 233, 234, 235, 237, 238, 242, 244, 246, 248, 250 (18/250)

3.4. Factor table 素因数分解表

9×101+1 = 91 = 7 × 13
9×102+1 = 901 = 17 × 53
9×103+1 = 9001 = definitely prime number 素数
9×104+1 = 90001 = definitely prime number 素数
9×105+1 = 900001 = definitely prime number 素数
9×106+1 = 9000001 = 61 × 147541
9×107+1 = 90000001 = 7 × 13 × 989011
9×108+1 = 900000001 = 409 × 2200489
9×109+1 = 9000000001<10> = definitely prime number 素数
9×1010+1 = 90000000001<11> = 113 × 796460177
9×1011+1 = 900000000001<12> = 634939 × 1417459
9×1012+1 = 9000000000001<13> = 1072157 × 8394293
9×1013+1 = 90000000000001<14> = 7 × 13 × 103 × 9602048437<10>
9×1014+1 = 900000000000001<15> = 1097 × 820419325433<12>
9×1015+1 = 9000000000000001<16> = 23 × 53 × 7383100902379<13>
9×1016+1 = 90000000000000001<17> = 29 × 12553 × 286469 × 863017
9×1017+1 = 900000000000000001<18> = 19 × 47368421052631579<17>
9×1018+1 = 9000000000000000001<19> = 17 × 173 × 264601 × 11565276061<11>
9×1019+1 = 90000000000000000001<20> = 7 × 13 × 9642641 × 102566401571<12>
9×1020+1 = 900000000000000000001<21> = 1669850621<10> × 538970365781<12>
9×1021+1 = 9000000000000000000001<22> = 101477 × 88690047991170413<17>
9×1022+1 = 90000000000000000000001<23> = definitely prime number 素数
9×1023+1 = 900000000000000000000001<24> = 59 × 89 × 419 × 409059485884947929<18>
9×1024+1 = 9000000000000000000000001<25> = 1277 × 34781 × 202632707706349273<18>
9×1025+1 = 90000000000000000000000001<26> = 7 × 13 × 989010989010989010989011<24>
9×1026+1 = 900000000000000000000000001<27> = 876653 × 2462224309<10> × 416953065713<12>
9×1027+1 = 9000000000000000000000000001<28> = definitely prime number 素数
9×1028+1 = 90000000000000000000000000001<29> = 53 × 7672134296041<13> × 221335177673237<15>
9×1029+1 = 900000000000000000000000000001<30> = 169148534693<12> × 5320767345892032557<19>
9×1030+1 = 9000000000000000000000000000001<31> = 661 × 9338569 × 1458010722709494472789<22>
9×1031+1 = 90000000000000000000000000000001<32> = 7 × 13 × 487 × 1493 × 28195807 × 48242279334679103<17>
9×1032+1 = 900000000000000000000000000000001<33> = 16901 × 48817 × 1090834891658648232287453<25>
9×1033+1 = 9000000000000000000000000000000001<34> = 47 × 909983219 × 1065587651<10> × 197479531885607<15>
9×1034+1 = 90000000000000000000000000000000001<35> = 17 × 41043601 × 128987650159127692753171553<27>
9×1035+1 = 900000000000000000000000000000000001<36> = 19 × 1289 × 36477404545339<14> × 1007423463151225049<19>
9×1036+1 = 9000000000000000000000000000000000001<37> = definitely prime number 素数
9×1037+1 = 90000000000000000000000000000000000001<38> = 72 × 13 × 23 × 87407 × 197339 × 356136186044107373212487<24>
9×1038+1 = 900000000000000000000000000000000000001<39> = 272429779957429<15> × 3303603593339310073120669<25>
9×1039+1 = 9000000000000000000000000000000000000001<40> = 38201 × 235595926808198738252925316091201801<36>
9×1040+1 = 90000000000000000000000000000000000000001<41> = 4129 × 51103721909<11> × 426525592954465283837529341<27>
9×1041+1 = 900000000000000000000000000000000000000001<42> = 53 × 31081 × 546350892039242563405538662520875157<36>
9×1042+1 = 9000000000000000000000000000000000000000001<43> = 1032841 × 200569872671203969<18> × 43445354086585722169<20>
9×1043+1 = 90000000000000000000000000000000000000000001<44> = 7 × 13 × 1652393935719810859<19> × 598532206897841844839929<24>
9×1044+1 = 900000000000000000000000000000000000000000001<45> = 29 × 97 × 313 × 8641 × 11813 × 16493429 × 607146191816885557369397<24>
9×1045+1 = 9000000000000000000000000000000000000000000001<46> = 1303 × 5532177317<10> × 10909587209<11> × 114444172630926939804739<24>
9×1046+1 = 90000000000000000000000000000000000000000000001<47> = 40697 × 2211465218566479101653684546772489372681033<43>
9×1047+1 = 900000000000000000000000000000000000000000000001<48> = 103 × 8737864077669902912621359223300970873786407767<46>
9×1048+1 = 9000000000000000000000000000000000000000000000001<49> = 2098659371971387633<19> × 4288452009029840199691181281297<31>
9×1049+1 = 90000000000000000000000000000000000000000000000001<50> = 7 × 13 × 87339225260767<14> × 11323789351899085812386611845621133<35>
9×1050+1 = 900000000000000000000000000000000000000000000000001<51> = 17 × 185177 × 285894989499712357874453344955494091662380889<45>
9×1051+1 = 9(0)501<52> = 5303 × 1697152555157458042617386385065057514614369224967<49>
9×1052+1 = 9(0)511<53> = 535637 × 28064609683944217<17> × 5987050673047259348191289748869<31>
9×1053+1 = 9(0)521<54> = 19 × 317 × 373 × 621654619 × 644423915856720982631763433468126261601<39>
9×1054+1 = 9(0)531<55> = 53 × 8788913350268140529281<22> × 19321082594304586677823683769757<32>
9×1055+1 = 9(0)541<56> = 7 × 13 × 20325049727<11> × 48659708207118277767203565032192406157797293<44>
9×1056+1 = 9(0)551<57> = 22349 × 40270258177099646516622667680880576312139245603830149<53>
9×1057+1 = 9(0)561<58> = definitely prime number 素数
9×1058+1 = 9(0)571<59> = 2836549 × 19745953963988218120980173<26> × 1606845419421940062477406913<28>
9×1059+1 = 9(0)581<60> = 232 × 223 × 433241 × 17609718952061731403087007685427467197151800957383<50>
9×1060+1 = 9(0)591<61> = 52069729 × 165220125649<12> × 2903138521729<13> × 360351625548496622538364964689<30>
9×1061+1 = 9(0)601<62> = 7 × 132 × 173 × 3889314411127<13> × 113067713261508411500006922947650419833838557<45>
9×1062+1 = 9(0)611<63> = definitely prime number 素数
9×1063+1 = 9(0)621<64> = 1846367 × 6443011 × 756546466489705346851565812353711496009046424433973<51>
9×1064+1 = 9(0)631<65> = 509 × 16715162760707934917<20> × 10578257079088291910027606345457172703854417<44>
9×1065+1 = 9(0)641<66> = 4721 × 7459 × 25558060971253457331200579406921787420600688835179728118459<59>
9×1066+1 = 9(0)651<67> = 17 × 61 × 537684018665889709<18> × 16141229955383838954779796325035290472200075897<47>
9×1067+1 = 9(0)661<68> = 7 × 13 × 53 × 89 × 967 × 216824706300274768218062939196360764018857398893392710120649<60>
9×1068+1 = 9(0)671<69> = 1937018929<10> × 464631494574310378357691309892201884620818798410410371369169<60>
9×1069+1 = 9(0)681<70> = 223849 × 8854438717133<13> × 56519161534037<14> × 80339773672359894075979909433788068169<38>
9×1070+1 = 9(0)691<71> = 177481 × 507096534276908514150810509293952592108451045464021500893053340921<66>
9×1071+1 = 9(0)701<72> = 19 × 1021624687<10> × 1127992566528760154341995397<28> × 41104681929792392767439545550068561<35>
9×1072+1 = 9(0)711<73> = 29 × 1193737 × 369568350763637<15> × 3803265121978231417<19> × 184962839464472374696671097901953<33>
9×1073+1 = 9(0)721<74> = 7 × 13 × 131 × 157 × 3434714219<10> × 40505281728310780921<20> × 345643109794933143493746424616869980967<39>
9×1074+1 = 9(0)731<75> = 26513 × 33945611586768754950401689737110096933579753328555802813714027081054577<71>
9×1075+1 = 9(0)741<76> = 761 × 27259 × 770146331600773683360157<24> × 563345308535846414525123654230410396421566407<45>
9×1076+1 = 9(0)751<77> = 39191309 × 2296427506414751290904827904574455525330883946744417238015703940891589<70>
9×1077+1 = 9(0)761<78> = 797 × 997 × 1347545921<10> × 840514975997107693570604695977849746413871622498980856073069009<63>
9×1078+1 = 9(0)771<79> = definitely prime number 素数
9×1079+1 = 9(0)781<80> = 72 × 13 × 47 × 1361 × 939179 × 362132527 × 6494282636470574357798239086613389616047164558265238476143<58>
9×1080+1 = 9(0)791<81> = 53 × 7228517 × 8649300328437453436924860432196733<34> × 271604183953600044068617132843666403597<39> (Makoto Kamada / msieve 0.83 / 3.2 minutes)
9×1081+1 = 9(0)801<82> = 23 × 59 × 103 × 9539 × 15569 × 433572640799482999983753283405797953951283348120523679061716819187841<69>
9×1082+1 = 9(0)811<83> = 17 × 197 × 4373989 × 444342046542949<15> × 3671809354584061<16> × 3765755685692309199255513351359290351036969<43>
9×1083+1 = 9(0)821<84> = 73235077 × 82599773 × 43082588561<11> × 3453366913153286556653523424034883035479542624501723609121<58>
9×1084+1 = 9(0)831<85> = 1229 × 166349 × 7272783344894506752237530908390190689<37> × 6052987567340882018702428727084789529529<40> (Makoto Kamada / GGNFS-0.70.1 / 0.13 hours)
9×1085+1 = 9(0)841<86> = 7 × 13 × 52301303 × 18909872838368654237715855549736284982976638058347972917405346268543042053637<77>
9×1086+1 = 9(0)851<87> = 2684897 × 16342553 × 54480808381<11> × 8406226122100292597<19> × 44786834372208198144524113843511052885709673<44>
9×1087+1 = 9(0)861<88> = 887 × 386371357 × 236255147171<12> × 111155942984264837424265452151937913841984420295647335851780876209<66>
9×1088+1 = 9(0)871<89> = 769 × 14660735954786333<17> × 62196933420067104176339596580486953<35> × 128348685461100483103749562395167021<36>
9×1089+1 = 9(0)881<90> = 19 × 1013 × 1637 × 28564773432627871239776865954944655910167469236294439209861550034422138918173953059<83>
9×1090+1 = 9(0)891<91> = 1913 × 6353 × 132840597418340897<18> × 12859187943990900293<20> × 433515190810669877226290663075470944758601165829<48>
9×1091+1 = 9(0)901<92> = 7 × 13 × 823 × 288931 × 399389392454346926675860819<27> × 10413833149628141442784411438682714753267783316927489613<56>
9×1092+1 = 9(0)911<93> = 1645448113<10> × 9480123974237142790153<22> × 157953409519630929548571869<27> × 365271086023415027274232621052946461<36>
9×1093+1 = 9(0)921<94> = 53 × 3253 × 7083946094974808924944084339<28> × 2230909539925799570887029026531<31> × 3303127731542927100919793136721<31> (Makoto Kamada / GGNFS-0.71.4)
9×1094+1 = 9(0)931<95> = 6113 × 13693948969<11> × 5497124074493<13> × 1171170382948606419965693035937581<34> × 166995122940312683736314427080836801<36>
9×1095+1 = 9(0)941<96> = 18374716688349200481047<23> × 48980347031454379028995841919619369493502916547701926929456719936658697383<74>
9×1096+1 = 9(0)951<97> = 821 × 353920196149253<15> × 12320837891262052071437478413<29> × 2513933370128468437396549479896274014744538673329629<52>
9×1097+1 = 9(0)961<98> = 7 × 13 × 11251 × 371135635889864816448450317<27> × 1216658351270915809990980393779<31> × 194674332501533702073581470782453127<36> (Makoto Kamada / GGNFS-0.71.4)
9×1098+1 = 9(0)971<99> = 17 × 665117 × 1302994037<10> × 61087606833217334930936140025570390625015013586542691774287192644976828132114177457<83>
9×1099+1 = 9(0)981<100> = 647 × 1159303 × 11998895445679379799918978391750473540741698203219135396897417073903734149720758838785348561<92>
9×10100+1 = 9(0)991<101> = 29 × 44497 × 852673 × 6267889 × 13049983777688172742896635745449048831681908684773511663795549758829314812199285941<83>
9×10101+1 = 9(0)1001<102> = 929 × 1087 × 62687801663<11> × 14217204524644415207780393657951435545559485039852289925018458324888753728301649466849<86>
9×10102+1 = 9(0)1011<103> = 857 × 4729 × 27724157 × 146688169 × 7824928201<10> × 1082959301461<13> × 64438650881125819456903404728709964010133394499896709654209<59>
9×10103+1 = 9(0)1021<104> = 7 × 13 × 23 × 6817147193929<13> × 6307693901839245662279188002838915868613967313464590717271270615162436918251411823620733<88>
9×10104+1 = 9(0)1031<105> = 173 × 401017 × 12972797010421811792073566252600451214059928931270279995193146281071704670643674584536446143483661<98>
9×10105+1 = 9(0)1041<106> = 146173 × 324660412100191757<18> × 189647015921930560555613778008392694518228331817885356768303090522447538729954849641<84>
9×10106+1 = 9(0)1051<107> = 53 × 109 × 601 × 273608402981042587412878642296398297<36> × 94740623536944631063360702956769539501899999853290343142238204929<65> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 1.31 hours on Pentium 4 2.80GHz / April 5, 2007 2007 年 4 月 5 日)
9×10107+1 = 9(0)1061<108> = 19 × 140725352693<12> × 3209015382997<13> × 14021490200609<14> × 101043252088451<15> × 24713519911140033558724499<26> × 2995771394891056123697829969739<31>
9×10108+1 = 9(0)1071<109> = 373777 × 4126417 × 516866967797<12> × 56849295635453<14> × 318262207989327241<18> × 1969570745833601789<19> × 316808116066994770590704313455437421<36>
9×10109+1 = 9(0)1081<110> = 7 × 13 × 18480611 × 36737531 × 1456715783890529448958356929556268261049304839622936526296628689514369386951968743985378548771<94>
9×10110+1 = 9(0)1091<111> = 535741 × 13711467855528170180393<23> × 1270514145578868772995123173<28> × 96432665403955779086149730071450484314220266525570368649<56>
9×10111+1 = 9(0)1101<112> = 89 × 76439746214259187150670786361768507023<38> × 1322919037723783381478589398425519069856963653988055358561452629090981383<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 1.17 hours on Cygwin on AMD 64 3200+ / April 5, 2007 2007 年 4 月 5 日)
9×10112+1 = 9(0)1111<113> = 179604761533489094411512153<27> × 501100300635507398407031482924168213889400921792034725619610165043624629901632661507817<87>
9×10113+1 = 9(0)1121<114> = 22699 × 1184459 × 184673635431641860805463910676143935673766213<45> × 181263705428764681773841097459967268253297158583781910475797<60> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 2.33 hours on Pentium 4 2.80GHz / April 5, 2007 2007 年 4 月 5 日)
9×10114+1 = 9(0)1131<115> = 17 × 4029232093952705808639019244540988181<37> × 131392720091863853149542807291473246596308272142652439543027874153558812956013<78> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 1.42 hours on Core 2 Duo E6300@2.33GHz / April 4, 2007 2007 年 4 月 4 日)
9×10115+1 = 9(0)1141<116> = 7 × 13 × 103 × 3391343 × 4528368424529<13> × 40963716780981360581121590745000013<35> × 15263392336091573406619034605037192244798168990720053726167<59> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 1.71 hours on Pentium 4 2.80GHz / April 5, 2007 2007 年 4 月 5 日)
9×10116+1 = 9(0)1151<117> = 3917 × 719189 × 1814814873154884385579882421783353<34> × 176040896601909387016192468843434263374254628094985647651842242628087932409<75> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 2.15 hours on Cygwin on AMD 64 3400+ / April 5, 2007 2007 年 4 月 5 日)
9×10117+1 = 9(0)1161<118> = 12527 × 12134790579207611427656536951386453899<38> × 59205649022301612078526981553969233951090001376598142943906491679184248013837<77> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 1.19 hours on Core 2 Duo E6300@2.33GHz / April 5, 2007 2007 年 4 月 5 日)
9×10118+1 = 9(0)1171<119> = 196073 × 186381179361616798004946995918881<33> × 1741085366837536144261031347273683656221<40> × 1414498837021419722168181729011819304044237<43> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 1.71 hours on Core 2 Duo E6300@2.33GHz / April 5, 2007 2007 年 4 月 5 日)
9×10119+1 = 9(0)1181<120> = 53 × 141413 × 8157992210918944356031188001<28> × 21390846892616080268751387717062038727<38> × 688122943822261605646355479136296441670952499967<48> (Makoto Kamada / Msieve 1.17 for P38 x P48 / 53 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / April 4, 2007 2007 年 4 月 4 日)
9×10120+1 = 9(0)1191<121> = 261066330188528555113<21> × 177543491136813067537023060576498121<36> × 194172127768048952704457311156481550648638322505777201579412750737<66> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 2.19 hours on Pentium 4 2.80GHz / April 5, 2007 2007 年 4 月 5 日)
9×10121+1 = 9(0)1201<122> = 72 × 13 × 8329 × 13099 × 45779 × 398459 × 7782345244798188203154573931<28> × 9122453056596871193844391369874307223847672767541887333118289467395936693<73>
9×10122+1 = 9(0)1211<123> = 113 × 229 × 2618281 × 2053239600061821515593493<25> × 6469529502156373506385505019204630074610658399452446570031177365503040875278827264072161<88>
9×10123+1 = 9(0)1221<124> = 2383 × 5569 × 35081 × 28502281 × 678249788730965343155876794263068283826182488644313608841077587266701477227270380314651873177483730318783<105>
9×10124+1 = 9(0)1231<125> = 168745086793<12> × 360847422557<12> × 1478045369332241890902656097128029833077561869578361464994129936119444146965960462980286762223022100301<103>
9×10125+1 = 9(0)1241<126> = 19 × 23 × 47 × 1091 × 2340179 × 17162849181227637954686586305558908249546272559153601351238220969425254370779811594520448516673293863019660069131<113>
9×10126+1 = 9(0)1251<127> = 61 × 1609 × 4480517 × 489006813651285661577821<24> × 41851746914137401114783396877147747465402212469861187936155145864696669256526001874056468957<92>
9×10127+1 = 9(0)1261<128> = 7 × 13 × 167 × 401 × 1289 × 112974047 × 101416511916384986434377207218778382110001626648805153438789813840049798877618436058332277078236972412647025251<111>
9×10128+1 = 9(0)1271<129> = 29 × 2833 × 6121 × 19705421 × 90821744521678073858476364997021996717514800118315880931365217585390573943501211754500252286470470063005559638673<113>
9×10129+1 = 9(0)1281<130> = 32801 × 2379277 × 4721270754216020253013<22> × 24425952708110930637045019522319838870076516710636340358528847569412668324375792540254249902835601<98>
9×10130+1 = 9(0)1291<131> = 17 × 24593 × 216594009296418960195645951195437<33> × 993883859583954448735204608842181266122491024424875540660278630042828155798346154067493353733<93> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 2.48 hours on Core 2 Duo E6300@2.33GHz / April 5, 2007 2007 年 4 月 5 日)
9×10131+1 = 9(0)1301<132> = 8299284248153821291347886062343<31> × 108443086546915815961290212547662608185723634371339940135709867135880497559893063530678305973289665207<102> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3271453043 / April 1, 2007 2007 年 4 月 1 日)
9×10132+1 = 9(0)1311<133> = 53 × 317 × 66451101285889<14> × 46727238867176438789<20> × 172518262538517256211201296934178206279773673815078420298703678317899978288552723100833170379181<96>
9×10133+1 = 9(0)1321<134> = 7 × 13 × 4968920397271493729905247<25> × 199039410966227048395930800201621775495118194835533213227230187549388956000123172044967043230129417917126413<108>
9×10134+1 = 9(0)1331<135> = 181 × 2753 × 16531089961<11> × 109258751591334591151303372851647591688655864712545289987012012810113495421933518921235388716934090390154756359979711637<120>
9×10135+1 = 9(0)1341<136> = 5927 × 3426823 × 4329778969<10> × 259922171552969<15> × 1684172380678722094703<22> × 233786976732721857354891289970301694664296598730453186421784242313375317460159807<81>
9×10136+1 = 9(0)1351<137> = 10037 × 17333 × 25821394384510406269905557<26> × 20034806731811563556317515354285137946810212466345951716652047292947478596158891683089943960150394732133<104>
9×10137+1 = 9(0)1361<138> = 12487 × 499844315469822755436751497077<30> × 22694932497912076567821810183311352533<38> × 6353612804509099688291593709903803564908420180194675150217717604303<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 6.82 hours on Core 2 Duo E6300@2.33GHz / April 5, 2007 2007 年 4 月 5 日)
9×10138+1 = 9(0)1371<139> = 2477 × 16193 × 95401 × 297051702914765761<18> × 7917794276392453813733352128005820521294962763082702780279765673387190228554203906926288871175245862306839581<109>
9×10139+1 = 9(0)1381<140> = 7 × 132 × 59 × 4424608127<10> × 78922087410589632675170017604509175183<38> × 80446991336116621276555908785459354423609<41> × 45901044757666544367296133139543971866289750757<47> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 7.37 hours on Core 2 Duo E6300@2.33GHz / April 6, 2007 2007 年 4 月 6 日)
9×10140+1 = 9(0)1391<141> = 97 × 149 × 293 × 4733 × 15127035346844083517<20> × 2968428278701030960390847160398665805832820067222560940788494279870037016639555085825216568275848011788840672529<112>
9×10141+1 = 9(0)1401<142> = 66031908616111316843093170997<29> × 10183815601095370522960916473439173<35> × 13383759748561580248834032773181350478449614572726727955728581327175944905132921<80> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 11.33 hours on Athlon XP 2100+ / April 6, 2007 2007 年 4 月 6 日)
9×10142+1 = 9(0)1411<143> = 229133 × 310418237090102149002920451352517921093<39> × 1265341173550541325953165241360932050982648906067589633583866154278345401523423025383948873896217729<100> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 9.89 hours on Core 2 Duo E6300@2.33GHz / April 6, 2007 2007 年 4 月 6 日)
9×10143+1 = 9(0)1421<144> = 19 × 77489 × 611292196990948120989668482657300764590695725233666442299789919248300777495753217264793440970568997569094696632662972197751667299467292811<138>
9×10144+1 = 9(0)1431<145> = 2237 × 13037 × 4866859180076729377<19> × 51314734681449885673<20> × 1235685617145325558299524025805769976067100096210061984084437289336349768789543780996327483772010049<100>
9×10145+1 = 9(0)1441<146> = 7 × 13 × 53 × 1171 × 223087 × 71432210402443879563413543498850639433397418526784449272113902643251546615538700296073783136343533299157202720662883596987399818198131<134>
9×10146+1 = 9(0)1451<147> = 17 × 593 × 4969 × 43311462465413<14> × 414827032242983066169768755751739547509414478568984740154577785626904744946199325072271275054311681358974385543488309046005093<126>
9×10147+1 = 9(0)1461<148> = 23 × 173 × 619 × 34179008207<11> × 2232476256742247<16> × 11256217824559833795361777689647<32> × 4254407909962889924194452125012698010158754770741473106917463514453834819046073932527<85> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1756400291 for P32 / April 1, 2007 2007 年 4 月 1 日)
9×10148+1 = 9(0)1471<149> = 653 × 2281 × 84913 × 31698046485101<14> × 261951712169089<15> × 2095543670347181<16> × 12564731965918073741<20> × 258782207455264963620629<24> × 12577425718924187164902411359943135119916884967529589<53>
9×10149+1 = 9(0)1481<150> = 103 × 58339727 × 1166377014449061208501451129<28> × 128410914744380971148367297133654714694280189508284997411663239770422292780242256394289470851646562594123742518849<114>
9×10150+1 = 9(0)1491<151> = 4253 × 3566992060520775519655367333427319075823880194840139594754009<61> × 593259886101759296204495700498020412031125484426971874909743168024374007473423673233213<87> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 20.35 hours on Cygwin on AMD XP 2700+ / April 7, 2007 2007 年 4 月 7 日)
9×10151+1 = 9(0)1501<152> = 7 × 13 × 157 × 1740270742464737399801648274260382251<37> × 6819290242424764524862346427986183895917940998262231863<55> × 530817791290284114816038893859259470090732398434626858971<57> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 18.56 hours on Cygwin on AMD 64 3400+ / April 5, 2007 2007 年 4 月 5 日)
9×10152+1 = 9(0)1511<153> = 2453694145358638423681793453<28> × 366793881667127514159991244654759652553502341108307784162958825376075982241849183509637602652073381767430229080916195981422117<126>
9×10153+1 = 9(0)1521<154> = 773 × 21663953434896401<17> × 12334939976056907489717<23> × 389973351927832109532862973<27> × 50855108656179945301710095305209161<35> × 2196942769126627989787668260704574508308842635667637<52> (Makoto Kamada / Msieve 1.17 for P35 x P52 / 45 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / April 4, 2007 2007 年 4 月 4 日)
9×10154+1 = 9(0)1531<155> = 10853 × 26821 × 28549 × 16267258734889<14> × 1901411797254127264433<22> × 350135609181819555812464717434349042876917394195532215257435914615091264169694418641882756172089510266656829<108>
9×10155+1 = 9(0)1541<156> = 89 × 38348003093<11> × 10408775320664023<17> × 25334370346380999588577332444700636857837271323408124361236405327634077592313937181311311768555333005844781154521489990877494531<128>
9×10156+1 = 9(0)1551<157> = 29 × 706993936910368903640116661982625450877<39> × 8380009192709174113059633311180980138633<40> × 52382271492126465895543889093087824425922340013871527868319133952371915809809<77> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 33.66 hours on Cygwin on AMD 64 3200+ / April 8, 2007 2007 年 4 月 8 日)
9×10157+1 = 9(0)1561<158> = 7 × 13 × 2130403278394440947268336034474352786160213379<46> × 464236512889873201316103265893901452919829671364175589843047024998926643175420109046920841497010559322144023409<111> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 28.69 hours on Cygwin on AMD 64 3200+ / April 16, 2007 2007 年 4 月 16 日)
9×10158+1 = 9(0)1571<159> = 53 × 297169 × 1147441 × 3134536849<10> × 4239692077429<13> × 975984724665859590593<21> × 14045487519807987354189692281<29> × 731065838605280441298711208972441<33> × 373928656032028718755230220853513167273321<42> (Makoto Kamada / Msieve 1.17 for P33 x P42 / 3.4 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / April 4, 2007 2007 年 4 月 4 日)
9×10159+1 = 9(0)1581<160> = 2617259 × 242181437 × 14198908344034847336575319741350686708681220266239586986186954292521964542514964603560170769429429159052564755825042072402510102485892918360726847<146>
9×10160+1 = 9(0)1591<161> = 196668336511615844317373683402996797341833<42> × 1739150909232723432175836807853304310816643860207313<52> × 263130261241924464291801141224892605010946153371020043305094966475369<69> (Jo Yeong Uk / GMP-ECM 5.0.3 B1=3000000, sigma=510691330 for P42 / April 6, 2007 2007 年 4 月 6 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 27.70 hours on Core 2 Quad Q6600 / November 4, 2007 2007 年 11 月 4 日)
9×10161+1 = 9(0)1601<162> = 192 × 268115868282277<15> × 1452612416148001223786387377375980929408933<43> × 6401224184307784221531476143753944364302696193784598490179821129689892756268275790197304471135782300801<103> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 50.93 hours on Cygwin on AMD 64 3200+ / July 27, 2007 2007 年 7 月 27 日)
9×10162+1 = 9(0)1611<163> = 17 × 233 × 5693 × 199673 × 3207278521<10> × 118788802665563673626749<24> × 152599297155465124131657187052166911440245078117469<51> × 34380518818628962059427663768446076926280486458367419362075072569669<68> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 / 87.52 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / June 30, 2007 2007 年 6 月 30 日)
9×10163+1 = 9(0)1621<164> = 72 × 13 × 179 × 470008183 × 259481291797001816650176355670832013<36> × 580459551785892461725007555092462668798367841<45> × 11149788091046450752175493549254706615173820321550790352125382027235333<71> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 66.05 hours on Cygwin on AMD 64 3200+ / August 2, 2007 2007 年 8 月 2 日)
9×10164+1 = 9(0)1631<165> = 206021 × 987313 × 288154417 × 941596665917777874062834896326197<33> × 16307446785923947920819586784374506111817003364273287474816055749579556455124440591984263685499136336546651516313<113> (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=2433879795 for P33 / April 25, 2007 2007 年 4 月 25 日)
9×10165+1 = 9(0)1641<166> = 8543 × 59663 × 3954007 × 395828143 × 308476461133<12> × 177394921202126672010300241<27> × 206167261153879385980988085801694230252224190918900189043640628173950040223577792748169151113262087142413<105>
9×10166+1 = 9(0)1651<167> = 31044228049<11> × 3156962265562069<16> × 918316216270703869309355611043163454536041928282487371533968756152838364897784813275043801939717925018733579383644373085052186912082380439021<141>
9×10167+1 = 9(0)1661<168> = 65011 × 331853765402124003677<21> × 7113900758268929663283411570479354669535798745893423331<55> × 5864096533496964606518020454924687639490103035820928855353490102504942263905443892896093<88> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.38 snfs / 31.92 hours, 2.63 hours / November 27, 2008 2008 年 11 月 27 日)
9×10168+1 = 9(0)1671<169> = 193 × 183122333 × 1365503329<10> × 70195540469<11> × 803534758897924386932162437579226018617463265776195233<54> × 3306259477416131198963892436083070510480940866548861316188259476731788862020584275713<85> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 43.37 hours, 1.92 hours / June 20, 2009 2009 年 6 月 20 日)
9×10169+1 = 9(0)1681<170> = 7 × 13 × 23 × 26680727 × 2783029903<10> × 11273267512862863753557060067341695659241008487576093151619<59> × 51369807273759613054098903544267959129913929401519425473243091409904983605073403539507467663<92> (matsui / GGNFS-0.77.1-20060513-pentium-m / October 25, 2008 2008 年 10 月 25 日)
9×10170+1 = 9(0)1691<171> = 10159789 × 88584516863489979959229468249783533890319966290638516213279626181213015349039236936908827535689963639992917175740559178935704274960828418779169528028584058192547109<164>
9×10171+1 = 9(0)1701<172> = 47 × 53 × 3036861280810645404931<22> × 51385746424530178231491293825778690117107805206225197788441809802689717<71> × 23152674067043755161598533865974421832973091656998852143841113795270050798893<77> (Serge Batalov / Msieve-1.38 snfs / 57.00 hours on Opteron-2.6GHz; Linux x86_64 / November 8, 2008 2008 年 11 月 8 日)
9×10172+1 = 9(0)1711<173> = 160373 × 9302113 × 96610277 × 39310818573473761<17> × 4325644542490474479111141763201<31> × 3672344386838070849076190962119037504153608805562136202004095912497329465957985573008491906892452695341017<106> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3869421807 for P31 / April 3, 2007 2007 年 4 月 3 日)
9×10173+1 = 9(0)1721<174> = 263 × 659 × 719503 × 119042288029767638893284897945328190576465889847<48> × 17758729179548142956399209216703776600136321973088783<53> × 3413937667616485389431567664007791715409001756176675366899769851<64> (Serge Batalov / Msieve-1.38 snfs / 50.00 hours on Opteron-2.6GHz; Linux x86_64 / October 11, 2008 2008 年 10 月 11 日)
9×10174+1 = 9(0)1731<175> = 6701858154129508946109631584557125937056799890919240999671909373<64> × 1342911143897373658594292493986198100072281134132513257099614367422167831910468286290583725850693432647730948437<112> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 173.62 hours on Core 2 Quad Q6600 / June 5, 2007 2007 年 6 月 5 日)
9×10175+1 = 9(0)1741<176> = 7 × 13 × 93455747615903<14> × 781769166175247748256859<24> × 1628016159426033701278393782246899502990135743608549066928747844161<67> × 8314915735262452439319787506005991721407656494214518451363732004308663<70> (matsui / Msieve 1.42 snfs / 107.83 hours / September 13, 2009 2009 年 9 月 13 日)
9×10176+1 = 9(0)1751<177> = 382561419661867013<18> × 4153302760261926665697975045884449<34> × 52071628666505176886879386813329622282926033465255605104727473<62> × 10877938191260780793629924957632742443982245852487077181777175101<65> (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=2985295769 for P34 / April 26, 2007 2007 年 4 月 26 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P62 x P65 / June 22, 2010 2010 年 6 月 22 日)
9×10177+1 = 9(0)1761<178> = 3167 × 387077 × 2076611 × 308752979 × 54988062023<11> × 212417999009<12> × 60289087720622533<17> × 479166086119340027893509641<27> × 54841284613190781418275599643521<32> × 618783381714794412883445208544663378606596249013437821041<57> (Jo Yeong Uk / Msieve 1.17 for P32 x P57 / 01:04:40 on Core 2 Duo E6300@2.33GHz / April 4, 2007 2007 年 4 月 4 日)
9×10178+1 = 9(0)1771<179> = 17 × 5948821 × 11127937531757<14> × 93538933098093421<17> × 16306895340312817570191844620226220723966622382644916217<56> × 52430537736556315336574992162476707617584521716213200794890062235644848407921473838157<86> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / June 29, 2010 2010 年 6 月 29 日)
9×10179+1 = 9(0)1781<180> = 19 × 5534131 × 18214292638284472887271115328822773<35> × 469923499542123655095299548274355767770965063630396022680637696097517816764183785764630747367951412450230567122540529548703822228674473333<138> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=8153338079 for P35 / May 24, 2010 2010 年 5 月 24 日)
9×10180+1 = 9(0)1791<181> = 197 × 677 × 8540277647845249<16> × 7901610622200460470784299047274434117414932293996553516196916846809334887302400903200935211332411879702681245947054177548931208164691085896512718667263943128521<160>
9×10181+1 = 9(0)1801<182> = 7 × 13 × 1634877253<10> × 4734601525921546333993043145682476935952954233075819983<55> × 127771070105660961006338772373918923933864341041637287729501831436725846598432633103762969123224517871011851684907289<117> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / July 7, 2010 2010 年 7 月 7 日)
9×10182+1 = 9(0)1811<183> = 96497 × 6693857016013088704017026959632722629<37> × 4726208631460930201446566903865009645466671656995429969<55> × 294808076575099116140601798039956053929616676312148580235298399540695811201520463984333<87> (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=2126479012 for P37 / April 16, 2007 2007 年 4 月 16 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / July 11, 2010 2010 年 7 月 11 日)
9×10183+1 = 9(0)1821<184> = 103 × 3233244966365310870649684607<28> × 298693157390062566861005989423<30> × 90477668522699163072144221687303949991107197335419536336160629162770149946285624825258787157424462314629011259798775595755047<125> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1982672773 for P30 / April 3, 2007 2007 年 4 月 3 日)
9×10184+1 = 9(0)1831<185> = 29 × 53 × 433 × 17907001038501948144357766109<29> × 56385136584339210524733082811161<32> × 13545949246627659985095780182634249171497673616306498864681<59> × 9887438744319177885322438170306294338262729295517657911743749<61> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2641429563 for P32 / April 3, 2007 2007 年 4 月 3 日) (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs for P59 x P61 / 104.60 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / May 23, 2007 2007 年 5 月 23 日)
9×10185+1 = 9(0)1841<186> = 14221071273845475492291671003825582287<38> × 1398746122436422798688279123652137496567869477528552063179<58> × 45245073785312358789412692354690874996272531432351403086796369814988138412789195525318379437<92> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=668692240 for P38 / May 15, 2007 2007 年 5 月 15 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / July 27, 2010 2010 年 7 月 27 日)
9×10186+1 = 9(0)1851<187> = 61 × 161271954417042232580477<24> × 71338953778563773721289257398483341<35> × 12824105714440400124634673307313813672129762979860127394144076399375268657498186011572935151644208597728853041885465975326330013<128> (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=127397403 for P35 / May 15, 2007 2007 年 5 月 15 日)
9×10187+1 = 9(0)1861<188> = 7 × 13 × 4373 × 5717 × 20183 × 24068660737760877432355395211891<32> × 62997737916659797227839645827292492524926253<44> × 1292679455591441076258485317684865804868369568936337678078930314592220711830210622816655197169909019<100> (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=339987454 for P32 / April 26, 2007 2007 年 4 月 26 日) (Jo Yeong Uk / GMP-ECM 6.2.3 B1=3000000, sigma=7718575470 for P44 / June 2, 2010 2010 年 6 月 2 日)
9×10188+1 = 9(0)1871<189> = 4141301 × 70442857268715121<17> × 93612864612448688176739475359012178966863730489880890167069<59> × 32955902837068997871149936500494996280626863944640658627790369500729978539872906785823410131283255626858449<107> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / August 1, 2010 2010 年 8 月 1 日)
9×10189+1 = 9(0)1881<190> = 292491769289<12> × 30770096614607442434998740550149853895569595410325501933751612480916630488207323840651677996626513818154443541121889883389415391379642385394042834145946927251212111970233595327609<179>
9×10190+1 = 9(0)1891<191> = 173 × 42037512353<11> × 7960021585261<13> × 12612461717629<14> × 170152793363537<15> × 724446316717717134607037007499933077187253954289961463613214636811007979491931912187393728040640579565260686886805540303793806234663736093<138>
9×10191+1 = 9(0)1901<192> = 23 × 10939 × 867042811 × 1225001135268909557516622349663613609998717<43> × 3367906439053285381936950921888631353303906507527672006959860287122215416584094679533588342746703239057395091175335389582530157988719659<136> (Jo Yeong Uk / GMP-ECM 6.3 B1=3000000, sigma=6287050982 for P43 / June 8, 2010 2010 年 6 月 8 日)
9×10192+1 = 9(0)1911<193> = 1109 × 14734116298400713270539985713991888026642775154005017603856013<62> × 550791043881235942395862556041076669468450897765276463896412425335034457457595786628772946981138862497150863003489314800842696753<129> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.36 / 151.51 hours / August 18, 2008 2008 年 8 月 18 日)
9×10193+1 = 9(0)1921<194> = 7 × 13 × 989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989011<192>
9×10194+1 = 9(0)1931<195> = 17 × 1249 × 8089 × 1037297 × 106869415441<12> × 6800424794926771388308831050471833<34> × 6950942827174514887338020534901240077527602856760093566826256645756923667399042440819259600295410278353642353978340831657491455631029153<136> (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=1421895638 for P34 / April 23, 2007 2007 年 4 月 23 日)
9×10195+1 = 9(0)1941<196> = 67173650371<11> × 15472533389903<14> × 29762810324360176001<20> × 203658158177534236244704846189208743851658240885596398738484413<63> × 1428585977387269745466709443000974110330528700186699457432420927230864187498147990946286729<91> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / August 15, 2010 2010 年 8 月 15 日)
9×10196+1 = 9(0)1951<197> = 937 × 815382640321<12> × 251608683962632814402459881<27> × 99308557252945961614442706199723845217343968319776579532989215553<65> × 4714429643417090128691236269578114128676753726802652267619816959659359140346193454278062641<91> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / August 29, 2010 2010 年 8 月 29 日)
9×10197+1 = 9(0)1961<198> = 19 × 53 × 59 × 83383 × 5391689 × 245839937164230974479691215063<30> × 137058584136541446774168911670541604476144697821768163614455130433232887280296804832661364194002488967472974602034234806509032799755754187638460748172517<153> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2973887166 for P30 / April 1, 2007 2007 年 4 月 1 日)
9×10198+1 = 9(0)1971<199> = 206641 × 1971332907858188412423521352631276953751910015856265250493673622099401969<73> × 22093577408287644837009510470494689478804802552229642889751303060701247374764381532930283372837715454765095820414492639969<122> (Wataru Sakai / Msieve / 761.36 hours / May 23, 2009 2009 年 5 月 23 日)
9×10199+1 = 9(0)1981<200> = 7 × 13 × 89 × 167198846303<12> × 45411881424226740485299069025369432622931<41> × 6647203192892529652115461963744432263856597807894849365733<58> × 220175699258898896235892825457521765429633446555106503667758849182137802340342658792171<87> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=1307396903 for P41 / May 23, 2010 2010 年 5 月 23 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / September 12, 2010 2010 年 9 月 12 日)
9×10200+1 = 9(0)1991<201> = 15173 × 2624002403996012093<19> × 54325560471366932864999735485799346169348921<44> × 48477262535846561278265393635044759914710178606530031107734721<62> × 8583502140540067502926748938713553299725402041889723082558733995093877849<73> (Jo Yeong Uk / GMP-ECM 6.3 B1=3000000, sigma=6119048325 for P44 / June 29, 2010 2010 年 6 月 29 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P62 x P73 / August 10, 2010 2010 年 8 月 10 日)
9×10201+1 = 9(0)2001<202> = definitely prime number 素数
9×10202+1 = 9(0)2011<203> = 223992464093<12> × 610708093047410605609<21> × 657923542142839466914630948267780451332882347228363225184192726191891508708915568681300053764480698519548412278136483780628932251333905873254440071632198610898305583742573<171>
9×10203+1 = 9(0)2021<204> = 131 × 811 × 3209 × 41787229087<11> × 14951910277363013<17> × 7092970766667844054985907011161062037<37> × 3702913682493323336581299106442629812590421141420403777193063<61> × 160867616745454565774616150885364079286162383091724459368539146658345689<72> (Serge Batalov / GMP-ECM B1=2000000, sigma=3276524334 for P37 / November 17, 2010 2010 年 11 月 17 日) (Andreas Tete / factmsieve76.py via Msieve v 1.48 gnfs for P61 x P72 / January 16, 2011 2011 年 1 月 16 日)
9×10204+1 = 9(0)2031<205> = 1880475173399211972492626483981<31> × 4786024366241054208459436101416312111947998058211587440990126084638985258868466143963609680826660883559332221090868411280383200073215398961348862216254213302021305518008724421<175> (Serge Batalov / GMP-ECM B1=2000000, sigma=1120915879 for P31 / November 17, 2010 2010 年 11 月 17 日)
9×10205+1 = 9(0)2041<206> = 73 × 13 × 69932763853967278320445120666245413<35> × 4129164716873954743253010394690702761300547601<46> × 69897579513495418720288064800574279513930674710039183302367093151386128617745545539654750164815909698285449870443183398103<122> (Serge Batalov / GMP-ECM B1=3000000, sigma=3802393790 for P35 / November 17, 2010 2010 年 11 月 17 日) (Serge Batalov / GMP-ECM B1=3000000, sigma=480125834 for P46 / January 9, 2014 2014 年 1 月 9 日)
9×10206+1 = 9(0)2051<207> = 1195709762581<13> × 318771913425636370736717<24> × [2361221260758674360585398370705172651231664475137628724547693016869059081916910029077568913807013672073845456414007896186268314261409938798496756683122487343677937211918513<172>] Free to factor
9×10207+1 = 9(0)2061<208> = 101744358586577166746015243493392929730174037841<48> × 24831821072539948693917561618331817272811491525172931753444826682677<68> × 3562243485541864308444681345963074165142517828234191257570133762236875298939335199663219412493<94> (Sinkiti Sibata / Msieve 1.42 snfs / December 22, 2010 2010 年 12 月 22 日)
9×10208+1 = 9(0)2071<209> = 3049 × 943009 × 200782004316193<15> × 155899406609264871115577276777051720427242271216271443042700312206363787515542293304496589544016660401099113979626381122866869595061600037953485179273015589864609465932231688250939073177<186>
9×10209+1 = 9(0)2081<210> = 808957107580887571<18> × [1112543534837548918915007849603804933007050570491763623547564868864297696763401551160626754032177992859433114403961289058701370702788181769551856059506181673303257929483960828785416320852834331<193>] Free to factor
9×10210+1 = 9(0)2091<211> = 172 × 53 × 257 × 23931301 × 651289621 × 6709137857<10> × 120228240862613581309<21> × [181853640204070860589884398802849127804893182751447898695413157243616286036695838385518900408413675076889103211174494392990851463831023456995377346451312868473<159>] Free to factor
9×10211+1 = 9(0)2101<212> = 7 × 13 × 317 × 15341903 × 1167734734922448619<19> × 79599115805915428361<20> × [2187812906459678891683829032310827326314291149852144820546103010634436383667987205371021060869629576277160780513953997113693104221469258421773495234773084827657579<163>] Free to factor
9×10212+1 = 9(0)2111<213> = 29 × 337 × 409 × 56209 × 414860090099525123534933<24> × 9655700500324773732243427814627644081007570625013848891447260477546086841458116587185460714994867198377508539450064317375316929053804413061425509657398253121828338323901969270569<178>
9×10213+1 = 9(0)2121<214> = 23 × 391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826087<213>
9×10214+1 = 9(0)2131<215> = 109 × 26113159619149<14> × 17987391532565906465074654046329<32> × 1757876660499880700254249311716198490453772375213999009824516426601648605264491709761742450789254811802731213479330512849250502262018644130992932239454570454840957988609<169> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=2457138703 for P32 / November 15, 2010 2010 年 11 月 15 日)
9×10215+1 = 9(0)2141<216> = 19 × 31397 × 205423 × 226367 × 8504299 × 1593940666078299449<19> × 2393469518363159900703101956679165261605944232450312614495855973409237726040883690183489820890549959319876125582366446367626948139780723029505717156982387248015814459788894677<175>
9×10216+1 = 9(0)2151<217> = 39341 × 13487616731736361<17> × 16961407883279557715344339378859429336612795969856784498432557683460499203110299815087112049238191214372983532930498817440173385103228343794963895859042412222780011592802534607151801444356038431901<197>
9×10217+1 = 9(0)2161<218> = 7 × 133 × 472 × 103 × [25720622298236352389961781478694368387699016019270253743967156951006478143682719676470648947730346457899775390178960983471524297383237643478036821821783372480925431465432401142924658919106343162628517201040397<209>] Free to factor
9×10218+1 = 9(0)2171<219> = 9730765449188606772028379689<28> × 92490154520685305905932898763922355772225085465357871097524964229974673460215181479124760936897866926579937639364601529173947917925164276323431168077680785129436135677979605954262582571805209<191> (Serge Batalov / GMP-ECM B1=2000000, sigma=3526446879 for P28 / November 17, 2010 2010 年 11 月 17 日)
9×10219+1 = 9(0)2181<220> = 1289 × 747660882435757<15> × 1038627098649676312499<22> × 89593185804434141629992850013<29> × 100357608549631033223395999241019243504603368704705743824987714538240783026216140073430581167403502705162756498799497797563555085377984651075432475345051<153>
9×10220+1 = 9(0)2191<221> = 250144994041<12> × 359791329604815339563431643480737826067747528584251225623350670569256414968114400827494911075744768435759559890028652920029353976513303668043640919754767198299617160716459096561513347898451058893321313419423561<210>
9×10221+1 = 9(0)2201<222> = 379 × 92284318510638791939<20> × 44646118825833651861153810263<29> × 576357142111786087429056669482517608859543755471549305119410032930162755679926029798774356995662979909711890331218008483507546472595546059538945399556372064240164029057367<171>
9×10222+1 = 9(0)2211<223> = 1697 × 33710657 × 319324851076226682529<21> × 13202660084326183145634333190095767809<38> × 1569397652660140245129651153698483440621284593<46> × 23777505527011124647611445221135219543368491664352255090845359354197059700350112200134414742434796967861438353<110> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3733869756 for P38 / March 9, 2011 2011 年 3 月 9 日) (Grubix / GMP-ECM B1=110000000, sigma=2179109855 for P46 / August 4, 2011 2011 年 8 月 4 日)
9×10223+1 = 9(0)2221<224> = 7 × 13 × 53 × 4317582253<10> × 29237419015386247597<20> × 222703331346061646803058654987776816203529<42> × [663771929107746393288407558857006598810691035175421948477275405804616589485080066806112981764490780266540322351658507509280482850663413677687460543383<150>] (Serge Batalov / GMP-ECM B1=3000000, sigma=2511615562 for P42 / May 26, 2014 2014 年 5 月 26 日) Free to factor
9×10224+1 = 9(0)2231<225> = 269 × 9601 × 2732799114909839268167233<25> × [127516402356001910676107862506855232972689108658940365712076018356824624224053579458399561367465730769135525368819692684873478394757136408805446478728318741873471915298318078961118062636005335813<195>] Free to factor
9×10225+1 = 9(0)2241<226> = 55860891436501654543388235514847701877446244157135259823<56> × 1789706850532559048876839886939939713204869553571156217335388536575634330448059<79> × 90022847726048101649529513026031808920766061566345195734033515858979950502970757919430285693<92> (RSALS + Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve SVN r688 for P56 x P79 x P92 / December 20, 2011 2011 年 12 月 20 日)
9×10226+1 = 9(0)2251<227> = 17 × 1521677 × 197461741 × 132972878033<12> × 6241293914500895258188801<25> × 21230022109075625411095065152702164546697614389302486767897217100224485519572339612528897798023977592075825023262533089278186165244651171179311743120815896051772658158258337113<176>
9×10227+1 = 9(0)2261<228> = 2626086447529<13> × 98566253768980862437<20> × 1068053861509502411968825115333<31> × 3255457919308633748825904657660218709563909818463777890381643600209147851220478141993481192532118426900202337511391862899361119527597884266424556439609592578466120289<166> (Serge Batalov / GMP-ECM B1=2000000, sigma=2118364013 for P31 / November 17, 2010 2010 年 11 月 17 日)
9×10228+1 = 9(0)2271<229> = 3889 × 108821 × 4769986093253<13> × 1067580885697858489<19> × 82532365054475634193094328789514681<35> × 131300091395089345276245471745601519582213<42> × 242888590509844146230181214782147550186096609<45> × 1586636781720114949261885059114082303248222518475110639122681826458181<70> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=4011758723 for P35 / November 15, 2010 2010 年 11 月 15 日) (Wataru Sakai / GMP-ECM 6.2.3 B1=11000000, sigma=2223484052 for P42, B1=11000000, sigma=3959951882 for P45 / December 6, 2010 2010 年 12 月 6 日)
9×10229+1 = 9(0)2281<230> = 7 × 13 × 157 × 571 × 428678799828685031389620580699<30> × 3308412581144796603307781214852569<34> × 7778819364100860394687199169295222550650599779047571129547538201303885407046441934892893197065971519835864925767609335240534450917225097885241985475763156777023<160> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=1044848662 for P30 / November 15, 2010 2010 年 11 月 15 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1303105766 for P34 / March 10, 2011 2011 年 3 月 10 日)
9×10230+1 = 9(0)2291<231> = 4038121 × 31893816529<11> × 2519852609371462193<19> × 2773202294029798983431332009990351701434447567456415846543527340616017187178700137676712948406490314588362989805373469213802642242936111917553488647283331582829011256731351294922796530171547587673<196>
9×10231+1 = 9(0)2301<232> = 112249 × 810898055837<12> × 98876655864159425883046557460804834515415412044856365394747989251170135039344777795567576729519598759562459872677603045374806838121473355053065915515398131566899514431154637587007506435704268671265624140240305768477<215>
9×10232+1 = 9(0)2311<233> = 982393 × 1307478629<10> × 16129529631749<14> × [4344111347704407624901982346288192446623683204804891385449676212414006663078402176667136512311387909946424950513536343564694121379737510967742921399660150194090013953484458395242229635110558821463928635217<205>] Free to factor
9×10233+1 = 9(0)2321<234> = 19 × 173 × 8117 × 4573192579<10> × [7376116531685351268465678061908039009930580700472006605850433057868049504418286604713971413888845411160720097259580610507067061854420250874249834348314800035514649268805910580736375955610667536700725186603225601010361<217>] Free to factor
9×10234+1 = 9(0)2331<235> = 113 × 662177 × 24965693 × 674208781373<12> × 945894779957<12> × [7554558954988758543795081184462770575986130942214738543778201969338424842917713837444560004338058106696080857691902120533079985346856769694190173038958008888299231814148593357129141967541138256037<196>] Free to factor
9×10235+1 = 9(0)2341<236> = 7 × 13 × 23 × [43000477783086478738652651696129956999522216913521261347348303870043000477783086478738652651696129956999522216913521261347348303870043000477783086478738652651696129956999522216913521261347348303870043000477783086478738652651696129957<233>] Free to factor
9×10236+1 = 9(0)2351<237> = 53 × 97 × 29008753 × 49045301 × 15664754905536509<17> × 2756261337895639342613545290729640254553<40> × 2849866023753230278785981257337245473891418868328105610048280107934854813382522241293538165105912938486930619812843536980667459488009048192239058341754278446622581<163> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=1021065449 for P40 / November 16, 2010 2010 年 11 月 16 日)
9×10237+1 = 9(0)2361<238> = 30689 × 4599761 × 895878892573367<15> × 1239342808084764461998719053<28> × [57422718662799277673586953395250157302798026419786763399750906944578562981500318240694187262640120066899105852300000177573957661068512882740076830268792499637043109329482676936648771219<185>] Free to factor
9×10238+1 = 9(0)2371<239> = 6043852774009<13> × 22361632117411387193<20> × 1703018166927869826197<22> × [391026196574410488750839046130737980886926491663996260136019279711642368674918404246786327687289220814489786048702693057246459616765489416113843257078599257625228973229328619361852365709<186>] Free to factor
9×10239+1 = 9(0)2381<240> = 373 × 1213601 × 179888686714637<15> × 389078853170089<15> × 141972859963365777967<21> × 358775157105879353084797074490157<33> × 23774197618897112647796310723148961<35> × 23457553255200662430101545373384353276971696952105087373108934764457068705985141868197925585129911695181724703518051<116> (Serge Batalov / GMP-ECM B1=2000000, sigma=1329695719 for P33 / November 17, 2010 2010 年 11 月 17 日) (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=2373952162 for P35 / November 18, 2010 2010 年 11 月 18 日)
9×10240+1 = 9(0)2391<241> = 29 × 121181 × 144701 × 1032433 × 313553547426213092827847021<27> × 54671986080998110764669991976220562355849377293313111968676775160486546351182103749718017491804872127792879937144646403035086721817136954969538840049765317193492135048678211593760431715416135338193<197>
9×10241+1 = 9(0)2401<242> = 7 × 13 × 1007785483937033106865729083369763828637884359552927906722937480523889481626091761179<85> × 981370544401275445621964695424872502587654717957112518160246580464897670480694215257878935926885484361084996022634988941120073037367539383644380377686589609<156> (matsui / Msieve 1.53 snfs for P85 x P156 / March 3, 2016 2016 年 3 月 3 日)
9×10242+1 = 9(0)2411<243> = 17 × 7276081 × 4081995329159416129<19> × [1782475460034129668261729724405889946928104690657579935815339084454220099421278074152443907022897368111395037348973058861389032010938682057052958471579615499578865069765824153047306259354999464084407893226070767271297<217>] Free to factor
9×10243+1 = 9(0)2421<244> = 89 × 997 × 319191782293<12> × 317764694361529844890605220680473098504116501484515924586523185364847214896565110971505152261627476962280109756521096044572670211108487221487851558911993530696276622703187075503911031148613769928689847557438646683791943066599329<228>
9×10244+1 = 9(0)2431<245> = 1760281 × 474965478409<12> × 34604913517538267833<20> × [3110718375415804676855678541595900083643111626969471028096297643057651765247253275749786232860974274251463310057870423456331100363646143220821889017207917003525308485621530276743320130078461344207529048749993<208>] Free to factor
9×10245+1 = 9(0)2441<246> = 1583 × 14557 × 1275057609647<13> × 8273709239797<13> × 26052285970891<14> × 394050728788663<15> × 8631644097262057253<19> × 3016799625677724273810031588043922114068771<43> × 4342441302640116208852838725871762493012452704326874655603213<61> × 3189243884512520629323626480635530100849756527675698196953938247<64> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3797615030 for P43 / November 30, 2010 2010 年 11 月 30 日) (Markus Tervooren / Msieve 1.48 for P61 x P64 / December 2, 2010 2010 年 12 月 2 日)
9×10246+1 = 9(0)2451<247> = 61 × 957409 × 33979861 × [4535169995812690664559155916413559712822846221590794877410623558074749539782258328133296273393990996150620409252390057543476735318362121908726887792591067545547736630569335578122071823333717827026468360637443146148189866732116083809<232>] Free to factor
9×10247+1 = 9(0)2461<248> = 72 × 13 × 569 × 35941397 × 6908692405385406430556732817869451345712958107139877030391858456887643488316186042939612148299549665750151911906103259135293166344239484909438179616672323445851079446414150942865085636041193877121471191264820007311405181239786987874761<235>
9×10248+1 = 9(0)2471<249> = 40523859866204024257372647251587112977<38> × [22209138097197386974421552873804494426609089168954298348491737217066053657007440573805672473088745490202628527778721019823798042341228054650156445825855282647211740935741152905877052168297171093813678116174876913<212>] (Serge Batalov / GMP-ECM B1=3000000, sigma=3376365797 for P38 / November 19, 2010 2010 年 11 月 19 日) Free to factor
9×10249+1 = 9(0)2481<250> = 53 × 1009 × 14953973 × 11254310202154782325846197564574537286084269004033591608137982974333597792248513150109924360152135905916577139734536089583080168451172975875993515085147078184242200963363818587943579540524912676864874359368524609121623575071194137879392281<239>
9×10250+1 = 9(0)2491<251> = 661 × 13142066104271161<17> × 789099144643915789<18> × [13129428727467192338452313099001880919463629066491315026588126273971262966923495221476241732745318333157413007451056839859811013920778520493151265429756303072950323037441582529639153979195582942904060639389636007929<215>] Free to factor
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