Table of contents 目次

  1. About 388...889 388...889 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 388...889 388...889 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 388...889 388...889 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 388...889 388...889 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

38w9 = { 39, 389, 3889, 38889, 388889, 3888889, 38888889, 388888889, 3888888889, 38888888889, … }

1.3. General term 一般項

35×10n+19 (1≤n)

2. Prime numbers of the form 388...889 388...889 の形の素数

2.1. Last updated 最終更新日

February 8, 2013 2013 年 2 月 8 日

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

  1. 35×102+19 = 389 is prime. は素数です。
  2. 35×103+19 = 3889 is prime. は素数です。
  3. 35×106+19 = 3888889 is prime. は素数です。
  4. 35×1017+19 = 3(8)169<18> is prime. は素数です。
  5. 35×1020+19 = 3(8)199<21> is prime. は素数です。
  6. 35×1045+19 = 3(8)449<46> is prime. は素数です。
  7. 35×1057+19 = 3(8)569<58> is prime. は素数です。
  8. 35×1078+19 = 3(8)779<79> is prime. は素数です。
  9. 35×10119+19 = 3(8)1189<120> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 2, 2005 2005 年 1 月 2 日)
  10. 35×10137+19 = 3(8)1369<138> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 2, 2005 2005 年 1 月 2 日)
  11. 35×10509+19 = 3(8)5089<510> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 29, 2006 2006 年 5 月 29 日)
  12. 35×10710+19 = 3(8)7099<711> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 29, 2006 2006 年 5 月 29 日)
  13. 35×101127+19 = 3(8)11269<1128> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 13, 2006 2006 年 9 月 13 日)
  14. 35×101518+19 = 3(8)15179<1519> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / August 26, 2006 2006 年 8 月 26 日)
  15. 35×101761+19 = 3(8)17609<1762> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / August 2, 2006 2006 年 8 月 2 日)
  16. 35×103086+19 = 3(8)30859<3087> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 18, 2004 2004 年 12 月 18 日) (certified by: (証明: Ray Chandler / Primo 4.0.1 - LX64 / January 29, 2013 2013 年 1 月 29 日)
  17. 35×103147+19 = 3(8)31469<3148> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 18, 2004 2004 年 12 月 18 日) (certified by: (証明: Ray Chandler / Primo 4.0.1 - LX64 / February 7, 2013 2013 年 2 月 7 日)
  18. 35×109926+19 = 3(8)99259<9927> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / January 4, 2005 2005 年 1 月 4 日)
  19. 35×1019854+19 = 3(8)198539<19855> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / May 11, 2010 2010 年 5 月 11 日)
  20. 35×1027842+19 = 3(8)278419<27843> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / May 11, 2010 2010 年 5 月 11 日)
  21. 35×1046799+19 = 3(8)467989<46800> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / May 15, 2010 2010 年 5 月 15 日)
  22. 35×1049682+19 = 3(8)496819<49683> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / May 15, 2010 2010 年 5 月 15 日)
  23. 35×1068718+19 = 3(8)687179<68719> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / May 22, 2010 2010 年 5 月 22 日)
  24. 35×10100542+19 = 3(8)1005419<100543> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / June 5, 2010 2010 年 6 月 5 日)
  25. 35×10106649+19 = 3(8)1066489<106650> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / June 14, 2010 2010 年 6 月 14 日)
  26. 35×10191073+19 = 3(8)1910729<191074> is PRP. はおそらく素数です。 (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / July 17, 2010 2010 年 7 月 17 日)

2.3. Range of search 捜索範囲

  1. n≤175000 / Completed 終了 / Serge Batalov / June 14, 2010 2010 年 6 月 14 日
  2. n≤200000 / Completed 終了 / Serge Batalov / April 2, 2011 2011 年 4 月 2 日

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

  1. 35×103k+1+19 = 3×(35×101+19×3+35×10×103-19×3×k-1Σm=0103m)
  2. 35×106k+1+19 = 13×(35×101+19×13+35×10×106-19×13×k-1Σm=0106m)
  3. 35×1016k+8+19 = 17×(35×108+19×17+35×108×1016-19×17×k-1Σm=01016m)
  4. 35×1018k+13+19 = 19×(35×1013+19×19+35×1013×1018-19×19×k-1Σm=01018m)
  5. 35×1022k+19+19 = 23×(35×1019+19×23+35×1019×1022-19×23×k-1Σm=01022m)
  6. 35×1028k+4+19 = 29×(35×104+19×29+35×104×1028-19×29×k-1Σm=01028m)
  7. 35×1032k+22+19 = 449×(35×1022+19×449+35×1022×1032-19×449×k-1Σm=01032m)
  8. 35×1035k+29+19 = 71×(35×1029+19×71+35×1029×1035-19×71×k-1Σm=01035m)
  9. 35×1041k+9+19 = 83×(35×109+19×83+35×109×1041-19×83×k-1Σm=01041m)
  10. 35×1043k+16+19 = 173×(35×1016+19×173+35×1016×1043-19×173×k-1Σm=01043m)

Read more続きを読むHide more続きを隠す

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 23.92%. 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 23.92% です。

3. Factor table of 388...889 388...889 の素因数分解表

3.1. Last updated 最終更新日

December 20, 2017 2017 年 12 月 20 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=201, 202, 205, 206, 211, 213, 215, 216, 217, 219, 221, 224, 226, 228, 229, 230, 231, 232, 235, 238, 239, 240, 241, 242, 244, 245, 246, 247, 248, 249 (30/250)

3.4. Factor table 素因数分解表

35×101+19 = 39 = 3 × 13
35×102+19 = 389 = definitely prime number 素数
35×103+19 = 3889 = definitely prime number 素数
35×104+19 = 38889 = 32 × 29 × 149
35×105+19 = 388889 = 157 × 2477
35×106+19 = 3888889 = definitely prime number 素数
35×107+19 = 38888889 = 3 × 13 × 997151
35×108+19 = 388888889 = 17 × 22875817
35×109+19 = 3888888889<10> = 59 × 83 × 794137
35×1010+19 = 38888888889<11> = 3 × 563 × 659 × 34939
35×1011+19 = 388888888889<12> = 1571 × 2713 × 91243
35×1012+19 = 3888888888889<13> = 22147 × 175594387
35×1013+19 = 38888888888889<14> = 34 × 13 × 19 × 16981 × 114467
35×1014+19 = 388888888888889<15> = 472 × 176047482521<12>
35×1015+19 = 3888888888888889<16> = 509 × 677 × 10771 × 1047763
35×1016+19 = 38888888888888889<17> = 3 × 173 × 5557 × 13483970083<11>
35×1017+19 = 388888888888888889<18> = definitely prime number 素数
35×1018+19 = 3888888888888888889<19> = 577 × 6653 × 14243 × 71126383
35×1019+19 = 38888888888888888889<20> = 3 × 13 × 23 × 27241 × 1591512469457<13>
35×1020+19 = 388888888888888888889<21> = definitely prime number 素数
35×1021+19 = 3888888888888888888889<22> = 853 × 7627091 × 597747234743<12>
35×1022+19 = 38888888888888888888889<23> = 32 × 449 × 4019 × 10177 × 235287526283<12>
35×1023+19 = 388888888888888888888889<24> = 307337 × 1265350051861275697<19>
35×1024+19 = 3888888888888888888888889<25> = 17 × 911 × 15823 × 15869725269287689<17>
35×1025+19 = 38888888888888888888888889<26> = 3 × 13 × 359 × 2777579379250688442889<22>
35×1026+19 = 388888888888888888888888889<27> = 22573 × 17228055149465684175293<23>
35×1027+19 = 3888888888888888888888888889<28> = 181 × 1423 × 2710571 × 73508693 × 75777901
35×1028+19 = 38888888888888888888888888889<29> = 3 × 36761 × 352628137508853485023883<24>
35×1029+19 = 388888888888888888888888888889<30> = 71 × 148062451 × 36993229932481008709<20>
35×1030+19 = 3888888888888888888888888888889<31> = 23974298520577<14> × 162210747711808057<18>
35×1031+19 = 38888888888888888888888888888889<32> = 32 × 13 × 19 × 191 × 91590979806282460824575273<26>
35×1032+19 = 388888888888888888888888888888889<33> = 29 × 974075801768653<15> × 13766856400164097<17>
35×1033+19 = 3888888888888888888888888888888889<34> = 523 × 33247 × 223651277203112211040872469<27>
35×1034+19 = 38888888888888888888888888888888889<35> = 3 × 1759 × 7369507085254669109131872065357<31>
35×1035+19 = 388888888888888888888888888888888889<36> = 113 × 797 × 19571 × 214213 × 1029982698744571972963<22>
35×1036+19 = 3888888888888888888888888888888888889<37> = 1123 × 3462946472741664193133471851192243<34>
35×1037+19 = 38888888888888888888888888888888888889<38> = 3 × 13 × 4931 × 202220847120461803081961264885621<33>
35×1038+19 = 388888888888888888888888888888888888889<39> = 1193459 × 91020654427<11> × 3579959201758030342873<22>
35×1039+19 = 3888888888888888888888888888888888888889<40> = 2037867355744537<16> × 1908313059692778290942497<25>
35×1040+19 = 38888888888888888888888888888888888888889<41> = 33 × 17 × 14212978037<11> × 5961118627171557234036605183<28>
35×1041+19 = 388888888888888888888888888888888888888889<42> = 23 × 116838383 × 58401438141269<14> × 2477927635438981309<19>
35×1042+19 = 3888888888888888888888888888888888888888889<43> = 42477959413352456857<20> × 91550746377578144623777<23>
35×1043+19 = 38888888888888888888888888888888888888888889<44> = 3 × 132 × 1481 × 1530911 × 33830823818366271776524879383197<32>
35×1044+19 = 388888888888888888888888888888888888888888889<45> = 33617 × 22533793279391948129<20> × 513372114567243467273<21>
35×1045+19 = 3888888888888888888888888888888888888888888889<46> = definitely prime number 素数
35×1046+19 = 38888888888888888888888888888888888888888888889<47> = 3 × 12962962962962962962962962962962962962962962963<47>
35×1047+19 = 388888888888888888888888888888888888888888888889<48> = 269 × 3761 × 384388088757625847836570485079097733527021<42>
35×1048+19 = 3888888888888888888888888888888888888888888888889<49> = 4103797 × 947631885516970963448944694118371081437237<42>
35×1049+19 = 38888888888888888888888888888888888888888888888889<50> = 32 × 13 × 192 × 54011 × 849652889 × 20063593242464858380319481201743<32>
35×1050+19 = 388888888888888888888888888888888888888888888888889<51> = 83 × 182641 × 25653650055935585062677034464733329904539763<44>
35×1051+19 = 3(8)509<52> = 1439 × 371016952109<12> × 7284017618451433227408815491187784739<37>
35×1052+19 = 3(8)519<53> = 3 × 14408341203229<14> × 899684618799690926868025651704174532847<39>
35×1053+19 = 3(8)529<54> = 61 × 151 × 1259 × 297996878653308803<18> × 112533365503087649712411935387<30>
35×1054+19 = 3(8)539<55> = 293 × 449 × 29560486244661165037883874585836473079265176987077<50>
35×1055+19 = 3(8)549<56> = 3 × 13 × 312828398625419623<18> × 3187533489710391182461010987351945737<37>
35×1056+19 = 3(8)559<57> = 17 × 887681 × 2580711567862520875283069<25> × 9985739232661094755226653<25>
35×1057+19 = 3(8)569<58> = definitely prime number 素数
35×1058+19 = 3(8)579<59> = 32 × 109 × 3719 × 10659340836717445634544621234180510333302055781792451<53>
35×1059+19 = 3(8)589<60> = 173 × 349 × 1109 × 79367 × 110219400560125721170793<24> × 663933296547372151129283<24>
35×1060+19 = 3(8)599<61> = 29 × 47 × 4442221494341092453581911047<28> × 642287499856536894781250958949<30>
35×1061+19 = 3(8)609<62> = 3 × 13 × 1103 × 31277231085091<14> × 28903944632177004293237169153915018269128987<44>
35×1062+19 = 3(8)619<63> = 2381 × 16273 × 477019 × 2503826121297910920503<22> × 8403470338848991147991124929<28>
35×1063+19 = 3(8)629<64> = 23 × 10847 × 61627 × 80473 × 3143162540299393308224448217040323290141214340539<49>
35×1064+19 = 3(8)639<65> = 3 × 71 × 7146768039889<13> × 25546784521519060676754729872050099936954671214277<50>
35×1065+19 = 3(8)649<66> = 403653881 × 1176294811<10> × 223185549094127<15> × 838426071795469<15> × 4376927724399657233<19>
35×1066+19 = 3(8)659<67> = 397 × 1901 × 5152914201181254051478790678760997975199171175834658000348337<61>
35×1067+19 = 3(8)669<68> = 33 × 13 × 19 × 59 × 234103 × 3268556447456625487<19> × 129166483756012857825038564753751381119<39>
35×1068+19 = 3(8)679<69> = 2663 × 30181225037<11> × 114848520676825652039<21> × 42130062107775791913015976288435021<35>
35×1069+19 = 3(8)689<70> = 2857 × 20393 × 4130969342317<13> × 16157799078179198666690535957981829371496436895917<50>
35×1070+19 = 3(8)699<71> = 3 × 23078246692099<14> × 1765602471912977<16> × 318132867948341166524669167774788127166881<42>
35×1071+19 = 3(8)709<72> = 227 × 4198079 × 408083533302921852435824440471126296958070593516248939600622733<63>
35×1072+19 = 3(8)719<73> = 17 × 167 × 307 × 3931 × 1821548730363382651011685001407<31> × 623128950562161858732813522934129<33>
35×1073+19 = 3(8)729<74> = 3 × 13 × 569 × 2711 × 92237 × 7008320827443485828277463232676865865000264788356577626168197<61>
35×1074+19 = 3(8)739<75> = 4461317449112963<16> × 17331997352688293768827<23> × 5029372397281797291550149958433817289<37>
35×1075+19 = 3(8)749<76> = 21191 × 871005564401606719<18> × 210694478197619655446188842640158461668175881330104641<54>
35×1076+19 = 3(8)759<77> = 32 × 14081 × 1779558941185625640541<22> × 172439656884370411436580748620363345265587396166501<51>
35×1077+19 = 3(8)769<78> = 82003 × 338947881824959436757667343119<30> × 13991454669831224531113702722501916021963277<44> (Makoto Kamada / msieve 0.81 / 5.1 minutes)
35×1078+19 = 3(8)779<79> = definitely prime number 素数
35×1079+19 = 3(8)789<80> = 3 × 13 × 3096625517<10> × 53388914347113160159<20> × 6031441919122115802061399537070352517807628234917<49>
35×1080+19 = 3(8)799<81> = 97 × 7643 × 140659 × 85572477592558230236746367081<29> × 43580108702405209902971085716134013387921<41>
35×1081+19 = 3(8)809<82> = 68217757 × 96705677 × 465201114301507<15> × 1267171461043049200068652246479230016556826975862443<52>
35×1082+19 = 3(8)819<83> = 3 × 383 × 227308831 × 1435332373<10> × 8887342316879353021862801<25> × 11672524903330042558497598132025395447<38>
35×1083+19 = 3(8)829<84> = 157 × 18408028411<11> × 106481262835450952640754502592321157<36> × 1263704155055091289617501013796919851<37> (Makoto Kamada / msieve 0.81 / 4.5 minutes)
35×1084+19 = 3(8)839<85> = 1307 × 4159 × 5301623 × 6636053551<10> × 20334912279295344596086956592539054912495145925042075785314061<62>
35×1085+19 = 3(8)849<86> = 32 × 13 × 19 × 23 × 233 × 3353293 × 973488471612773335126584912554788124522844439200311485504976871198582589<72>
35×1086+19 = 3(8)859<87> = 449 × 1657 × 9967 × 41478023 × 11156966039<11> × 113325610677999343249941915727420808593823475480975728458927<60>
35×1087+19 = 3(8)869<88> = 88993733 × 43698457832855363971403344647750520689910702913079159055940364799495363217192933<80>
35×1088+19 = 3(8)879<89> = 3 × 17 × 29 × 737147 × 8957567 × 7166814139<10> × 35688358980289<14> × 5177889154079489503<19> × 3006822031335932048044134609143<31>
35×1089+19 = 3(8)889<90> = 49196616277077143063354507<26> × 8744396583248029541014490372771<31> × 903983400640637350562110397790137<33>
35×1090+19 = 3(8)899<91> = 16119017813<11> × 398933302809421<15> × 590474772634138039<18> × 656855377663847865593<21> × 1559249306936742338909510359<28>
35×1091+19 = 3(8)909<92> = 3 × 13 × 83 × 1801 × 4597 × 44771 × 69254873 × 16115233855975383859281116271139<32> × 29040953721872029532557692391093520873<38>
35×1092+19 = 3(8)919<93> = 709 × 20981 × 2439267766642859257243<22> × 6128306037756620896520012947<28> × 1748852547278417582001463040231638321<37>
35×1093+19 = 3(8)929<94> = 193 × 39667 × 49620469 × 2897758091403457809344852339947<31> × 3532774181124489349033473555946059342957771252133<49> (Makoto Kamada / GGNFS-0.70.5 / 0.32 hours)
35×1094+19 = 3(8)939<95> = 34 × 9807316369<10> × 24090623109590310937<20> × 9222665790462397211043874543<28> × 220336185478153430664166325669135311<36>
35×1095+19 = 3(8)949<96> = 5659 × 54433195680823537693<20> × 1262472739555888185558320871219244051542094581625070456776595906600737847<73>
35×1096+19 = 3(8)959<97> = 4496313690997279<16> × 25338588384722118617199393679288336673<38> × 34133947450974421879682793470528524821050567<44> (Makoto Kamada / GGNFS-0.70.5 / 0.29 hours)
35×1097+19 = 3(8)969<98> = 3 × 13 × 778333421 × 15178770321851<14> × 84403150802860867085658304481478728526614955371181586205281338961656849281<74>
35×1098+19 = 3(8)979<99> = 31742492112627851<17> × 35341311296138071079<20> × 346658501312777122726425298720412521980308578259371212639076541<63>
35×1099+19 = 3(8)989<100> = 71 × 11887 × 12963407 × 210482224778251<15> × 140828015852497602171593<24> × 11991438406530062096913793673412536444148514811957<50>
35×10100+19 = 3(8)999<101> = 3 × 12962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962962963<101>
35×10101+19 = 3(8)1009<102> = 148961 × 506078597 × 10738588658153813704579<23> × 4920687016062689446959408823<28> × 97625222312494436340905731735230992801<38>
35×10102+19 = 3(8)1019<103> = 173 × 433 × 8269 × 15766901957467<14> × 9742259964282491<16> × 1926724412799189678439<22> × 21213526067901242311459050466715165290503823<44>
35×10103+19 = 3(8)1029<104> = 32 × 13 × 19 × 7549 × 11351 × 167597 × 100755942974597228137872420680604757516957<42> × 12089980789218005875422642451041062453834791133<47> (Sinkiti Sibata / Msieve 1.39 for P42 x P47 / 1.54 hours / December 7, 2008 2008 年 12 月 7 日)
35×10104+19 = 3(8)1039<105> = 17 × 587 × 156052517 × 30709292989<11> × 6944972451328721219376352184621055703307<40> × 1170920445025306782041523698236118310551201<43> (Makoto Kamada / Msieve 1.39 for P40 x P43 / 37 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 6, 2008 2008 年 12 月 6 日)
35×10105+19 = 3(8)1049<106> = 52882637 × 73538104555733271941202343765287061779632677714027174720672285856109801954257479423518325852186397<98>
35×10106+19 = 3(8)1059<107> = 3 × 47 × 589270812408601<15> × 468049183513586093075134494080135158436197943720187501146661792626543439520597541714803429<90>
35×10107+19 = 3(8)1069<108> = 23 × 15948174209489<14> × 20772044583119<14> × 27773495908941242371998260189083<32> × 1837709807402200552846077017391573923468285571331<49> (Makoto Kamada / Msieve 1.39 for P32 x P49 / 20 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 6, 2008 2008 年 12 月 6 日)
35×10108+19 = 3(8)1079<109> = 434165947 × 1291865406702552878597671<25> × 54121150718196496864666003805036599<35> × 128110724322470564725425077304824438414203<42> (Makoto Kamada / Msieve 1.39 for P35 x P42 / 7.8 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 6, 2008 2008 年 12 月 6 日)
35×10109+19 = 3(8)1089<110> = 3 × 13 × 131 × 7879904196779<13> × 1997509070272423438356929<25> × 483592920898916617605984497346955205539335571689171596066563658200031<69>
35×10110+19 = 3(8)1099<111> = 1193 × 66905171 × 35217087107<11> × 80849420996075131<17> × 1711177497985405487601598242980026193201076232388260227092213639334682939<73>
35×10111+19 = 3(8)1109<112> = 2309 × 21559903 × 19087047928763<14> × 82395787249172569<17> × 71435093435000828399215697267<29> × 695343518291176939509950650955613463174643<42>
35×10112+19 = 3(8)1119<113> = 32 × 283 × 467 × 250453453 × 36104262471899527<17> × 13336498499815433565173<23> × 271114276471706266319697078374466708936793603640504451590647<60>
35×10113+19 = 3(8)1129<114> = 61 × 6375227686703096539162112932604735883424408014571948998178506375227686703096539162112932604735883424408014571949<112>
35×10114+19 = 3(8)1139<115> = 832687381 × 15259609591<11> × 690449786536111858913383994784646317701<39> × 443269683332469302110610036873532000388386015468986749559<57> (Serge Batalov / Msieve-1.39 snfs / 0.50 hours on Opteron-2.6GHz; Linux x86_64 / December 7, 2008 2008 年 12 月 7 日)
35×10115+19 = 3(8)1149<116> = 3 × 13 × 5384849 × 9260966999<10> × 19995444445726772487774446068797546149565184504501896629567745082202434974588504041573619258049001<98>
35×10116+19 = 3(8)1159<117> = 29 × 1217 × 249083851 × 830455361077513<15> × 71461387560590832743287<23> × 1724187335734720957047469157189<31> × 432333808487090847150132654591438997<36> (Makoto Kamada / Msieve 1.39 for P31 x P36 / 1.3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 6, 2008 2008 年 12 月 6 日)
35×10117+19 = 3(8)1169<118> = 23671 × 27783859669<11> × 586508325901909<15> × 2220068530298034077903598290054113895052823<43> × 4541253968601200953821721286835487419928638673<46> (Sinkiti Sibata / Msieve 1.39 for P43 x P46 / 0.91 hours / December 7, 2008 2008 年 12 月 7 日)
35×10118+19 = 3(8)1179<119> = 3 × 449 × 87388643 × 2090588845492757479591352053<28> × 158028098642604385909015462747386204667066108621009485141870602673651178537235053<81>
35×10119+19 = 3(8)1189<120> = definitely prime number 素数
35×10120+19 = 3(8)1199<121> = 17 × 181881354947198077<18> × 19156490385171207353<20> × 65655707661755645308329737431237186890650695045372506166183848421554515446856855557<83>
35×10121+19 = 3(8)1209<122> = 33 × 132 × 19 × 4393481 × 576497030951<12> × 10893233812821375277847322667<29> × 16257689025833320198369114269139116243731070091977674453964179801083181<71>
35×10122+19 = 3(8)1219<123> = 14905840003<11> × 1448286619933<13> × 27989612154499<14> × 643602438063655812449143578769466266886660477918847414046695333011804932574097782791589<87>
35×10123+19 = 3(8)1229<124> = 1381587624671<13> × 163716152369726009<18> × 10384299710970978120359331535825259223245131889<47> × 1655687449944933127582920897860547628511068233359<49> (Sinkiti Sibata / Msieve 1.39 for P47 x P49 / 3.27 hours / December 8, 2008 2008 年 12 月 8 日)
35×10124+19 = 3(8)1239<125> = 3 × 4799 × 8123 × 84311039 × 33834482543131321119226369<26> × 31800310826219221812134739687650759<35> × 3665740619432123827736592764940676340653483639151<49> (Makoto Kamada / Msieve 1.39 for P35 x P49 / 39 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 6, 2008 2008 年 12 月 6 日)
35×10125+19 = 3(8)1249<126> = 59 × 1558891 × 122285521 × 1524368842813<13> × 22682591520338165985808385785387719844561623525304008562522093927040641854254853723443048699238997<98>
35×10126+19 = 3(8)1259<127> = 191 × 67114366454671786121<20> × 11448376571066039089838683423737211<35> × 26499200218749713130300387657045233622273874435357161710361980927082109<71> (Erik Branger / GGNFS, Msieve snfs / 3.51 hours / December 8, 2008 2008 年 12 月 8 日)
35×10127+19 = 3(8)1269<128> = 3 × 13 × 599 × 7151 × 35509 × 3897717493<10> × 1968303984853<13> × 157350569567152147220378732576837537803910029<45> × 5430727809728405538160402721839618815472716167071<49> (Sinkiti Sibata / Msieve 1.39 for P45 x P49 / 0.01 hours / December 8, 2008 2008 年 12 月 8 日)
35×10128+19 = 3(8)1279<129> = 151 × 6823 × 23913427 × 131438117 × 120090891519761440761050264585118472766825783074038787305201523581493108957731998170125939773089429555696327<108>
35×10129+19 = 3(8)1289<130> = 232 × 152275729 × 1492446089298751288678077876217<31> × 32347485229795269773911159388783041653533759798264519105022059164983778109899469987259937<89> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=3756860056 for P31 / December 3, 2008 2008 年 12 月 3 日)
35×10130+19 = 3(8)1299<131> = 32 × 86377609459<11> × 249857905108748581<18> × 200211376035752268927609227598616423780773881325329540181284043608449586954547912904520801130923357999<102>
35×10131+19 = 3(8)1309<132> = 985547 × 2047369 × 192731220407898597924576513928825750076189007414980129142310111248923195098691963839037358784549564534565698270133361523<120>
35×10132+19 = 3(8)1319<133> = 83 × 6911 × 7561 × 80639189 × 3633643667<10> × 3837435949<10> × 146360442746779252461375979039<30> × 5448462546809631269992966923096928341449858700851669952651980451961<67> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=544301459 for P30 / December 3, 2008 2008 年 12 月 3 日)
35×10133+19 = 3(8)1329<134> = 3 × 13 × 2447766620080220042610121031721960294871<40> × 407371760432911602911335890107629294263445550349909740419175681492591667237407264967405890681<93> (Erik Branger / GGNFS, Msieve snfs / 3.86 hours / December 8, 2008 2008 年 12 月 8 日)
35×10134+19 = 3(8)1339<135> = 71 × 44943757 × 47011049 × 630801161 × 313345459492701247<18> × 13115413285834281189187469742998831758055539950839255275906999015473759688037757670359866389<92>
35×10135+19 = 3(8)1349<136> = 1949 × 60127 × 1566450836866909116124109<25> × 21184947456388194242329460126605735558451350250877049029308496688596800273321847958805380266874269972127<104>
35×10136+19 = 3(8)1359<137> = 3 × 17 × 5417 × 1119871 × 358467107 × 951810720294636454280684312778970536173<39> × 368407634918623356591770151280494496467035113520864797303587770043237865921507<78> (Sinkiti Sibata / Msieve / 5.38 hours / December 8, 2008 2008 年 12 月 8 日)
35×10137+19 = 3(8)1369<138> = definitely prime number 素数
35×10138+19 = 3(8)1379<139> = 179 × 5113 × 152989 × 1894729 × 13168637 × 1113136892389417748386263420477763654758808860810541133565735920642676939369930058363274077190833187560678679964331<115>
35×10139+19 = 3(8)1389<140> = 32 × 13 × 19 × 4711525053547959827836928818968407243<37> × 3712996735489369150035175179729829418336017039152098603856719661184231606787193174795497182427779301<100> (Serge Batalov / Msieve-1.39 snfs / 3.00 hours on Opteron-2.6GHz; Linux x86_64 / December 9, 2008 2008 年 12 月 9 日)
35×10140+19 = 3(8)1399<141> = 1013 × 9337 × 2817599 × 6564499925209<13> × 611638929239007925767467375009<30> × 803891202777135445640155016729933566543<39> × 4521010369312349646185629427249033351108388757<46> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=3169444869 for P30 / December 3, 2008 2008 年 12 月 3 日) (Makoto Kamada / Msieve 1.39 for P39 x P46 / 54 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 6, 2008 2008 年 12 月 6 日)
35×10141+19 = 3(8)1409<142> = 494089291 × 3254984177<10> × 7991538184059115127147<22> × 49496312414403119917367633<26> × 919663280307249304984867643<27> × 6647206068560036763580200617250356609622466153939<49>
35×10142+19 = 3(8)1419<143> = 3 × 1061 × 15860642001115756856472209121303190876727<41> × 770314607968882846559673942076146333468438492173211262631406081919930865891145617675420812966181729<99> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=4239433639 for P41 / December 7, 2008 2008 年 12 月 7 日)
35×10143+19 = 3(8)1429<144> = 456857563587797981911<21> × 30807845048722372798703<23> × 27630159646748859897008752542207086824303957968728880264215949851985882405657172000508811511650575233<101>
35×10144+19 = 3(8)1439<145> = 29 × 784957 × 2005931 × 5394847 × 7101533 × 3602804419<10> × 981283272449<12> × 628780921527409936769622519262033690975208217673886274677499701408818919996672715977816855558683<96>
35×10145+19 = 3(8)1449<146> = 3 × 13 × 173 × 46301 × 17045617 × 1842706471<10> × 74365896181<11> × 80482065692066908416612753751129845520716852307<47> × 662190027785962142176186013718138487763144980919115337331166223<63> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 snfs / 16.16 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / December 10, 2008 2008 年 12 月 10 日)
35×10146+19 = 3(8)1459<147> = 4973 × 198710299 × 388205239 × 949775366340054803<18> × 3633369814248146679087833579<28> × 43740576084151262595014110169769593<35> × 6715994054043100705636974076007153320020152393<46> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=2543563693 for P35 / December 4, 2008 2008 年 12 月 4 日)
35×10147+19 = 3(8)1469<148> = 113 × 1087 × 33829 × 16824541 × 49352957 × 28969518268133097555490043<26> × 38907265660965437995846947939075439541051172448978436540124414161993390764261320650982013538148521<98>
35×10148+19 = 3(8)1479<149> = 33 × 923910619 × 1558948656381874408106205078091357252932489441138962113650443082640871654245660912184330265942095297828439128958998595628216158400559038753<139>
35×10149+19 = 3(8)1489<150> = 26091809 × 11465034896004908807461<23> × 1088707817387439431350379964842563<34> × 1194083292946011325405761931527911769362936033665647008316544335094461381186494573304247<88> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2177793751 for P34 / December 7, 2008 2008 年 12 月 7 日)
35×10150+19 = 3(8)1499<151> = 449 × 2251 × 670051 × 2672290540824465915914614009423625553247516207069<49> × 2148880004904170262568464197161540753125392466048489311759094604779127603367722353590597069<91> (Serge Batalov / Msieve-1.39 snfs / 9.00 hours on Opteron-2.6GHz; Linux x86_64 / December 8, 2008 2008 年 12 月 8 日)
35×10151+19 = 3(8)1509<152> = 3 × 13 × 23 × 85243321277118516416223291923<29> × 508595753085885009678633441259990785487468732003027824661020701838237762565748455755919371907776767399652422887120889219<120>
35×10152+19 = 3(8)1519<153> = 17 × 47 × 149 × 174466321 × 690711607 × 694720525906272967<18> × 5617937763096129305063<22> × 338727578734245577642330909<27> × 20504374150743174271290700437096077772778152482760813031911340433<65>
35×10153+19 = 3(8)1529<154> = 337 × 171847463083151491501<21> × 38559715265314947042590710270001<32> × 17390443877201234143891250701031139775259666719<47> × 100140100604561495228549337527256127066996322341408163<54> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=2328995801 for P32 / December 4, 2008 2008 年 12 月 4 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P47 x P54 / 3.09 hours on Core 2 Quad Q6700 / December 8, 2008 2008 年 12 月 8 日)
35×10154+19 = 3(8)1539<155> = 3 × 9629 × 1346241869660708584792082559244258278425897077885861767884823238442513548962816799559971228888042679713673586349876722708792497971021182154217775777647<151>
35×10155+19 = 3(8)1549<156> = 17328426330280651<17> × 8737120079789454811139398762185632204595767732620207073<55> × 2568609627631786308344700400368235052270213245925487584490856911668202549658932772843<85> (Serge Batalov / Msieve-1.39 snfs / 13.00 hours on Opteron-2.6GHz; Linux x86_64 / December 9, 2008 2008 年 12 月 9 日)
35×10156+19 = 3(8)1559<157> = 42879765185315430497<20> × 292878855232275740887814418726995651773<39> × 309660006169512256602650575144116413031660682773563091399663989195394753951491151864966823095355469<99> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2088941172 for P39 / December 7, 2008 2008 年 12 月 7 日)
35×10157+19 = 3(8)1569<158> = 32 × 13 × 19 × 48490980049404849877083686413436375909387700361<47> × 360765592388035467312597513412831108601623865988953111824323565795743335616112041862817403331969655385010463<108> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.39 snfs / 19.89 hours, 1.74 hours / December 10, 2008 2008 年 12 月 10 日)
35×10158+19 = 3(8)1579<159> = 6479735363<10> × 1930617658092374610982383853322441180442017<43> × 31086511703887452946743635557423166013615764652218926546381262043929479546241125975302646673487898198639859<107> (Serge Batalov / Msieve-1.39 snfs / 14.00 hours on Opteron-2.6GHz; Linux x86_64 / December 8, 2008 2008 年 12 月 8 日)
35×10159+19 = 3(8)1589<160> = 7829 × 1982316236372128463169333701<28> × 20276996658433163995117586251763240946991<41> × 12357843020120421119265960598992168176546184213774282216299622263920595989161202430965951<89> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=758478317 for P41 / December 8, 2008 2008 年 12 月 8 日)
35×10160+19 = 3(8)1599<161> = 3 × 48889 × 14158995281<11> × 3104396736833870181492437190327522026318664958142209<52> × 6032307486523415111941507522986185399490762371629962271727902737700672557187363638130272688123<94> (Sinkiti Sibata / GGNFS-0.77.1-20060513-nocona snfs / 45.77 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / December 10, 2008 2008 年 12 月 10 日)
35×10161+19 = 3(8)1609<162> = 157 × 3499 × 2162183 × 571876901252956296758416030882298904111353<42> × 572515087772493770133642628444432834628357213143562046017527857271537229085382174829411992559101277600579177<108> (Serge Batalov / Msieve-1.39 snfs / 22.00 hours on Opteron-2.6GHz; Linux x86_64 / December 11, 2008 2008 年 12 月 11 日)
35×10162+19 = 3(8)1619<163> = 991 × 1864897813393<13> × 2104247600835510265097708306758799271287177874833532292433231239011792816766205668364869689295342375226795901068513718744040726895858992946422880503<148>
35×10163+19 = 3(8)1629<164> = 3 × 13 × 22027 × 3772305601451741110693896034844369021299802372207123480191799<61> × 12000482490194027628192717775525574707938989420059163916800025995974556673997774191103348024966187<98> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.39 snfs / 29.93 hours, 2.35 hours / December 12, 2008 2008 年 12 月 12 日)
35×10164+19 = 3(8)1639<165> = 282833 × 347981 × 1195263561592703068137949500679<31> × 39575882037420828963570411917339240644716762775903<50> × 83530607544231245392846006539898621111183905857449706817593594044549213589<74> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1440214857 for P31 / December 8, 2008 2008 年 12 月 8 日) (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 snfs / 79.80 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / January 30, 2009 2009 年 1 月 30 日)
35×10165+19 = 3(8)1649<166> = 397 × 9902507529972705094099711<25> × 7969168206574953146277054418993341701964192859<46> × 124130027950451329601018911129048488882630366948490024869787253847677630490858463394940065113<93> (Ignacio Santos / GGNFS, Msieve snfs / 38.30 hours / March 6, 2009 2009 年 3 月 6 日)
35×10166+19 = 3(8)1659<167> = 32 × 109 × 1032107 × 1671053 × 25037040739<11> × 918033614587760796181356597566868542497064382497226138073290341568653492986741415799807091750167732687279457280351109737385242746227528534601<141>
35×10167+19 = 3(8)1669<168> = 9399905186263<13> × 1641584855370881<16> × 117604162223291467981<21> × 127461987854538798090991<24> × 233497123122207430579337078165623812031<39> × 7200353378046645802084948687027325444285796669256644994363<58> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P39 x P58 / 2.18 hours on Core 2 Quad Q6700 / December 7, 2008 2008 年 12 月 7 日)
35×10168+19 = 3(8)1679<169> = 17 × 13117932255751<14> × 512637923965839327881<21> × 34017351568411059332111497443854526817487043699921894789514557796944808948960297215251901507548179580488337636173166793778604570528407<134>
35×10169+19 = 3(8)1689<170> = 3 × 13 × 712 × 31819595777<11> × 6382207139613545645860787237<28> × 33883009715076389055208625207<29> × 28747275855313972686022339866790782111280841337363152219254249752490458803546328003452745990362677<98>
35×10170+19 = 3(8)1699<171> = 821 × 149892588592261503731<21> × 3160110129601481471520724256242281061840005378654306778594468870354244918703975469623298585832423161392006963440835680156546957692004684620809026039<148>
35×10171+19 = 3(8)1709<172> = 1315747 × 12878217459996999966612430708842525173647<41> × 229507769468070544234606674705372447688355761067510543219870223637687579557401800773214413613089328397784365674061380352422621<126> (Dmitry Domanov / GGNFS/msieve 1.42 snfs / 78.20 hours / October 1, 2009 2009 年 10 月 1 日)
35×10172+19 = 3(8)1719<173> = 3 × 29 × 499 × 3072469 × 89289139 × 224628099463<12> × 189446458458487<15> × 1284451861424479502826555202924565884956993576244951<52> × 59738069771743625944379752433485046844244815846525917970514657759808631975293<77> (ruffenach timothee / Msieve 1.44 snfs / May 18, 2010 2010 年 5 月 18 日)
35×10173+19 = 3(8)1729<174> = 23 × 61 × 83 × 43457 × 18974211313350521302318093<26> × 4050105130172981475172455469669100233219958084116052273280555984952318980147987213424688416111459031121054554235097131596636190159081072061<139>
35×10174+19 = 3(8)1739<175> = 3411004078387097156980920467<28> × 2105176968861672882237448575911<31> × 541570108905610066269020582875116224021983237559023073664656659211662593948250765859851511176229999450549945025574597<117> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=2585290844 for P31 / December 4, 2008 2008 年 12 月 4 日)
35×10175+19 = 3(8)1749<176> = 35 × 13 × 19 × 349 × 13626800067413174777<20> × 23252900373422007589629461587056302592594913<44> × 5859031949217806020337744575699589917552376077729095173813659362031905084846067101662329800284634781654241<106> (Wataru Sakai / GMP-ECM 6.3 B1=11000000, sigma=2633087626 for P44 / September 1, 2011 2011 年 9 月 1 日)
35×10176+19 = 3(8)1759<177> = 97 × 894892931 × 3077380928843896764925489109984745450893664351952347353215229050129931145160011283<82> × 1455799162202271447193121599869180825476869398830946632767808759970121625546395515169<85> (matsui / Msieve 1.46 snfs / August 17, 2010 2010 年 8 月 17 日)
35×10177+19 = 3(8)1769<178> = 1091 × 9341 × 3158478689449393489<19> × 281910154882292856538537842099413<33> × 428567013892142686122317248368508819380733631232867037321240754177582129396851273466877401926451847753636501150791965667<120> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=1485808196 for P33 / December 4, 2008 2008 年 12 月 4 日)
35×10178+19 = 3(8)1779<179> = 3 × 723328843723621<15> × 1604042672514887393<19> × 113924427578431510728409<24> × 52353651649346759585876888758979954129<38> × 1873219822685721131438109990191872553706066300586969533989207471921093745994540622111<85> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=4024858816 for P38 / January 19, 2009 2009 年 1 月 19 日)
35×10179+19 = 3(8)1789<180> = 6887149 × 56465874179415733402731506010526110134816146549013080577883372189114666880139937278674947919507605961318520753491595562821261582824604039913887283241423829931498344073707261<173>
35×10180+19 = 3(8)1799<181> = 6257 × 4220863619149<13> × 136381056711978494135193541037<30> × 1079702256355837774314705659099646008613439619319488765483129074856700822672384953134750738052098815447491399859784657792158977177502529<136> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=3618090261 for P30 / December 4, 2008 2008 年 12 月 4 日)
35×10181+19 = 3(8)1809<182> = 3 × 13 × 14134739 × 3758264504002963<16> × 3732676911230891630950972091962751396205877773898905701909<58> × 5028811904090829270025243529316863503320901432279976846521779058163405691059316823895070735229910827<100> (Dmitry Domanov / Msieve 1.50 snfs / July 1, 2013 2013 年 7 月 1 日)
35×10182+19 = 3(8)1819<183> = 449 × 4900386613<10> × 194201406386591<15> × 17476954301408338279<20> × 1399716730252105807483880635558366774936507205502791219011813<61> × 37204080397027306381683172603006822987788478994579005232415879635252199301721<77> (Dmitry Domanov / Msieve 1.50 snfs / July 1, 2013 2013 年 7 月 1 日)
35×10183+19 = 3(8)1829<184> = 59 × 4877 × 95276399 × 101941127 × 51078483307<11> × 10472393160158247827<20> × 2601369662432934411945595234592888895329332591677180665801185353093963558661301861396505697483440114583127434391654386881781612695359<133>
35×10184+19 = 3(8)1839<185> = 32 × 17 × 227 × 1237 × 3028427 × 6880873 × 106942088993<12> × 938679944328740548919086924469<30> × 8184269571777502631981099728373<31> × 73116907767253706535802059911323219242216637<44> × 723125958039174656868976766045499019103903811041<48> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=32890131 for P30 / December 4, 2008 2008 年 12 月 4 日) (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=2090537978 for P31 / December 4, 2008 2008 年 12 月 4 日) (Robert Backstrom / Msieve 1.39 for P44 x P48 / 1.56 hours / December 8, 2008 2008 年 12 月 8 日)
35×10185+19 = 3(8)1849<186> = 401 × 1423 × 9893774377<10> × 10068225948804048229865636405698802015913480152447496629470743665601557397828853<80> × 6841657144590094786821613695881897773039655358718965129439288382069841695175265313688274003<91> (Dmitry Domanov / Msieve 1.50 snfs / August 12, 2013 2013 年 8 月 12 日)
35×10186+19 = 3(8)1859<187> = 4001 × 3473279263930386643<19> × 360840367047808632995182317683<30> × 86985188403331936441287705736459673051125567<44> × 8915728924504989066111014865640984733447763204073103394685822909030779953273037763643986543<91> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=2472517506 for P30 / December 5, 2008 2008 年 12 月 5 日) (Ignacio Santos / GMP-ECM 6.3 B1=43000000, sigma=4196353134 for P44 / July 17, 2011 2011 年 7 月 17 日)
35×10187+19 = 3(8)1869<188> = 3 × 13 × 229 × 6803 × 165946619 × 555455585147537219<18> × 4965159428650814398623665321<28> × 38675511208479660394046433269<29> × 29605251527267858956304593927958498437<38> × 1221431769936255690871056105778224165151337790826816109487361<61> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P38 x P61 / 3.53 hours / December 8, 2008 2008 年 12 月 8 日)
35×10188+19 = 3(8)1879<189> = 173 × 20807 × 32423 × 37409 × 1841401 × 48371805134531796383725494506959571408282103900363958852818239072876525341903829110309691021671609165247008666938024060529224663462943596081518779169481987030957621557<167>
35×10189+19 = 3(8)1889<190> = 20293470058904574878183102843477356409653799265487560509<56> × 191632524038562972599764005358059709580489479276799676408280772785787623231363395916154199246135197563472355670762941811936146063579821<135> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 242.97 hours on Core 2 Quad Q6700 / December 18, 2008 2008 年 12 月 18 日)
35×10190+19 = 3(8)1899<191> = 3 × 18133 × 387285994369780603<18> × 209624376426807196690783<24> × 3919701941592254012158021<25> × 63257351576766423947399512515745629216260427114779<50> × 35513787691764778266303377928648484869380394953958769263504184367442221<71> (Ignacio Santos / GGNFS, Msieve gnfs for P50 x P71 / 47.85 hours / February 1, 2009 2009 年 2 月 1 日)
35×10191+19 = 3(8)1909<192> = 419 × 9973 × 362570759141<12> × 256680523885667465626001327490196032785113335931531461477234010294738064615522398935800239970293375181654544153631687025529906771924638285031579822295038287323898286095025467<174>
35×10192+19 = 3(8)1919<193> = 2039 × 63773 × 297872670657383<15> × 5144178297385089373709<22> × 19517527034434877372781126520731079207083154219444708077025496503532078038162518056295315923159199849721414378963098509960458337758404678844543578721<149>
35×10193+19 = 3(8)1929<194> = 32 × 13 × 19 × 491083 × 148113696550363521337224777943<30> × 240511557634175469989758300396345551898577490270185503686329727880684699638227636465836184018991233490919263160520251562173783674545876544438574724044704547<156> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=3971589362 for P30 / December 5, 2008 2008 年 12 月 5 日)
35×10194+19 = 3(8)1939<195> = 1089969148057409<16> × 10219198755552835523723<23> × 9323979225759446991275928931<28> × 12643344099626450719036094127714479<35> × 296163291907625435082616666878492839479545213079224774475849163360422699627509912557439311446423<96> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1697095651 for P35 / December 7, 2008 2008 年 12 月 7 日)
35×10195+19 = 3(8)1949<196> = 23 × 2657 × 3227618633<10> × 1428097873210962441563<22> × 14814628864316358818501<23> × 93346064495153945838319036260229359259<38> × 9983416029813247020011105758206744810979295600468377265562050175448882256431254130673713886397945059<100> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4083896266 for P38 / July 3, 2013 2013 年 7 月 3 日)
35×10196+19 = 3(8)1959<197> = 3 × 332179 × 11088048895176551020181292564409681<35> × 28368849008730415796034214312208650779700947865423543721820228374610663872479<77> × 124060994616880209288033422733266001039097144761757588785917837823987732072997103<81> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2788871739 for P35 / December 8, 2008 2008 年 12 月 8 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P77 x P81 / October 13, 2017 2017 年 10 月 13 日)
35×10197+19 = 3(8)1969<198> = 52145677 × 516369250757245745147387083<27> × 276684966949382452545925126122397675460406215494387<51> × 1493424987721602369695519132387453395423255450358227033<55> × 34952470283000349603518617405799175226099225488861932820149<59> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P51 x P55 x P59 / December 20, 2017 2017 年 12 月 20 日)
35×10198+19 = 3(8)1979<199> = 47 × 6326374989656440646106970407770659705730121493408302755378873328843303115001775919<82> × 13078945987260134036462322502917867367044969527869559453471699062092522781634351546825345197002805196515382338315673<116> (Wataru Sakai / Msieve / 569.79 hours / November 6, 2009 2009 年 11 月 6 日)
35×10199+19 = 3(8)1989<200> = 3 × 132 × 4861 × 152840603 × 1156566239497<13> × 2515923827839<13> × 217505594603821<15> × 6497775628529706959<19> × 24582654665588546304875938307<29> × 521482237316465123045134535692157<33> × 1958311477916142932716389871913675734578597034889255207588628076663<67> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1731595855 for P33 / December 7, 2008 2008 年 12 月 7 日)
35×10200+19 = 3(8)1999<201> = 172 × 29 × 293 × 3999019603<10> × 200892193437289<15> × 6728470765532169399958286068096229<34> × 57731747949917285702879793337026006282003208710681265823354791757<65> × 507474709442129400275576945781130020602660116312023172153037343922420283<72> (Makoto Kamada / GMP-ECM 6.2.1 B1=25e4, sigma=1961032907 for P34 / December 5, 2008 2008 年 12 月 5 日) (Erik Branger / GGNFS, Msieve gnfs for P65 x P72 / September 7, 2012 2012 年 9 月 7 日)
35×10201+19 = 3(8)2009<202> = 431 × 12595475713148530667<20> × [716363896309824114877888899222964157069202601348187977171155306252678853139277120870748818844887234648222292551732957661238360808038282241261728331090057416687877324294727303185157<180>] Free to factor
35×10202+19 = 3(8)2019<203> = 33 × 250067171 × 9619709867<10> × [598746676792000566499001874842761236310505497107265006110880058349352259184367913436881014549581914873551329783959554767032934728497894500211382234961037016126315854210167066361097051<183>] Free to factor
35×10203+19 = 3(8)2029<204> = 151 × 35879 × 38651597856270173<17> × 1857123583651763949049654697676015382191167286955007563423640054815258430483706197941528175493353590517978274368293273072902273315991117336903601679739364257632882644578945782968717<181>
35×10204+19 = 3(8)2039<205> = 71 × 359 × 10399 × 114531542096417446468313<24> × 84236514375392918434791697369357<32> × 1520742429925480309249157950965972233006436876279608768273203997250036059628029585673421815262936750036842572532516227046661639296824396080139<142> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1498511238 for P32 / December 7, 2008 2008 年 12 月 7 日)
35×10205+19 = 3(8)2049<206> = 3 × 13 × 11719 × 24155994319<11> × [3522455009742933813083925591542111258354259022344605384229591363070965906548232676179907712374140114342751927652602987374493504917457651853611205856260771238691214270255367867087612603352391<190>] Free to factor
35×10206+19 = 3(8)2059<207> = 11226918883<11> × [34638968441978444540337994788101194913469019751969725609434501593244377669285854489137568741520664008247193896545488106283745106211870444213388451618412649832351059028212708686129810428495717215283<197>] Free to factor
35×10207+19 = 3(8)2069<208> = 181 × 8233 × 57451409 × 200422493 × 1516274883705737<16> × 246016846549688282082941<24> × 275450051221332909486832109929<30> × 1742196129019091351024533160914564537<37> × 1266073766031989948416133323727068416037157586223954722004525286624081295297345229<82> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1093113026 for P30 / June 21, 2013 2013 年 6 月 21 日) (Dmitry Domanov / Msieve 1.50 gnfs for P37 x P82 / June 26, 2013 2013 年 6 月 26 日)
35×10208+19 = 3(8)2079<209> = 3 × 2184236683<10> × 5934779442106349315882706912199113067895931387469955316634045818267654725109734347851790456795914439352433017884153428515128991157485730662899485313223705694426780654412698993647916388813328506379161<199>
35×10209+19 = 3(8)2089<210> = 7929510539<10> × 4268634679318419000451823781507892571117249190000442722792171481<64> × 11489209955909131945878151780998270619873909457812311906186972937553085446695742635208875449450141697885401060024367055299638642778677571<137> (Bob Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs for P64 x P137 / August 7, 2017 2017 年 8 月 7 日)
35×10210+19 = 3(8)2099<211> = 367 × 29869436526225204756177557943060263745040933120883712367613292836607799337163492161<83> × 354758198429918615804849902659482662502383439587434530086468693035373009470388393570288069461245814858480108388880228560487447<126> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs / December 31, 2013 2013 年 12 月 31 日)
35×10211+19 = 3(8)2109<212> = 32 × 13 × 19 × 330887 × 6264645939833<13> × 876831393716651701<18> × [9624845033021818970887266014415455287009962370360196816029675162355246572281471230874966266638830997929324851658573873774434521968659973814483823455673455061726898063401333<172>] Free to factor
35×10212+19 = 3(8)2119<213> = 314836989595243<15> × 1235207112699329307536993418148355864532826856048910544668457712727020504544715432728836193275492946271966287516251338589865923767430410877777480036718266097356807151715997796815428228857451510118123<199>
35×10213+19 = 3(8)2129<214> = 2228243 × 883826893 × 2226465833348389<16> × [886910378491489040450319537697660790250590768146402204848955419485522242536402453248035327820993316149713669978802652852362816134582437388377779816301552466609000982406484806190846499<183>] Free to factor
35×10214+19 = 3(8)2139<215> = 3 × 83 × 449 × 727 × 3378629 × 50293823 × 2815725289416069101708733900814656422729348827724519048111052533620945746108377676478228852563275433628450516004336919680364420486413374428509633232709883868628918393614416413735713448016764421<193>
35×10215+19 = 3(8)2149<216> = 4143871717445765792143051<25> × 3776656506046318578516690281<28> × [24849161906495879792157645912604241422451679042633989237068749358788970163157343987455447348794831652506685301316190124118322711139212727456736277592194435450801619<164>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=380083552 for P28 / July 3, 2013 2013 年 7 月 3 日) Free to factor
35×10216+19 = 3(8)2159<217> = 17 × 154324757965518861209011967<27> × 1357976630825264426985757657<28> × [1091562764877459328343498316736168323183009423575425735675596155775238292293998133568333762755762330532883689057162475430411530150838734230336930134675838647968943<163>] Free to factor
35×10217+19 = 3(8)2169<218> = 3 × 13 × 23 × 263 × 20124113 × 423407404165353569814656068039919<33> × [19346488422038219785367691081815597966039384740512408432539856743196003454402909512828273741633134036149938435317489164693087585496710759246113552315491841168210342603573217<173>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3331746343 for P33 / July 3, 2013 2013 年 7 月 3 日) Free to factor
35×10218+19 = 3(8)2179<219> = 223 × 593 × 98523289 × 326012377 × 2407536049<10> × 38029462746543463308329141580351952919060703806503799321184069185597026540562066268102253752278342533941468486087678992302830229382331518015316340955413809489068153681552738354027418210583<188>
35×10219+19 = 3(8)2189<220> = 17923 × 1440847 × 3208367 × [46936740054726654836490216606117611219848018371649391935824255073000095595709374186800619027754590088026820236129861752839790242084273382893315197511227559587483034991570129203783315971371707135959679507<203>] Free to factor
35×10220+19 = 3(8)2199<221> = 32 × 5813 × 359599 × 123028975317338727483284606212117<33> × 16801839055622790891716080046983767259735266166761098306741917532585279300132725379763651058360293227519987144399342620041422832089069567354543186935338780178918113367164053446199<179> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3425529913 for P33 / July 3, 2013 2013 年 7 月 3 日)
35×10221+19 = 3(8)2209<222> = 191 × 811 × 60431561 × 2046474226715159792623<22> × 43217203963433109770423<23> × [469725952303785399620013238768898991634851964749102950633010217013510290795499344077603869489230256672537077486319805001105619432246475740275116816270852037592678581<165>] Free to factor
35×10222+19 = 3(8)2219<223> = 18026343166397500836403<23> × 911595715460917634462198565605243407<36> × 236654967612781607753848907404822118958458522450236114576832363205646412417792464773540381023104683570288714786965753391887614838307459507365166280499637021720489709<165> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=4184087625 for P36 / September 9, 2013 2013 年 9 月 9 日)
35×10223+19 = 3(8)2229<224> = 3 × 13 × 743 × 110491 × 6475103383741<13> × 1875851707956401971825759107513781047786032152807552394087808285765919637125684927817550190707577405640336338650249721203507377363487753663643332635707259635277947877948931949101348019632078628803584647<202>
35×10224+19 = 3(8)2239<225> = 2833 × 26557 × 409967 × 3232001272660042626042494609<28> × 14365496612999858860092293929283<32> × [271555672847088135972778910414683116808140597231480509053542111113860179867149238311413412313637262045599434394884040768994483023164986731539169140737281<153>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2998872404 for P32 / July 3, 2013 2013 年 7 月 3 日) Free to factor
35×10225+19 = 3(8)2249<226> = 307 × 98412304051<11> × 401546919127<12> × 81163342323344867<17> × 3949494728657246958760078565221318811641146517606241116017320060826628648117494631176159385712927406394949005231961984010995835096280816040119601093937859808169664038852254653606777853<184>
35×10226+19 = 3(8)2259<227> = 3 × 425080009 × 508011960907213421719<21> × [60028799958774217148408335317117627996632403087517277700571005512817737734287549751615901185320918949755052000907704978648536896682562359811284243767432307980899586652539875693492743469360867733053<197>] Free to factor
35×10227+19 = 3(8)2269<228> = 590352997093<12> × 62752021718155345575148226708185855082353<41> × 10497503792653949256024412553906327597627681026662549708501194439445879713120565535345832507236586709546922487191889680871907652616309054040900335825420599019206322505386197141<176> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1214694646 / June 21, 2013 2013 年 6 月 21 日)
35×10228+19 = 3(8)2279<229> = 29 × 198868685955344619720593<24> × [674312379618927152923992029452713917439167510651230029513300033834578825547455974107093059807408141603026472687101944599084844577720227165914277941555278421919610857276395590676121621675949782524898355837<204>] Free to factor
35×10229+19 = 3(8)2289<230> = 33 × 13 × 19 × 19751 × 785857 × 2370506161<10> × 11308832566883040979597<23> × 1633739595687938784791300727549277<34> × [8578088155816911172954529909086765724535278100686072306368667840024238751526783292070610927939379866362103476683509583604971469261262991218123851311587<151>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1895477422 for P34 / June 21, 2013 2013 年 6 月 21 日) Free to factor
35×10230+19 = 3(8)2299<231> = 18104909 × 626386661671<12> × [34291516161007848645240653492794613564666813762224692523710016467578417059354513320589618721445772892162845335908992778414375999547047156466306112299781920300941347532047073191748527061432006905980628917341041051<212>] Free to factor
35×10231+19 = 3(8)2309<232> = 173 × 2851951 × 349106359432063961613667<24> × [22577695531124905639007606075243335957487078981220978268264894458517708069595798009529895623198531392946314520849673699146220342850486747832930448007052387280862602240854272669873812866588572034640529<200>] Free to factor
35×10232+19 = 3(8)2319<233> = 3 × 17 × 23605493803129118235415621500571<32> × [32302956230230974460199948932805439512907611844645403449284662386911727555184067853978855867907523961008786656248305598454289519388495551096146579919289029859199107669035120426662993207016098419230809<200>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2357237576 for P32 / July 3, 2013 2013 年 7 月 3 日) Free to factor
35×10233+19 = 3(8)2329<234> = 61 × 6375227686703096539162112932604735883424408014571948998178506375227686703096539162112932604735883424408014571948998178506375227686703096539162112932604735883424408014571948998178506375227686703096539162112932604735883424408014571949<232>
35×10234+19 = 3(8)2339<235> = 797 × 853 × 1697 × 2917 × 47805607481<11> × 277473617728733<15> × 1075604894860472159738988277692660683994222101<46> × 8079389247150714237979875846305089816601762849<46> × 10024623512605688601678514893009372879419328535112826377596612908712983704138191658695443439596343659080173<107> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=393350677 for P46(1075...) / September 9, 2013 2013 年 9 月 9 日) (Ignacio Santos / GMP-ECM 7.0 B1=11000000, sigma=1:3463576907 for P46(8079...) x P107 / December 23, 2015 2015 年 12 月 23 日)
35×10235+19 = 3(8)2349<236> = 3 × 13 × 111653 × [8930803445953061279116109707316392313660636052331752402507330722425704199592944185565969127539349566523041485648849535175921390353604445478376317673067424529543773988616491728812938274394751157578846937843113494461868441967498867<229>] Free to factor
35×10236+19 = 3(8)2359<237> = 257 × 6208566925044597689<19> × 65664281503571792115892963<26> × 96967310407098745869250680191790559037<38> × 673779026422468214509493224116267365918917843561<48> × 771883559937352204280236363785934808480872279816793<51> × 73599899137320825601445843442161214163422752403443111<53> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4051843547 for P38 / July 3, 2013 2013 年 7 月 3 日) (Serge Batalov / GMP-ECM B1=11000000, sigma=150307247 for P48 / November 8, 2013 2013 年 11 月 8 日) (Serge Batalov / Msieve 1.51 gnfs for P51 x P53 / November 9, 2013 2013 年 11 月 9 日)
35×10237+19 = 3(8)2369<238> = 56284967 × 250541723 × 470343587944907881<18> × 248161011416761191915389<24> × 2362676605320683844643842694080573083899088512819345979477593952188189802830271340076847604228682199833759070747103968939808411936096512153198197780213573690406932831886071588472681<181>
35×10238+19 = 3(8)2379<239> = 32 × 167 × [25874177570784357211502920085754417091742441043838249427071782361203518888149626672580764397131662600724476971981962001922081762401123678568788349227470983958009906113698528868189546832261403119686552820285355215494936053818289347231463<236>] Free to factor
35×10239+19 = 3(8)2389<240> = 23 × 71 × 131 × 157 × 167017 × 130448916149<12> × [531455919288021032425574865591419670751730047163721215240737618486113003126834541977149513705356220473744952340708337535154456616223058451475312435112786597442320097796238781138940095297981433222877750677945752897403<216>] Free to factor
35×10240+19 = 3(8)2399<241> = 3501537041<10> × 577271085592747172819139901883<30> × 4387469544650586032839495757162403019<37> × [438503324294969958654851458346078471430401884263558037122211152463962363418754228552847606886017825000114450118457942478274636338268311760933275882289294640602375777<165>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=976686479 for P30 / July 3, 2013 2013 年 7 月 3 日) Free to factor
35×10241+19 = 3(8)2409<242> = 3 × 13 × 59 × 2029 × 197887 × 607442192540157629838147303824753<33> × 37691334692150463672251850681635697613<38> × [1838497880858324721147036012512840290706000950911651594116996338220532669876237719048427624905766056008049859890387627598557803353703198951718439307045715916587<160>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=104402667 for P33 / July 3, 2013 2013 年 7 月 3 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2802236843 for P38 / July 4, 2013 2013 年 7 月 4 日) Free to factor
35×10242+19 = 3(8)2419<243> = [388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889<243>] Free to factor
35×10243+19 = 3(8)2429<244> = 17202397727<11> × 22386196237<11> × 143136932285239<15> × 8571168708027000842605877<25> × 8231225417092349953458501257459139653815175874286353027745893919910028412836336070962592386737115663956125973171811156506343637820554217997150527539382993060113602598590509004623120737<184>
35×10244+19 = 3(8)2439<245> = 3 × 47 × 1012765551552421660944185489<28> × [272331263828494464105208073850350534652320783540602679046735571118230152794702279248613857354742544923066687320893113034402359531794301169595875634880401663591722734634725871235390521665371633236928556263864038402061<216>] Free to factor
35×10245+19 = 3(8)2449<246> = 6317 × [61562274638101771234587444813818092273055071851969113327352998082774875556259124408562432941093697781999190895819042091006631136439589819358696990484231263081983360596626387349832022936344608024202768543436582062512092589661055705063936819517<242>] Free to factor
35×10246+19 = 3(8)2459<247> = 449 × 3739 × [2316454257738893114763299078269613964221635960741792190359062984986927586779505786469643628073016491367336102091830997586320847843437342791349883273869952537175947077359445994152342871763938221091527806816186508718902180703419794657581400699<241>] Free to factor
35×10247+19 = 3(8)2469<248> = 32 × 13 × 19 × 21974627 × 9777519075963077533<19> × 174108634422620070448714172219<30> × 1278522130339608052601857061857627<34> × [365769365736036937625131696400959477791718560550524788484961753338634936968309911405550979681889062592818625609053068589203266844168305748954464990328706921<156>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1581637529 for P30, B1=3000000, sigma=1552407292 for P34 / July 3, 2013 2013 年 7 月 3 日) Free to factor
35×10248+19 = 3(8)2479<249> = 17 × 2324145827<10> × 6184279303<10> × 51455719681<11> × 295168112111967419446454392019063<33> × 1560503394283318639314668491018819040051<40> × [67151594888228678969901882862709688004981144474209931832521751045300946426271586057241704044994927200859237633927665914679014506059011140515078769<146>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2924551863 for P33 / July 3, 2013 2013 年 7 月 3 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1269528613 for P40 / September 9, 2013 2013 年 9 月 9 日) Free to factor
35×10249+19 = 3(8)2489<250> = 35081 × 1952051813<10> × 1355812883059<13> × [41885381273548957448287556296080614183122596327860088197495167017452206020173673040282891395806996318911817776518322340048733227620052768679302448883049810626596897983479065677381633104199264109577234928986213472877362797807<224>] Free to factor
35×10250+19 = 3(8)2499<251> = 3 × 2731 × 30763 × 1201633 × 128405033319652502118334123493175900839330220024600633141147146782754049795196414662536566411067535926423052362224287860865391025211068986550239873043362360523363927497021376861203798908190776337846307735300740153127524399573622201064587<237>
plain text versionプレーンテキスト版

4. Related links 関連リンク