Table of contents 目次

  1. About 300...007 300...007 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 300...007 300...007 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 300...007 300...007 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 300...007 300...007 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

30w7 = { 37, 307, 3007, 30007, 300007, 3000007, 30000007, 300000007, 3000000007, 30000000007, … }

1.3. General term 一般項

3×10n+7 (1≤n)

2. Prime numbers of the form 300...007 300...007 の形の素数

2.1. Last updated 最終更新日

December 11, 2018 2018 年 12 月 11 日

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

  1. 3×101+7 = 37 is prime. は素数です。 (Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日)
  2. 3×102+7 = 307 is prime. は素数です。 (Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日)
  3. 3×105+7 = 300007 is prime. は素数です。 (Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日)
  4. 3×108+7 = 300000007 is prime. は素数です。 (Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日)
  5. 3×1024+7 = 3(0)237<25> is prime. は素数です。 (Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日)
  6. 3×1029+7 = 3(0)287<30> is prime. は素数です。 (Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日)
  7. 3×1084+7 = 3(0)837<85> is prime. は素数です。 (Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日)
  8. 3×10110+7 = 3(0)1097<111> is prime. は素数です。 (Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日)
  9. 3×10129+7 = 3(0)1287<130> is prime. は素数です。 (Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日)
  10. 3×10176+7 = 3(0)1757<177> is prime. は素数です。 (Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日)
  11. 3×10593+7 = 3(0)5927<594> is prime. は素数です。 (discovered by:発見: Julien Peter Benney / November 23, 2004 2004 年 11 月 23 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 29, 2006 2006 年 5 月 29 日)
  12. 3×101137+7 = 3(0)11367<1138> is prime. は素数です。 (discovered by:発見: Mark Hudson / November 26, 2004 2004 年 11 月 26 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 13, 2006 2006 年 9 月 13 日) [certificate証明]
  13. 3×102675+7 = 3(0)26747<2676> is prime. は素数です。 (discovered by:発見: Hugo Pfoertner / November 29, 2004 2004 年 11 月 29 日) (certified by:証明: Ray Chandler / Primo 4.0.1 - LX64 / December 24, 2012 2012 年 12 月 24 日) [certificate証明]
  14. 3×104992+7 = 3(0)49917<4993> is PRP. はおそらく素数です。 (Hugo Pfoertner / November 29, 2004 2004 年 11 月 29 日)
  15. 3×1026904+7 = 3(0)269037<26905> is PRP. はおそらく素数です。 (Erik Branger / PFGW / June 10, 2010 2010 年 6 月 10 日)
  16. 3×1031572+7 = 3(0)315717<31573> is PRP. はおそらく素数です。 (Erik Branger / srsieve, PFGW / November 22, 2013 2013 年 11 月 22 日)
  17. 3×1055077+7 = 3(0)550767<55078> is PRP. はおそらく素数です。 (Erik Branger / srsieve, PFGW / November 22, 2013 2013 年 11 月 22 日)
  18. 3×1081021+7 = 3(0)810207<81022> is PRP. はおそらく素数です。 (Erik Branger / srsieve, PFGW / November 22, 2013 2013 年 11 月 22 日)
  19. 3×10122274+7 = 3(0)1222737<122275> is PRP. はおそらく素数です。 (Bob Price / July 17, 2015 2015 年 7 月 17 日)

2.3. Range of search 捜索範囲

  1. n≤30000 / Completed 終了
  2. n≤100000 / Completed 終了 / Erik Branger / November 22, 2013 2013 年 11 月 22 日
  3. n≤200000 / Completed 終了 / Bob Price / July 17, 2015 2015 年 7 月 17 日

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

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

  1. 3×103k+1+7 = 37×(3×101+737+27×10×103-19×37×k-1Σm=0103m)
  2. 3×108k+7+7 = 73×(3×107+773+27×107×108-19×73×k-1Σm=0108m)
  3. 3×1015k+3+7 = 31×(3×103+731+27×103×1015-19×31×k-1Σm=01015m)
  4. 3×1016k+6+7 = 17×(3×106+717+27×106×1016-19×17×k-1Σm=01016m)
  5. 3×1018k+16+7 = 19×(3×1016+719+27×1016×1018-19×19×k-1Σm=01018m)
  6. 3×1022k+12+7 = 23×(3×1012+723+27×1012×1022-19×23×k-1Σm=01022m)
  7. 3×1028k+7+7 = 29×(3×107+729+27×107×1028-19×29×k-1Σm=01028m)
  8. 3×1035k+25+7 = 71×(3×1025+771+27×1025×1035-19×71×k-1Σm=01035m)
  9. 3×1042k+13+7 = 127×(3×1013+7127+27×1013×1042-19×127×k-1Σm=01042m)
  10. 3×1044k+26+7 = 89×(3×1026+789+27×1026×1044-19×89×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 19.75%. 捜索難易度 (周期的に現れる素因数で割り切れない項の割合) は 19.75% です。

3. Factor table of 300...007 300...007 の素因数分解表

3.1. Last updated 最終更新日

November 20, 2023 2023 年 11 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=208, 209, 211, 217, 223, 225, 228, 232, 234, 236, 237, 238, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 251, 252, 253, 256, 257, 258, 260, 261, 264, 265, 267, 268, 270, 271, 272, 273, 274, 276, 280, 283, 284, 285, 286, 287, 288, 289, 291, 295, 296, 297, 298, 299, 300 (55/300)

3.4. Factor table 素因数分解表

3×101+7 = 37 = definitely prime number 素数
3×102+7 = 307 = definitely prime number 素数
3×103+7 = 3007 = 31 × 97
3×104+7 = 30007 = 37 × 811
3×105+7 = 300007 = definitely prime number 素数
3×106+7 = 3000007 = 17 × 109 × 1619
3×107+7 = 30000007 = 29 × 37 × 73 × 383
3×108+7 = 300000007 = definitely prime number 素数
3×109+7 = 3000000007<10> = 439 × 6833713
3×1010+7 = 30000000007<11> = 37 × 810810811
3×1011+7 = 300000000007<12> = 61 × 277 × 17754631
3×1012+7 = 3000000000007<13> = 23 × 139 × 257 × 367 × 9949
3×1013+7 = 30000000000007<14> = 37 × 127 × 577 × 11064709
3×1014+7 = 300000000000007<15> = 22691 × 13221100877<11>
3×1015+7 = 3000000000000007<16> = 73 × 17789 × 2310185531<10>
3×1016+7 = 30000000000000007<17> = 19 × 37 × 107 × 3299 × 120892633
3×1017+7 = 300000000000000007<18> = 1213 × 4561 × 78691 × 689089
3×1018+7 = 3000000000000000007<19> = 31 × 8747 × 809143 × 13673357
3×1019+7 = 30000000000000000007<20> = 37 × 521 × 8677121 × 179351971
3×1020+7 = 300000000000000000007<21> = 1291 × 379325719 × 612608083
3×1021+7 = 3000000000000000000007<22> = 233 × 65413057 × 196834348847<12>
3×1022+7 = 30000000000000000000007<23> = 17 × 37 × 4236946003<10> × 11256870761<11>
3×1023+7 = 300000000000000000000007<24> = 73 × 4109589041095890410959<22>
3×1024+7 = 3000000000000000000000007<25> = definitely prime number 素数
3×1025+7 = 30000000000000000000000007<26> = 37 × 71 × 58211 × 196180628657816431<18>
3×1026+7 = 300000000000000000000000007<27> = 89 × 3370786516853932584269663<25>
3×1027+7 = 3000000000000000000000000007<28> = 13339 × 3429403 × 65581215046280671<17>
3×1028+7 = 30000000000000000000000000007<29> = 37 × 810810810810810810810810811<27>
3×1029+7 = 300000000000000000000000000007<30> = definitely prime number 素数
3×1030+7 = 3000000000000000000000000000007<31> = 7481 × 25373 × 15804828241213478275339<23>
3×1031+7 = 30000000000000000000000000000007<32> = 37 × 73 × 97002180449987<14> × 114502554033761<15>
3×1032+7 = 300000000000000000000000000000007<33> = 283 × 4917712573<10> × 215561738438773101673<21>
3×1033+7 = 3000000000000000000000000000000007<34> = 31 × 34261 × 934366717 × 3023027973554365081<19>
3×1034+7 = 30000000000000000000000000000000007<35> = 19 × 23 × 37 × 41257393 × 44971390050462397330271<23>
3×1035+7 = 300000000000000000000000000000000007<36> = 29 × 167 × 3438397 × 18015684450198264652154617<26>
3×1036+7 = 3000000000000000000000000000000000007<37> = 494964632939586937<18> × 6061039113407050111<19>
3×1037+7 = 30000000000000000000000000000000000007<38> = 37 × 181 × 4479617739286247573540391219949231<34>
3×1038+7 = 300000000000000000000000000000000000007<39> = 17 × 7669 × 966109 × 2381811937996778938635030551<28>
3×1039+7 = 3000000000000000000000000000000000000007<40> = 73 × 12203 × 12697 × 25117 × 10559975197250851647251897<26>
3×1040+7 = 30000000000000000000000000000000000000007<41> = 37 × 191 × 4245082779114192726758171784349794821<37>
3×1041+7 = 300000000000000000000000000000000000000007<42> = 59 × 677 × 2526823751<10> × 2972388853179168412767713399<28>
3×1042+7 = 3000000000000000000000000000000000000000007<43> = 1439 × 4723 × 5108447 × 599857123 × 9720717983<10> × 14818609697<11>
3×1043+7 = 30000000000000000000000000000000000000000007<44> = 37 × 47 × 164029508385733973<18> × 105171892647938417827681<24>
3×1044+7 = 300000000000000000000000000000000000000000007<45> = 1350073 × 3982801 × 751262095538089<15> × 74264954268615031<17>
3×1045+7 = 3000000000000000000000000000000000000000000007<46> = 23923484947967329<17> × 125399790478890765348654497383<30>
3×1046+7 = 30000000000000000000000000000000000000000000007<47> = 37 × 246223 × 3292993793475064517980898660201568540757<40>
3×1047+7 = 300000000000000000000000000000000000000000000007<48> = 73 × 8731 × 33845659 × 379510763 × 109314123739<12> × 335220876209903<15>
3×1048+7 = 3000000000000000000000000000000000000000000000007<49> = 31 × 96774193548387096774193548387096774193548387097<47>
3×1049+7 = 30000000000000000000000000000000000000000000000007<50> = 37 × 113 × 373 × 27382739 × 800068027857012989<18> × 878068611972447209<18>
3×1050+7 = 300000000000000000000000000000000000000000000000007<51> = 416289971957<12> × 720651517473949661346586161431491808651<39>
3×1051+7 = 3(0)507<52> = 55862579 × 11970569406041699<17> × 4486270582333434712229720767<28>
3×1052+7 = 3(0)517<53> = 19 × 37 × 374557 × 113932600914063787468060277075502500400938317<45>
3×1053+7 = 3(0)527<54> = 8929 × 155377 × 58392533 × 801685817 × 7025543263<10> × 657491696048499853<18>
3×1054+7 = 3(0)537<55> = 17 × 176470588235294117647058823529411764705882352941176471<54>
3×1055+7 = 3(0)547<56> = 37 × 73 × 127 × 87456672506828908511574890606278806041506936771741<50>
3×1056+7 = 3(0)557<57> = 23 × 2115660643<10> × 4865734697<10> × 163601709050232403<18> × 7744816814619022993<19>
3×1057+7 = 3(0)567<58> = 25337833 × 929602302663456843877529<24> × 127366318120422347627412551<27>
3×1058+7 = 3(0)577<59> = 37 × 139 × 761 × 11731 × 54443 × 12001706183556157265510919553109415378640873<44>
3×1059+7 = 3(0)587<60> = 25844353 × 11607951648083432384629632631933173177134672320874119<53>
3×1060+7 = 3(0)597<61> = 71 × 179 × 659 × 215243312633913318217<21> × 1664158904458664023398585924083441<34>
3×1061+7 = 3(0)607<62> = 37 × 1604019283<10> × 1014996059197106936561<22> × 498018630459316095843098338697<30>
3×1062+7 = 3(0)617<63> = 866932563239<12> × 1184380150589<13> × 292176187908106405066152236398184564917<39>
3×1063+7 = 3(0)627<64> = 29 × 31 × 73 × 258362736189931<15> × 176932994415494167247508849050708762654045711<45>
3×1064+7 = 3(0)637<65> = 37 × 810810810810810810810810810810810810810810810810810810810810811<63>
3×1065+7 = 3(0)647<66> = 11597 × 476766564965980967<18> × 54258752737197570588646840676304118198649893<44>
3×1066+7 = 3(0)657<67> = 880413593 × 2768750173925419<16> × 1230695874355229930412252183745242948470621<43>
3×1067+7 = 3(0)667<68> = 37 × 8789091672849499727036081<25> × 92251946047564539252294359643557463628331<41>
3×1068+7 = 3(0)677<69> = 4219 × 50593 × 75810347 × 32098538872562066591712923<26> × 577573885385671200291134941<27>
3×1069+7 = 3(0)687<70> = 107 × 18017693548490897<17> × 89426539136530607339<20> × 17400905858269130024753402397647<32>
3×1070+7 = 3(0)697<71> = 17 × 19 × 37 × 89 × 4217 × 934535879 × 7156940736968775637854219931676104798881872523864991<52>
3×1071+7 = 3(0)707<72> = 61 × 73 × 229 × 521 × 2277848267<10> × 13173005009<11> × 18818530431881587158932329574305765333752197<44>
3×1072+7 = 3(0)717<73> = 30931 × 7293569 × 8572474297<10> × 246844426924254793<18> × 6284311149248704160062154842197053<34>
3×1073+7 = 3(0)727<74> = 37 × 284741 × 485890311221409753395066599<27> × 5860454325164264734412524615630507385129<40>
3×1074+7 = 3(0)737<75> = 23747641 × 91238521219<11> × 268340845699<12> × 65661498166169<14> × 7858234242360731652028636150943<31>
3×1075+7 = 3(0)747<76> = 293 × 796384271 × 747149183367091843994819363<27> × 17207732031763458234935687162445804263<38>
3×1076+7 = 3(0)757<77> = 37 × 347674709719261<15> × 376029032094798769<18> × 41335540481765452729<20> × 150038057386969993657951<24>
3×1077+7 = 3(0)767<78> = 7103 × 310721 × 69392692739<11> × 17815667421934982054968724377<29> × 109949433731598778093224841163<30>
3×1078+7 = 3(0)777<79> = 23 × 31 × 4207573632538569424964936886395511921458625525946704067321178120617110799439<76>
3×1079+7 = 3(0)787<80> = 37 × 73 × 1039 × 1223 × 1847 × 572657 × 625955860492510637<18> × 13202296647663702684922382029001071334833297<44>
3×1080+7 = 3(0)797<81> = 277 × 11411 × 94911269036432323361428123537773261407464518212997971746180691441249766281<74>
3×1081+7 = 3(0)807<82> = 1070683 × 157863750089668623431<21> × 17749165225483606522027927538441692526936337438655527059<56>
3×1082+7 = 3(0)817<83> = 37 × 7333 × 7681 × 14395278802292036060417159795935809822275019391748117845247433324068803807<74>
3×1083+7 = 3(0)827<84> = 513769 × 902800583 × 2361932737<10> × 33062619979<11> × 99756304721<11> × 83026433674730925599643777137972543227<38>
3×1084+7 = 3(0)837<85> = definitely prime number 素数
3×1085+7 = 3(0)847<86> = 372 × 67477 × 741163 × 9976434378762229507<19> × 726728774267084507874023<24> × 60436680681922112979298419173<29>
3×1086+7 = 3(0)857<87> = 17 × 1607 × 15733 × 33655393597439835659<20> × 20739115961968251612049950865027079498714359321952033396999<59>
3×1087+7 = 3(0)867<88> = 73 × 199 × 359 × 14169341 × 31098751 × 1421270425501426514718779<25> × 918505055963463910076241392500382916824591<42>
3×1088+7 = 3(0)877<89> = 19 × 37 × 8269 × 713857699000365908951<21> × 183594440313011252445911<24> × 39376921914948715310180926483901588941<38>
3×1089+7 = 3(0)887<90> = 47 × 2620085153369389<16> × 2674430404638894104042554343<28> × 910912558498503181307118855316906932618920203<45>
3×1090+7 = 3(0)897<91> = 263 × 310397 × 16150622431<11> × 15740346658681<14> × 144558766545391788172988240042912482282678808919745707117667<60>
3×1091+7 = 3(0)907<92> = 29 × 37 × 2368463 × 11122369031<11> × 1061347564479302758227709668616387114551821907958905701434169873919038303<73>
3×1092+7 = 3(0)917<93> = 958393 × 495086659559<12> × 2745914643721<13> × 230255156259078301782490273594219252920268073364717458477983841<63>
3×1093+7 = 3(0)927<94> = 31 × 96774193548387096774193548387096774193548387096774193548387096774193548387096774193548387097<92>
3×1094+7 = 3(0)937<95> = 37 × 141061537 × 1240987674787980091256650071993361<34> × 4631732303336888622217180085281253989404018318017323<52> (Makoto Kamada / GGNFS-0.54.5b)
3×1095+7 = 3(0)947<96> = 71 × 73 × 312929769011<12> × 32838137201600323<17> × 5632674477183462008448784970927863576084560908828308373300666593<64>
3×1096+7 = 3(0)957<97> = 121173603679670875523<21> × 24757867298645882940751558153470261457888796078573314140899701373994659416109<77>
3×1097+7 = 3(0)967<98> = 37 × 127 × 1579 × 4497395087<10> × 899026800639003032177953119210735756671288510422300183167912453887606833326312641<81>
3×1098+7 = 3(0)977<99> = 1959184687<10> × 18358551180638802532928817679<29> × 8340795484256794379858794115887051224428587896130311236194759<61>
3×1099+7 = 3(0)987<100> = 59 × 97 × 1279 × 81119024200702703<17> × 2869617189581715235822903<25> × 29092333577231525589382213<26> × 60520390659918817871834263<26>
3×10100+7 = 3(0)997<101> = 232 × 37 × 7678967 × 1000866991<10> × 46248401599818479379883<23> × 4312091457950501485337287857027747282974290083457420899209<58>
3×10101+7 = 3(0)1007<102> = 1667 × 179964007198560287942411517696460707858428314337132573485302939412117576484703059388122375524895021<99>
3×10102+7 = 3(0)1017<103> = 17 × 31183 × 47147 × 1288933 × 1746463 × 53322517204295489809480305702983110188955975714888120860086581601244316863338449<80>
3×10103+7 = 3(0)1027<104> = 37 × 73 × 8131353049<10> × 3500349912571<13> × 5454615958313<13> × 165556922073283387<18> × 432126469624198278826666829300413256680789639643<48>
3×10104+7 = 3(0)1037<105> = 139 × 23743 × 90901460695571917145136605200108960550887092204684637077433197274046996661189348651643483259132491<98>
3×10105+7 = 3(0)1047<106> = 1993 × 4289 × 124776136970633<15> × 4807194448933665149<19> × 28860364448854363372017120293<29> × 20273693351933343509455160294262628711<38>
3×10106+7 = 3(0)1057<107> = 19 × 37 × 223 × 2693 × 7883 × 13622737 × 6580345675035756693857460719<28> × 100558805553383969719058940946122882365167575230597714732879<60>
3×10107+7 = 3(0)1067<108> = 131 × 713533 × 3209489029768577760832151180455949212104142826626729782195622785459255895160029562817419133687660209<100>
3×10108+7 = 3(0)1077<109> = 31 × 2797 × 115607210891348457052787<24> × 433281452608477152130090427<27> × 690735969625772006836944498829857936179847407952595549<54>
3×10109+7 = 3(0)1087<110> = 37 × 2845252117<10> × 3713924441<10> × 12504288313116615501097427<26> × 19571965808741818874482698385709<32> × 313525077971325739601067364163441<33> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1340883278 for P32 x P33 / August 27, 2007 2007 年 8 月 27 日)
3×10110+7 = 3(0)1097<111> = definitely prime number 素数
3×10111+7 = 3(0)1107<112> = 73 × 15982711 × 8729351929<10> × 673840872641<12> × 29534344527152687<17> × 6547792133200043993<19> × 2260405600467595500562401249746577803868165431<46>
3×10112+7 = 3(0)1117<113> = 37 × 8287 × 86688607 × 7223154329<10> × 51298510637495653901363<23> × 3045990308019871902430191141160812557793618513008639223149911675777<67>
3×10113+7 = 3(0)1127<114> = 9958794049<10> × 54305905957<11> × 554711845956529035779901603384095911608092759418946322823072623936745821785747652491457474299<93>
3×10114+7 = 3(0)1137<115> = 89 × 109 × 2820563 × 432040087316862334144741897<27> × 363408045426901508336853965827<30> × 698313378637433319644312675482359830254117350331<48> (Makoto Kamada / Msieve 1.26 for P30 x P48 / 11 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / September 3, 2007 2007 年 9 月 3 日)
3×10115+7 = 3(0)1147<116> = 37 × 1202857 × 122658774730152389<18> × 5495496158905196200091295440221378382924315504636677126346633227761598698101098371920658407<91>
3×10116+7 = 3(0)1157<117> = 941 × 7229 × 1005413 × 1768241 × 793456171721645674090119834605962552118405123<45> × 31263997790510739426533319802087948467956549868101057<53> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs for P45 x P53 / 2.15 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 3, 2007 2007 年 9 月 3 日)
3×10117+7 = 3(0)1167<118> = 991608181877<12> × 3025388510128411573298005142434025047727354352215767200398654400825662500737167664466358369287197026599691<106>
3×10118+7 = 3(0)1177<119> = 17 × 37 × 47694753577106518282988871224165341812400635930047694753577106518282988871224165341812400635930047694753577106518283<116>
3×10119+7 = 3(0)1187<120> = 29 × 73 × 141709966934341048653755314123760037789324515824279641001417099669343410486537553141237600377893245158242796410014171<117>
3×10120+7 = 3(0)1197<121> = 9746255741<10> × 21886913773<11> × 93792876069619<14> × 1014838616150641<16> × 147751564092636026549460363590839067806919556303848343368829011104122581<72>
3×10121+7 = 3(0)1207<122> = 37 × 2153 × 283193 × 45016298861<11> × 24521474895583<14> × 172367199446977<15> × 1093269834500648855661843412047037<34> × 6392851589358087090204524857849663762157<40> (Makoto Kamada / msieve 0.81 for P34 x P40 / 5.8 minutes)
3×10122+7 = 3(0)1217<123> = 23 × 107 × 105943 × 2044607702751648523<19> × 6979230306835332966261470773<28> × 80634305897026311868291137188315959326968015903591041646130428132371<68>
3×10123+7 = 3(0)1227<124> = 31 × 521 × 2657 × 144071 × 139782905835241<15> × 528131554443915112320432461<27> × 6572907672325994368234960644661984811352078028138564021130575701041131<70>
3×10124+7 = 3(0)1237<125> = 19 × 37 × 193 × 435811428691633<15> × 416592103205978657<18> × 2606793020110011769<19> × 339553265471003892270018410791<30> × 1375892525928161011267693952476821720167<40> (Makoto Kamada / msieve 0.81 for P30 x P40 / 2.5 minutes)
3×10125+7 = 3(0)1247<126> = 240353 × 967787 × 133187693714671747037424021997<30> × 9683398946669705008572309264729499781958600622317451617147818679362578763890277809321<85> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2528618589 for P30 x P85 / August 28, 2007 2007 年 8 月 28 日)
3×10126+7 = 3(0)1257<127> = 4720909 × 10534455986864899<17> × 42697713463908436112197336349<29> × 1412794170457977634954503119767881062698761257562555945470260957432227561173<76>
3×10127+7 = 3(0)1267<128> = 37 × 73 × 6762030461<10> × 78363271672974846821<20> × 41050596016202387245201<23> × 510607889803239347870049292765825535164528782394367612040521179773646147<72>
3×10128+7 = 3(0)1277<129> = 2685101 × 33851255863<11> × 12978558218195034379386149<26> × 275313088291577407642928246977003907<36> × 923703385381580265251720036954725538332661715176123<51> (Sinkiti Sibata / Msieve v. 1.26 for P36 x P51 / 5.86 hours on Pentium 3 750MHz, Windows Me / September 4, 2007 2007 年 9 月 4 日)
3×10129+7 = 3(0)1287<130> = definitely prime number 素数
3×10130+7 = 3(0)1297<131> = 37 × 71 × 33810961 × 1648142131729004126563<22> × 21200147141676683625158187167<29> × 9666519480363108756410741342046902197031024406908628685646707177884961<70>
3×10131+7 = 3(0)1307<132> = 61 × 3889 × 16673127629<11> × 654750113451724387<18> × 367843730195277468720927798645873350770134361<45> × 314917983297778113935616240983926140815612293301748461<54> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs for P45 x P54 / 6.51 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 4, 2007 2007 年 9 月 4 日)
3×10132+7 = 3(0)1317<133> = 20590611374091488546520676374415000816224551<44> × 145697470827641601340741249542086188044830839410971692164392935223681417160709307626970657<90> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P44 x P90 / 2.88 hours on Core 2 Quad Q6600 / September 4, 2007 2007 年 9 月 4 日)
3×10133+7 = 3(0)1327<134> = 37 × 29581 × 71206879090633339569010774993897538969<38> × 384932630573456592303493441248187029453637827755687637553671267379325800269120529793395199<90> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P38 x P90 / 2.83 hours on Core 2 Quad Q6600 / September 5, 2007 2007 年 9 月 5 日)
3×10134+7 = 3(0)1337<135> = 17 × 24547 × 515490719 × 30606905471<11> × 93372706503094537<17> × 7920075015505035621361<22> × 61614708112120683019353383604747871764589775720558852796938289744784901<71>
3×10135+7 = 3(0)1347<136> = 47 × 73 × 191 × 153701 × 24308048293<11> × 1225294222783659149674745891790542477846384760640765453178552304749161043457493805781151039210462781583819589281719<115>
3×10136+7 = 3(0)1357<137> = 37 × 6556535936327394866605979149660371778651962509<46> × 123664511059628497811157288760274150729201758246527989892496823924203364385516946923141479<90> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P46 x P90 / 4.25 hours on Core 2 Quad Q6600 / September 5, 2007 2007 年 9 月 5 日)
3×10137+7 = 3(0)1367<138> = 36225266507960712217403<23> × 8281512571731480890323903115149992908549080258941491179820186231956479289243636743385510859771195448631106956546469<115>
3×10138+7 = 3(0)1377<139> = 31 × 30347 × 27582727203473715137972750799973321<35> × 9338357328303256578758498008894337760073<40> × 12380440690635148293553334360514326357608119969517531812347<59> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs for P35 x P40 x P59 / 11.09 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 7, 2007 2007 年 9 月 7 日)
3×10139+7 = 3(0)1387<140> = 37 × 127 × 433 × 599 × 24615070895674894344095305163179405402499186034989389546512553042472690274217001507540991479613823309524129773696184760748399011379<131>
3×10140+7 = 3(0)1397<141> = 886591 × 21345509 × 870020740547606992047908247418054629224598409723907992361<57> × 18220563960260903608607526139448840316782587407515464316476336274810173<71> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs for P57 x P71 / 12.05 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 7, 2007 2007 年 9 月 7 日)
3×10141+7 = 3(0)1407<142> = 1159240267<10> × 3355488484559<13> × 689605891019146429<18> × 16044985525176124301<20> × 48029630362478262569811764243<29> × 1451250916352368211846287345233501107250419128707398177<55>
3×10142+7 = 3(0)1417<143> = 19 × 37 × 415553 × 4356998080213<13> × 4263373964673773<16> × 5528390479771761027088740445384511407888467191613266882495942970115243448045557566628782102388820352357577<106>
3×10143+7 = 3(0)1427<144> = 73 × 347 × 7793 × 14087 × 20681 × 25999009 × 7420475865516949471<19> × 472866768427802125793929<24> × 57180355199406003395710694670294872255933992610016221680979619117994690260997<77>
3×10144+7 = 3(0)1437<145> = 23 × 459383 × 128248879471<12> × 1352119565902402853<19> × 412360496428279684134266762455314955302583<42> × 3970752049300281989132003305040428926587105565745390502436467127587<67> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs for P42 x P67 / 13.30 hours on Cygwin on AMD XP 2700+ / September 9, 2007 2007 年 9 月 9 日)
3×10145+7 = 3(0)1447<146> = 37 × 149 × 4548472797563<13> × 77229184368528211553<20> × 15491241068552540105036234877156957913331632434707419884397089665026362420987079081715814031706642272209382301<110>
3×10146+7 = 3(0)1457<147> = 4813 × 5413 × 28477 × 2544313 × 13055969 × 12172884001913546407930227034471808163291537380024752217093389071137834033229275152059466733077673902911687232036254866987<122>
3×10147+7 = 3(0)1467<148> = 29 × 2437 × 553525949 × 3997619504444745287<19> × 6556640848925693764421202281051<31> × 2925815201213225488015353783615323323721015839286569481343687648583824330951467747743<85> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2420608976 for P31 x P85 / August 29, 2007 2007 年 8 月 29 日)
3×10148+7 = 3(0)1477<149> = 37 × 523 × 11819993 × 131159762755336138006427200282890755609778787971735622504379717325360965624796738067777153954145101463965096328132385415307660841907961849<138>
3×10149+7 = 3(0)1487<150> = 277 × 423242333 × 1269402691<10> × 2842318663<10> × 709218743323941559738817511999175046691509040094900367572317654521204390728324360432435174823587866229394134765594867019<120>
3×10150+7 = 3(0)1497<151> = 172 × 139 × 200475091 × 13089255395208126389<20> × 18215291062445336232193<23> × 99269467818197763097793<23> × 14846281069698988924500032578739<32> × 1060141324047330217134733111652288596956953<43> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1447189635 for P32 x P43 / August 29, 2007 2007 年 8 月 29 日)
3×10151+7 = 3(0)1507<152> = 37 × 73 × 1244863 × 20628811590269<14> × 1197832543309205649377891301884244716228803440401897936550987217<64> × 361081131072503212385537651948543045335365693158346674560705560593<66> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs for P64 x P66 / 27.46 hours on Cygwin on AMD XP 2700+ / September 11, 2007 2007 年 9 月 11 日)
3×10152+7 = 3(0)1517<153> = 8347351 × 7811046197<10> × 858719673857<12> × 250559653015574120385408539<27> × 577938539278524803843369748270872920429<39> × 37001485905141343750684997572615954124281964070904019247443<59> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs for P27 x P39 x P59 / 36.57 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 5, 2007 2007 年 9 月 5 日)
3×10153+7 = 3(0)1527<154> = 31 × 1960320883<10> × 234995429723777<15> × 12766708087797880775647643713694004841381361147278295433889<59> × 16454854639373394037106403236176282020045812281709905847229481803749603<71> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P59 x P71 / 16.75 hours on Core 2 Quad Q6600 / September 15, 2007 2007 年 9 月 15 日)
3×10154+7 = 3(0)1537<155> = 37 × 25735367917376428887903352224467<32> × 31505701158573848678701736130318189705992101267109759254218977833513289599982530505291377571538661224594650439297325530233<122> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=133750624 for P32 x P122 / August 29, 2007 2007 年 8 月 29 日)
3×10155+7 = 3(0)1547<156> = 307 × 947 × 17011 × 85013863614622230403517<23> × 81026516161317424585126385687853691355677579362917<50> × 8806151149339157734770802696564069152769229056077368044884311562147487877<73> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P50 x P73 / 16.65 hours on Core 2 Quad Q6600 / September 18, 2007 2007 年 9 月 18 日)
3×10156+7 = 3(0)1557<157> = 1428660435500894737<19> × 23751015386450850890960912782656510193131256880878674102473<59> × 88411764036120295668516229411892223895453769985635566390071101529293788597427807<80> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P59 x P80 / 24.47 hours on Core 2 Quad Q6600 / September 19, 2007 2007 年 9 月 19 日)
3×10157+7 = 3(0)1567<158> = 37 × 59 × 6271 × 119927861 × 18273032659591471572351258393792764128146724729192556969491941599651410105396297348901809018790775415066902115813536137657291680668027377119459<143>
3×10158+7 = 3(0)1577<159> = 89 × 2076619 × 259656955391<12> × 252655059854571780687683274450095709673880513<45> × 24742664377819752522172823349240990874103759568271850621675059742047926996980289580771977958019<95> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs for P45 x P95 / 32.13 hours on Cygwin on AMD 64 3400+ / September 25, 2007 2007 年 9 月 25 日)
3×10159+7 = 3(0)1587<160> = 73 × 1843607 × 222421799613457<15> × 100219607114202835442269081027255566630476151518805879599117844637392912859235645420536824043996720508825277514316030576926119809262344441<138>
3×10160+7 = 3(0)1597<161> = 19 × 37 × 5987 × 190783 × 2301583954628587<16> × 30214589326193078803<20> × 168821492926505124753835321037510889107<39> × 3182333894509189879957908738033612846872644789961813377047250471481774358607<76> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs for P39 x P76 / 62.61 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 10, 2007 2007 年 9 月 10 日)
3×10161+7 = 3(0)1607<162> = 113 × 103559004733<12> × 4634104042845913<16> × 5532089060402440837642968427106740040240958322867769746577136672372914761060455709275644038815423563734951865595093501849011518573691<133>
3×10162+7 = 3(0)1617<163> = 3733216672222512252402080024047876262175838601063<49> × 1801107624738145935914817354265795383914325232132040341<55> × 446167973934504101158694839309139582095409259666991720176029<60> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P49 x P55 x P60 / 43.21 hours on Core 2 Quad Q6600 / September 14, 2007 2007 年 9 月 14 日)
3×10163+7 = 3(0)1627<164> = 37 × 4361501 × 2951989138764677700040777<25> × 242727769684516588041691481<27> × 259447406437644695945964880358107079598502865896649596963355067931719255377640092560152213601875749473303<105>
3×10164+7 = 3(0)1637<165> = 93463 × 102367 × 5561993 × 2697746404826036755483<22> × 4075016412566873951820653<25> × 85121969595848139659769186241637634013<38> × 6024471790877011640388025283913980838326383051453673075231227837<64> (JMB / for P38 x P64 / September 5, 2007 2007 年 9 月 5 日)
3×10165+7 = 3(0)1647<166> = 71 × 739 × 24680319817<11> × 12015226484473081913<20> × 7814625344423111337812529497145365416512918941<46> × 24673318295604171900567002523536315906661600240732917021551158395138773289853506329223<86> (matsui / GGNFS-0.77.1-20060513-prescott snfs for P46 x P86 / March 9, 2008 2008 年 3 月 9 日)
3×10166+7 = 3(0)1657<167> = 17 × 23 × 37 × 19833927073<11> × 8996469684187<13> × 588640457649593408813104957<27> × 10602713652271671635338735723<29> × 1862064839791754846142240803810488476144261366504628162915046324765101490861512485961<85>
3×10167+7 = 3(0)1667<168> = 73 × 2820908683<10> × 47840528956935069857729<23> × 1357442863346680718028321638854705863851<40> × 22433231368448594492739585313305402233259675370737675880559365524717784659590253895181940293287<95> (Robert Backstrom / GMP-ECM 6.0 B1=2230000, sigma=3075737986 for P40 x P95 / February 7, 2008 2008 年 2 月 7 日)
3×10168+7 = 3(0)1677<169> = 312 × 220442934797851<15> × 68134668790873592384459578322644469894232860523283147276193<59> × 207842105702935771469899396383940505601339931626765063877009064283675813950588095504388659109<93> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.36 for P59 x P93 / 52.57 hours on Cygwin on AMD 64 X2 6000+ / July 7, 2008 2008 年 7 月 7 日)
3×10169+7 = 3(0)1687<170> = 37 × 321485385345676762706421506544388644469<39> × 2522076734340466176982866611144735500345304211081851607078673956180783695480227990278425308960588927381717464690492823021851851119<130> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=769407356 for P39 x P130 / September 23, 2007 2007 年 9 月 23 日)
3×10170+7 = 3(0)1697<171> = 11900149 × 116810359621<12> × 333724949161<12> × 351770377281652245322691967098920378125785292375511986421626711343961<69> × 1838398065903311066272707877014113500727599586799929165989126913413817423<73> (Serge Batalov / Msieve-1.38 snfs for P69 x P73 / 35.00 hours on Opteron-2.6GHz; Linux x86_64 / November 6, 2008 2008 年 11 月 6 日)
3×10171+7 = 3(0)1707<172> = 31620332097111024989233352721851562907652707<44> × 119542069001731768208656345412449977669924073427695871<54> × 793659208661801859516537543036477671956372358203480550399351605739016658931<75> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=4020180606 for P44 / September 7, 2007 2007 年 9 月 7 日) (Jeff Gilchrist / GGNFS & Msieve 1.41 snfs for P54 x P75 / 44.42 hours on Intel Core2 Q9550 @ 3.4GHz in Vista 64bit / April 13, 2009 2009 年 4 月 13 日)
3×10172+7 = 3(0)1717<173> = 37 × 337 × 114262317715380613<18> × 21056520170116679937455595003008874793699061658220099394077770991979796131391815754696100648637827420202655065065068813932148398207730911366301481522831<152>
3×10173+7 = 3(0)1727<174> = 283 × 1913 × 12781 × 123368533577<12> × 273075549184718167710054152780236687<36> × 1286968141075529714067699681620509401294955843542948675197022676011814934805266689072732719905213815274493968019250807<118> (Lionel Debroux / GMP-ECM 6.2.3 B1=1000000, sigma=4028931106 for P36 x P118 / September 24, 2009 2009 年 9 月 24 日)
3×10174+7 = 3(0)1737<175> = 2131 × 2539 × 388785044783<12> × 372247744413533552867<21> × 3918018457203894704610101<25> × 83101205384307732797112639371594904845329<41> × 11766835380003014836384610732539311187782328395943642994305646727529367<71> (JMB / GGNFS-0.77.1-20060513-pentium4 gnfs for P41 x P71 / 48.39 hours / September 6, 2007 2007 年 9 月 6 日)
3×10175+7 = 3(0)1747<176> = 292 × 37 × 73 × 107 × 521 × 661 × 90911 × 51322051021<11> × 828460334753<12> × 92722590232649274446142280534945064984657986755894010810494070455177597514980562558484084216931492824452182353744336309886774660549367<134>
3×10176+7 = 3(0)1757<177> = definitely prime number 素数
3×10177+7 = 3(0)1767<178> = 6949 × 3054553 × 27056747 × 493404835963026012897437638151<30> × 10586984945347812569293655796156978605781927234580251298728859025464296926453574495799663305462065258099367037772156197388089569823<131> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1041251524 for P30 x P131 / August 31, 2007 2007 年 8 月 31 日)
3×10178+7 = 3(0)1777<179> = 19 × 37 × 877 × 2377 × 955091 × 1475151073734211096553921<25> × 142740304627110833486422688998330293019789397894891<51> × 101790977042959291906914808841036511141159577020041503769999368278340596550847833365932261<90> (Youcef Lemsafer / GGNFS-SVN430, msieve 1.50 (SVN 408) snfs for P51 x P90 / November 1, 2012 2012 年 11 月 1 日)
3×10179+7 = 3(0)1787<180> = 724309 × 8113870839505271363511368113<28> × 51046889397874516674374640886900341936443838751528546555919718907710596677177554361021463321261206354156874905727408705794753863231816679987975771<146>
3×10180+7 = 3(0)1797<181> = 139123445599<12> × 3357886592224964813424893960925970858540249084816807<52> × 6421772340762707259521884513510240331991395754693705229521694663499363397052934796480061189870059727049936465643276799<118> (Robert Backstrom / Msieve 1.44 snfs for P52 x P118 / February 8, 2012 2012 年 2 月 8 日)
3×10181+7 = 3(0)1807<182> = 37 × 47 × 127 × 13725913 × 21623826491768316731972267<26> × 457661270578095137164137504134980583396871387947601110795572534703070051277670769241048807880195755464389757497291473633113527278035439907990089<144>
3×10182+7 = 3(0)1817<183> = 17 × 79283 × 31405992767627<14> × 269704249852213941977849110996392473758794465820651509487583869814723723<72> × 26277977836457813672653924866477178778975794876037608850035378717787586434503082719743426997<92> (Youcef Lemsafer / GGNFS-SVN430, msieve 1.50 (SVN 408). snfs for P72 x P92 / May 8, 2013 2013 年 5 月 8 日)
3×10183+7 = 3(0)1827<184> = 31 × 73 × 31387 × 18897703666390959239523719317917845075054654445979389633511<59> × 2235001705157404158463405732593419570696376461969687718092389576575647380791201282404260098119332443793067631748163077<118> (Wataru Sakai / for P59 x P118 / June 27, 2010 2010 年 6 月 27 日)
3×10184+7 = 3(0)1837<185> = 37 × 48825826060803420560275940333<29> × 16606187262476579971995760906943210586269694906092527719070492669074651946268267950831190725861763313025790106859512466549588197667323602041976271696074567<155>
3×10185+7 = 3(0)1847<186> = 1053148237<10> × 367359565561<12> × 9079315667762293<16> × 85405783470340571065076845909287543052200952350363226757713830415120497877703268968962293157264152219723022901790644421184243671490216153670724604207<149>
3×10186+7 = 3(0)1857<187> = 199 × 1483 × 61643 × 226307 × 3756989 × 409626733064891561693<21> × 473496810509582046821742464177596727335266811070198096053958472058069940681500075130313819549016230654385285739848949606960963289322741981781323<144>
3×10187+7 = 3(0)1867<188> = 37 × 605922879342007975663171<24> × 4806057246094980532459373243264236165811<40> × 278428212742383267914444914208047124305927368854314682108586270515137640422520152091667989368583141234316043633289010327731<123> (Youcef Lemsafer / GMP-ECM 6.4.2 B1=3000000, sigma=1133709058 for P40 x P123 / February 4, 2013 2013 年 2 月 4 日)
3×10188+7 = 3(0)1877<189> = 23 × 247068535739<12> × 1356701864133060161<19> × 2433152966732430024183070123007353531902806309832285192601048887931<67> × 15992712967036895948718699514895828611711981478735377666486535908861535915202603440781142841<92> (Youcef Lemsafer / GGNFS (SVN 430), msieve 1.50 (SVN 708) snfs for P67 x P92 / May 10, 2013 2013 年 5 月 10 日)
3×10189+7 = 3(0)1887<190> = 33521 × 8814854900159220551<19> × 131252454624516158629116042379<30> × 43954143253151000858584551069129739498328693<44> × 1759875184287334760567985008578206708383415261155223604501023422877699018454009608577912043111<94> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=791822475 for P30 / September 1, 2007 2007 年 9 月 1 日) (Youcef Lemsafer / GMP-ECM 6.4.2 B1=11000000, sigma=71571980 for P44 x P94 / February 11, 2013 2013 年 2 月 11 日)
3×10190+7 = 3(0)1897<191> = 37 × 12023821039<11> × 24740182686490123<17> × 834345923564404036855216234597229<33> × 1533754569246596800343579035700691859618492126401129432620297<61> × 2129963233079639445425492414094497020193914553913848036384671909368451<70> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=718876711 for P33 / September 1, 2007 2007 年 9 月 1 日) (Erik Branger / GGNFS, Msieve gnfs for P61 x P70 / September 27, 2010 2010 年 9 月 27 日)
3×10191+7 = 3(0)1907<192> = 61 × 73 × 4768139 × 11421913 × 1237031629937293209007439027146779589755228870871341611433436503570390796986837227129487100598490302577692315166847909176373244767505642951434728276295287500127591953321116217<175>
3×10192+7 = 3(0)1917<193> = 22039 × 375097 × 1112059787454691<16> × 642068743400393347285001478997421167763<39> × 1681024249843140161747771597374151664910161406779701<52> × 302344543644923459390790323502278773143278762026603255174869342665706773115613<78> (Youcef Lemsafer / GMP-ECM 6.4 B1=3000000, sigma=484142988 for P39, Msieve 1.50 snfs for P52 x P78 / February 10, 2013 2013 年 2 月 10 日)
3×10193+7 = 3(0)1927<194> = 37 × 4957 × 374537 × 2347550130303692987846536043<28> × 186033436713641467706744823075248193665097195594585990256073158564928103657674858202179097657763773806147132076266602430334149993988521991536520679398302653<156>
3×10194+7 = 3(0)1937<195> = 1734986326637479007<19> × 431168604266382453431<21> × 248787236500857218390561<24> × 439982137238951968875436976379228563<36> × 2181760916727482904956744337987008327579<40> × 1679220662527382761557265816940310453170712534544646764943<58> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=974592591 for P36 / September 2, 2007 2007 年 9 月 2 日) (JMB / for P40 x P58 / September 4, 2007 2007 年 9 月 4 日)
3×10195+7 = 3(0)1947<196> = 97 × 48305287 × 2620757107<10> × 51098821185311<14> × 11924605305477772589540332494963999896302871<44> × 400934277057996480858505066557758567993715884073205231275836329565022162411055295222107073259669869072646637934767577539<120> (Youcef Lemsafer / GMP-ECM 6.4.2 B1=11000000, sigma=3479621926 for P44 x P120 / February 13, 2013 2013 年 2 月 13 日)
3×10196+7 = 3(0)1957<197> = 192 × 372 × 139 × 443 × 36091254020598556209326577995494244927464115130739574091707<59> × 27314301942871410508815654558572642467742232077001241089872808230959660848582635043807507801145627359640160760847685024248893757<128> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs for P59 x P128 / September 10, 2012 2012 年 9 月 10 日)
3×10197+7 = 3(0)1967<198> = 2357 × 8929 × 1802680774763383<16> × 97148865973080265245073984193<29> × 81395854489413446318803739695291383680562514323245286068600107617125030508665056235124237334794958273834035260731457900762605517868916643151494701<146> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1336248685 for P29 x P146 / October 21, 2008 2008 年 10 月 21 日)
3×10198+7 = 3(0)1977<199> = 17 × 31 × 709 × 353042910133991541918917440370516843496015546212267909038130357<63> × 22742432269025299197225941631406058277981194146870968014849567950717154661158756620175583489442241367223874181066482274509852878657<131> (matsui / Msieve 1.43 snfs for P63 x P131 / 1205.18 hours / October 22, 2009 2009 年 10 月 22 日)
3×10199+7 = 3(0)1987<200> = 37 × 73 × 2753 × 6011 × 175837 × 11755019 × 2818428660441879356444251135174380528389149<43> × 115213424050479694234130033057298575833274994888455285113974117573080141096803655508144418190494874414193245252957994580865763147179507<135> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs for P43 x P135 / September 11, 2012 2012 年 9 月 11 日)
3×10200+7 = 3(0)1997<201> = 71 × 3881 × 15824563 × 1401171022897<13> × 1108993863080776935793291<25> × 28695538725855189461541207724094731927846842107655409102635929051<65> × 1542953595882576632076367515659010122547109956089668180409524374435450128767744409278907<88> (Youcef Lemsafer / GGNFS (SVN 430), msieve 1.50 (SVN 708) snfs for P65 x P88 / May 16, 2013 2013 年 5 月 16 日)
3×10201+7 = 3(0)2007<202> = 167 × 4480806397<10> × 16098464849561<14> × 20640840878222830361<20> × 29822878112774732139151957<26> × 404563968552860957554114345693870272759057775354797298394146752092092648939324529196581084513766079411962916903089745735099544821169<132>
3×10202+7 = 3(0)2017<203> = 37 × 89 × 10937 × 437647254442200871<18> × 1903299368935117038762202127087391621869007684158926911747066465339934583588913792176627834090520773155470988362511396812768681956921949456829734729902605268605974698021871538237<178>
3×10203+7 = 3(0)2027<204> = 29 × 62057 × 43125287759<11> × 35471066646755293<17> × 108974836411015028757750711986016543220783381879699504976036837048029909454657431752518292287872960388598846327069505280210618355440413981903551060820015690493149687203737<171>
3×10204+7 = 3(0)2037<205> = 2111 × 12379 × 80141 × 360193 × 36529453 × 83762087274812203759<20> × 4269986142493572515510539041322472993083083125849142037361<58> × 304396957359293809435131697777670257413950147980070263033236390457958665868388838721348354477163418973<102> (Youcef Lemsafer / GMP-ECM 6.4.4 B1=260000000, sigma=2078429522 for P58 x P102 / October 23, 2013 2013 年 10 月 23 日)
3×10205+7 = 3(0)2047<206> = 37 × 3455209 × 3534497567<10> × 324732461981<12> × 39276464439197211640627<23> × 5205463783813303785261694765096463111777693694813810284172846250844767504076990057204611602468040887997483885901458999414284569067823119138298630819501051<154>
3×10206+7 = 3(0)2057<207> = 57571187 × 15557878282469<14> × 21651171190959241<17> × 309862899046280533<18> × 197694964518197399767<21> × 3111798304100902138163965386768954663591679<43> × 81153579522963849609520526889367170542293005842928107070828858437001152440449294513323461<89> (Warut Roonguthai / GMP-ECM 6.3 B1=3000000, sigma=221886097 for P43 x P89 / February 18, 2013 2013 年 2 月 18 日)
3×10207+7 = 3(0)2067<208> = 73 × 12049 × 20401344697<11> × 13517769210499<14> × 1039453663496936952421<22> × 9432433874058054019969977334241830982668833401295286097283153632918611<70> × 1261405341237284280025488123184306749297634328292156828106939370955274955045833298797987<88> (Youcef Lemsafer / GGNFS-SVN430, msieve1.50 (SVN708), Msieve 1.50 snfs for P70 x P88 / May 6, 2013 2013 年 5 月 6 日)
3×10208+7 = 3(0)2077<209> = 37 × 431 × 3930569 × 409705217 × 649507979 × 711991376789893<15> × [2526132448373684387392587442344985993571181769024482685734617685264512434954640425855956007563497816454094811479119801134117885819013830191666184455099488766990498651<166>] Free to factor
3×10209+7 = 3(0)2087<210> = 269020061 × 473284516123<12> × 32168106280008062849145337<26> × [73246823695618669062791828070732995680694584415532410034186585090636713022538597833293320486263958295290158307621663069174543585611064749029324637932363295858165137<164>] Free to factor
3×10210+7 = 3(0)2097<211> = 23 × 5479 × 134649782557888060308791003<27> × 176801710292993682592052588384665813916031608791840858751299286523556560079735718717557026828145755403689403483862737142705560771737618552739822192858845571804783402701657709617157<180>
3×10211+7 = 3(0)2107<212> = 37 × 953 × 175333 × 2383169 × [2036142295109864932825841359544354720031301730205960408838992758337733914959486494412302211704800888168388909197283925554541820786709309625846382028580199017846105544560821910089896952489781225431<196>] Free to factor
3×10212+7 = 3(0)2117<213> = 8387 × 6816599359<10> × 2104478221463<13> × 141130881727709<15> × 291179699617744834032197<24> × 105302178752345098917153823<27> × 1175632029747201560722147952723780985322274976581<49> × 490129103362120975472383181391068484852476506979787990886015367023341959567<75> (Dmitry Domanov / for P49 x P75 / February 17, 2013 2013 年 2 月 17 日)
3×10213+7 = 3(0)2127<214> = 31 × 256138979 × 256466957 × 323739399756221177<18> × 404606877942395817011766713<27> × 11246662164720455194679301275822197440489848222382329333154619499423570654618049078233015321537779978267971117327468717008177949096251531080632944709199<152>
3×10214+7 = 3(0)2137<215> = 17 × 19 × 37 × 683 × 4203804056816289073472794303279470241000729095124703<52> × 132529256046524403310704082852968707296003826722941373<54> × 6596933095852949776565774399108017101273378542196582965177686649514960025136222473057240305364592397641<103> (Bob Backstrom / GMP-ECM 6.2.3 B1=900100000, sigma=3738441443, Msieve 1.54 snfs for P52 x P54 x P103 / November 28, 2019 2019 年 11 月 28 日)
3×10215+7 = 3(0)2147<216> = 59 × 73 × 977 × 461467 × 1152677483046521<16> × 15309508366871707406062728790691<32> × 36984778148192734600624644012817451<35> × 119170281303569645345574388800989299473635468109349386201137<60> × 1986328771028970138601686290970375607792144439596114344242848927<64> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1469045866 for P32 / February 16, 2013 2013 年 2 月 16 日) (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3311041823 for P35, Msieve 1.49 gnfs for P60 x P64 / February 18, 2013 2013 年 2 月 18 日)
3×10216+7 = 3(0)2157<217> = 492016580249<12> × 6896459787426653543771836220821139<34> × 884128333165563487895755529159740581457857083087773846312080545210327786496677455819207427860083287674188394628305072186699618138489176451577048455649585476961328510842437<171> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=931395692 for P34 x P171 / February 17, 2013 2013 年 2 月 17 日)
3×10217+7 = 3(0)2167<218> = 37 × 181 × 1264997 × 225895062247<12> × 307270178000367387812659<24> × [51018103471605800367956575474397215392279971283523577894215462369142805159398799263389400274521100136221923061939892322343984851084475557057226939774919166562890444245464551<173>] Free to factor
3×10218+7 = 3(0)2177<219> = 277 × 2389 × 442475057 × 139697411283202441<18> × 13790071564294055963<20> × 50522099578618355254635154907<29> × 10526894566428900590332689956307222395822960377469595363110611604105377687280750588331237820655499100206812622234672040951724197041238309007<140> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2966099369 for P29 / February 16, 2013 2013 年 2 月 16 日)
3×10219+7 = 3(0)2187<220> = 1213 × 38726057603<11> × 94687179317<11> × 5147993858489<13> × 3807784524128821<16> × 1799238761569059182807683896651713913868734425786131807632242843<64> × 19123474636457497325474709993591955484189686213476891086121709092614837586069221001500251087622197290067<104> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P64 x P104 / December 16, 2020 2020 年 12 月 16 日)
3×10220+7 = 3(0)2197<221> = 37 × 11801 × 139024810376199218392715794966308012198369755129297552949636349522328522960053<78> × 494206449681261094435562424256838679222486167579750700800096967311654756544017661813095496416164047495382275165707303694647392488054138887<138> (Bob Backstrom / Msieve 1.53 snfs for P78 x P138 / April 24, 2018 2018 年 4 月 24 日)
3×10221+7 = 3(0)2207<222> = 293 × 10903 × 969497 × 2804383 × 5618707 × 83360122622417570220171590970859<32> × 4750364721408905675428950139070656528735597436347<49> × 15523946656666842390118678740483270319932677240057492029640131258967469988699028608387495140465320370608660582368753<116> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1811546908 for P32 / February 16, 2013 2013 年 2 月 16 日) (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P49 x P116 / June 17, 2021 2021 年 6 月 17 日)
3×10222+7 = 3(0)2217<223> = 109 × 2826627203<10> × 20977398881<11> × 298009268733479068836827661738322101452083<42> × 1557560104054918098210221476103358154732756144608676124558729843062905037802321758707828086704645286945471069207955746633796104752130875535100550181090568989467<160> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=338538793 for P42 x P160 / April 2, 2013 2013 年 4 月 2 日)
3×10223+7 = 3(0)2227<224> = 37 × 73 × 127 × 313 × 51061 × 97790078124103<14> × 5202357941686062457<19> × [10756333845761009575202805557939182309032300414644855034455578374703369976350990972857893234381917274615022081844352184956122968220187330184669108504209735593653324693961964658847<179>] Free to factor
3×10224+7 = 3(0)2237<225> = 1627 × 8867493990672899<16> × 262987182984499018299453599<27> × 31154060880295010326525915046378405163979<41> × 270373237759043910478489482172585012737937<42> × 9386849390463998353709406138259548987924165849516805950312719296985314506515030586606522682014667<97> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=68468456 for P42 / April 2, 2013 2013 年 4 月 2 日) (Youcef Lemsafer / msieve 1.52 (SVN 942) win64 CUDA, GGNFS (SVN 440) for P41 x P97 / December 1, 2013 2013 年 12 月 1 日)
3×10225+7 = 3(0)2247<226> = 145243384103533<15> × [20654985550746513734316195728027386828787606321917787006896546542973550153350320121797639380461728997051292964561390868585556497380504293102288562914788312944727462394387145619809544320065266779454014473545917379<212>] Free to factor
3×10226+7 = 3(0)2257<227> = 37 × 652699 × 5893973016991957<16> × 21738226090892510077<20> × 9695592156476918686134016909974464954089776207237027055643355969088523619491245015339906451011641296076059350505551074675822667667138650594250260868247580253639927569282782617021839201<184>
3×10227+7 = 3(0)2267<228> = 47 × 521 × 4942709 × 180612171151<12> × 10626528255439<14> × 583765589058891691564933<24> × 175269876742234189806058709071<30> × 12622240301920220600381504470576698668348838195349861607167989349802977901999289110507155541966739340441634356097546975632991355540392697527<140> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=581379968 for P30 x P140 / February 8, 2013 2013 年 2 月 8 日)
3×10228+7 = 3(0)2277<229> = 31 × 107 × 439 × 3313 × 581639 × 4375141 × 40110514861<11> × 580176994673<12> × [10500875596903032763884309441558918803861922232986971594456955027000192790084387788630012678747486520874488888526565390910437999145099165518984335765125293067805513199192226682332790699<185>] Free to factor
3×10229+7 = 3(0)2287<230> = 37 × 1365583 × 206850031 × 2870422586299533582937309773096125845159212328550355560364611294551480663564144413663132435769681046449694311253848007340443208597104106022609362352892027685456464819486489920093597248452694895716222828296087114107<214>
3×10230+7 = 3(0)2297<231> = 17 × 191 × 598669 × 620010577 × 563583601417<12> × 1478702394077<13> × 1972153302189752657<19> × 92601571170695111544465326458176329<35> × 1635516564225167887613216362315714885798530094290990438103212631946304042995363657738055469047619485256352962875229196631682016831961281<136> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3260755387 for P35 x P136 / February 16, 2013 2013 年 2 月 16 日)
3×10231+7 = 3(0)2307<232> = 29 × 73 × 2720562250019<13> × 147308663712661707798483604427<30> × 3536009630961050321561175321710845883798072147904267883837873278552389154321443076151290248796229520373397347300565982396269373580965222236040192339552759496378349135801533008368681562267<187> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=2914894320 for P30 x P187 / February 8, 2013 2013 年 2 月 8 日)
3×10232+7 = 3(0)2317<233> = 19 × 23 × 37 × 380867 × 29269541803<11> × 353888218208284019133101279391804886403<39> × [470308383715615733943781897782939854837085069873393126899110055781329611624299030798331809282032109410933458739331865208113536333669579466213146065729149581139706787118142501<174>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2091588175 for P39 / April 2, 2013 2013 年 4 月 2 日) Free to factor
3×10233+7 = 3(0)2327<234> = 18199 × 85014889 × 193900414561514676676875624465894072777130299574017010076799341892191441530045832787898951189182359636927827229667622161658129035825097782727387720753230531759016775547438793515504810453008425609857280394394799176646575337<222>
3×10234+7 = 3(0)2337<235> = 322501 × 39564673 × [235116229497571765491837189764099880150451154319651287996106515301444788113703441822628944269215307480139661504806740339189429552617407273574123724292866428263559361437603507013122921773936065134872669967799761658051901659<222>] Free to factor
3×10235+7 = 3(0)2347<236> = 37 × 71 × 373 × 115477384313<12> × 38070751597116457927<20> × 6964083364416778314475677207833974838706979363732012804227270812224380032996832530254802135966406639249095563973235561901406650427898722644618330987931148392791090353543589238750169764554347249950167<199>
3×10236+7 = 3(0)2357<237> = 6737 × 41422096069617839<17> × 6709529360460776329<19> × 249729026332675607530766195161099<33> × [641595861880340467557832794450234066553478993140900191782203091496087524716547162168227709617616084503209147064885363934543425447808732351348905841028018139062441619<165>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=246550503 for P33 / February 17, 2013 2013 年 2 月 17 日) Free to factor
3×10237+7 = 3(0)2367<238> = 131 × 3527 × 14783513819749<14> × [439204547145612724775767602345372509528084800543887024792429405359817538531480904703063835189737537116130038970692925243330701693708139282788719712088189908165391498299020354045893261565411074081151768133107457975895439<219>] Free to factor
3×10238+7 = 3(0)2377<239> = 37 × 179 × 46997 × 108949 × 4904225780431<13> × 50895226174703<14> × [3544260302883648546057867289912837191904022323016174724623091685649020528557556522763075295221426421013662644819611172164262559279096479853486764955259469200919259851913654232978022765854856341642721<199>] Free to factor
3×10239+7 = 3(0)2387<240> = 73 × 13873 × 8315833741<10> × 83269011521<11> × 459227736727<12> × 931559695519781173279123381638849077864286350874787269450679410022025725713780564128876058420926296806861407088459183320969921477610432687434745657413390133166077376123024277273278249480637914533488189<201>
3×10240+7 = 3(0)2397<241> = 269 × 29272728393737<14> × 1081913159420212215283775993<28> × [352138385196499252842075374294924596067115522718400742704461702917624909200282156397884898904717952463358856842023616015231460012236807196525809123904101562529614779407876023179291638065701335522083<198>] Free to factor
3×10241+7 = 3(0)2407<242> = 37 × [810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810811<240>] Free to factor
3×10242+7 = 3(0)2417<243> = 139 × 3371 × [640247220793522405451491669316578774950967733674229409115839929658172008818338387729448597751878592053678326991328918473053061555501964491889134791247393660272019702541141219329490427236970435517501157780390934953016524780768680813284703<237>] Free to factor
3×10243+7 = 3(0)2427<244> = 31 × 51421 × 18713437 × 515469167078298127<18> × [195102480167271339396771789451034079470802404204563286852445183572712028526388109546180435103572178730015789391170008943408096471545442545383606054189027579470376051771099023667074096783449173813798172094794013343<213>] Free to factor
3×10244+7 = 3(0)2437<245> = 37 × 749249352958559349051537209085323256352699<42> × [1082164178866706874308313035483424502524613749412168821147200771417651397116615857833095536061322955028770737458749922755480420258184823128017313369761534007405665329112903500002276317257541080584959489<202>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=4055770585 for P42 / March 7, 2013 2013 年 3 月 7 日) Free to factor
3×10245+7 = 3(0)2447<246> = 640223 × 108689465987<12> × 1314689353188586192902247<25> × [3279286655557191176518750077414630949464635348358714556483172448130202169366760858443908205213601085738984766391137067365196159761705682378702596557195509867997153459098634964706228747475768171513571400981<205>] Free to factor
3×10246+7 = 3(0)2457<247> = 17 × 89 × [1982815598149372108393919365499008592200925313945803040317250495703899537343027098479841374752148050231328486450760079312623925974884335756774619960343688037012557832121612690019828155981493721083939193654990085922009253139458030403172504957039<244>] Free to factor
3×10247+7 = 3(0)2467<248> = 37 × 73 × 3301546613865931<16> × [3364180097206497791529406241910466126987742494793752636667413381438428315870225679099764080308465206325354032701903526666795836832930423204778704365020025273156797760832089138089438657865178020633066839508668533091351588156141897<229>] Free to factor
3×10248+7 = 3(0)2477<249> = 665796868817<12> × 11993271422864609744246017402556166679877<41> × [37570056131254015473810888385615588001199942971836739219168001628287912224313900119414207560912536255034332784614416687276365438702623251403496012548991074833244529912545359538287164535125897183723<197>] (Seth Troisi / GMP-ECM 7.0.6 dev B1=1e9 for P41 / November 15, 2023 2023 年 11 月 15 日) Free to factor
3×10249+7 = 3(0)2487<250> = 40050167 × 1723638127<10> × [43458109637678067108006543122258383638000416730645592232829359630649843948462669037381003301983672335902564281623142717357097280615906581045498742652651559132009939610549401190875297652331982685058476767159718036521226342632647393823<233>] Free to factor
3×10250+7 = 3(0)2497<251> = 19 × 37 × 1037860459249771<16> × 41117524827390138339408680524167213214423543414702156198476659514705797572953563533895846710592867544458111900404721106243630818626914552652522787693639199876254353073837717665072470108749354172531981713377631399345948395946322194539<233>
3×10251+7 = 3(0)2507<252> = 61 × 1229434062673<13> × 76923699133670093<17> × 2697260391814113539312508557649147883769<40> × [19279827445128695681286994521451236318215416880570383267836739361265782578450039505541555028812458950028197210747050397138014195768607928154496199928148470016095298203561016495471207<182>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=599025282 for P40 / August 19, 2016 2016 年 8 月 19 日) Free to factor
3×10252+7 = 3(0)2517<253> = 702077 × 1021196959<10> × 618151588361667754213<21> × 335037618566124702952390519264883<33> × [20204049947148368536599946042875025309903113153658015631269215564806420086114764670902028595324160215115074938857940320763235003141576630895008185178353341414410848001233374114542632531<185>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=4281918355 for P33 / February 7, 2016 2016 年 2 月 7 日) Free to factor
3×10253+7 = 3(0)2527<254> = 37 × 233 × 141631309721485840264479021442263641<36> × [24569953715410791983447245767573831839016426209700744800742215982674684866498337635017193699322282945005788212942216911168204570590230200386185381968502569302287544702594927061739974196647613943634000240609821849787<215>] (Serge Batalov / GMP-ECM B1=6000000, sigma=3835349630 for P36 / June 23, 2016 2016 年 6 月 23 日) Free to factor
3×10254+7 = 3(0)2537<255> = 23 × 4057 × 25639 × 3186899 × 41132400319<11> × 956610128475176482640016376848738637092598476905827475942525449408471212637644266962389630885943874589679501324023474107224975839102023489914629589595319527179401151200180614931817039421623050975282325263030028482337389988722043<228>
3×10255+7 = 3(0)2547<256> = 73 × 344873 × 1064341 × 910116266999<12> × 941066467036928077972288021<27> × 130719757106617003619853309832425031548680320426164533539282447472540056718316693079392649082372318233619259765962275272630810696130174057149080839559958235801437734444978187018142685267053572981060061897<204>
3×10256+7 = 3(0)2557<257> = 37 × 1015812071<10> × 6332218676621<13> × [126052149829630259629864946918532697966993726830345426335058529514556952405250326551368722038097475124148104587915716501452166925374041308838731507307293953065443274607459418392803192055363404554449579931647204610487652068599607745921<234>] Free to factor
3×10257+7 = 3(0)2567<258> = 887 × 60307397 × 1210767970499<13> × 150831343903573<15> × 8766744791214661<16> × 3705056361251938702181041943546677<34> × [945456047275081639132979173684342256988899923093211164579300542107619127751519303548917351733143480301926761682802247286468152444839831295933982702716103054871628209691627<171>] (Serge Batalov / GMP-ECM B1=6000000, sigma=2305041146 for P34 / June 23, 2016 2016 年 6 月 23 日) Free to factor
3×10258+7 = 3(0)2577<259> = 31 × 53681 × 3018307 × 12466331879<11> × 297551552633<12> × [161018081262837378916147323384926829237264948657931173003207125486558229677123713572399202506330878222472576251206905038592116258491476065270548287158228428590985371011842878365921488856853500794095690997034188597614626310413<225>] Free to factor
3×10259+7 = 3(0)2587<260> = 29 × 37 × 1346593 × 12290904793<11> × 58016268703<11> × 265747871780797246907771<24> × 109567495988151759082209987647312274703435291615914865616167938684308056228211916531921676726569676364932834906775580338996939133297976510229220365844506164365807269934498593848219733336828782529278411707907<207>
3×10260+7 = 3(0)2597<261> = 16491841 × [18190813263358529833024705974305718809682921391250376474039496257573669307144059902105532062793959752583110642407964035064369102273057325740649573325379501294003501489009019672212459482237307526794613166595530480799566282502966163692701136277023286848327<254>] Free to factor
3×10261+7 = 3(0)2607<262> = 3361 × 4961621324557<13> × 82504232317393<14> × 15279115396065107591<20> × [142710092693937874724248609065069421658618783172567577301943774000488282082277733404542484436605927733198750591768039737121492736373851913549795304985539248631199920291974530590063302198706299311729261834323524757<213>] Free to factor
3×10262+7 = 3(0)2617<263> = 17 × 37 × 18551821 × 40523387 × 63442213460817740532760511695310159958981714159885652477154048600757364859305205812134233820410234007047829324311213547024576429429189237930767105585497608207075549486099240876692771474771092814304470368472684070961101145693019842172379125144629<245>
3×10263+7 = 3(0)2627<264> = 73 × 4109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410959<262>
3×10264+7 = 3(0)2637<265> = 4365179173247<13> × [687257013042256517193953596335710699521629797993668160455956606931098522880270020212655611194421426337859490125114437298974241666747126283036872678694486304963973097989006336899041059084136901797276623553631317113006180072573958815154970082749618761081<252>] Free to factor
3×10265+7 = 3(0)2647<266> = 37 × 127 × 41149 × 556279 × [278909854388298892825907541136820381044216272696253722269263026998561743476155492824024593735543257811734982716434386064478404218619547900097371727432418951100981355761763363293858054151107518038270911018487104631118386468881421146056103874297171538783<252>] Free to factor
3×10266+7 = 3(0)2657<267> = 359 × 1103 × 1783 × 3623 × 15881 × 40519 × 329961127 × 1677861288709<13> × 2339255452643<13> × 13687292579788837<17> × 62344803742832881657<20> × 25263508209260142365190782809<29> × 321327234650634537440057132755759<33> × 20316063481433238395896661553423651239436992428274557399624017515398881588433186887457729395366864600560854102692971<116> (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=1568538400 for P33 x P116 / May 27, 2016 2016 年 5 月 27 日)
3×10267+7 = 3(0)2667<268> = [3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<268>] Free to factor
3×10268+7 = 3(0)2677<269> = 19 × 37 × 257 × 83497 × 638209971901628382001<21> × [3116006456554113343538745764579030928085617578869576076562507969382286821143080546621842768294371280545910713303713095881618979511549819806083758880128498839342089484420432663770910643867243544533412742990785722126650344503794826627476961<238>] Free to factor
3×10269+7 = 3(0)2687<270> = 3673 × 8839 × 151289 × 190825846726078087743388244738449851329<39> × 320075654425433440208923621435842794289157885636758660222053416446596880545898542741307124099104882258955435487033289449721857725724779128579527169066547655746562690589942838803895900495764410290394466732423305849578801<219> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2841532960 for P39 x P219 / September 26, 2016 2016 年 9 月 26 日)
3×10270+7 = 3(0)2697<271> = 71 × 2927434787<10> × 99857393665809931493<20> × 15664445388958650492406787969625611<35> × [9227422944002407612207340006688567333501321670635545219077585732393095367232330014972444411385236467800264647573530019718567955239973374831681064979145442815409333741401898828462934680492918762023989382317<205>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=1279789687 for P35 / May 27, 2016 2016 年 5 月 27 日) Free to factor
3×10271+7 = 3(0)2707<272> = 37 × 73 × 124161491 × 755252089 × [118445295604753296681667418798448369372924815553661925645014192009781705532748991818399151614734367469789991384602324525444039678251610851383433295895923360165579655124889930060218020265755689907725546444685047116912559822078746458949817438285115455993<252>] Free to factor
3×10272+7 = 3(0)2717<273> = 4026991337487226013<19> × 1299568899013677342601983965238973<34> × [57324628639882258030076295068523555632538186040130493015081667158751301350699039293943313274050352321415913123086656741965659393591901155114865847875697458799758326799960464207586698044123468997595072017893671981380984943<221>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=2992273977 for P34 / May 27, 2016 2016 年 5 月 27 日) Free to factor
3×10273+7 = 3(0)2727<274> = 31 × 47 × 59 × 113 × 1123696851473806795362713<25> × 4349826818487243959492423<25> × [63184436589732388746797983640510821526828326643937870782408073771720067619996644224829914071552550793437976319559115791898786067731980004206820971203097932012361453842325742089301019774620890785072341983492594592268747<218>] Free to factor
3×10274+7 = 3(0)2737<275> = 37 × 3461 × 302927 × 1905984383<10> × 119062390104523<15> × 79218769770939311<17> × 124257586329525269160594214913349211<36> × [346206331487231016938737441267310577042970079833363353680161914440283395400260021857386464238325531981080991519076399842311553482114330421378282048573012410510895061821129299714788855664217<189>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2695176849 for P36 / August 19, 2016 2016 年 8 月 19 日) Free to factor
3×10275+7 = 3(0)2747<276> = 89653 × 3346234928000178465862826676184846017422729858454262545592450894002431597381013463018526987384694321439327183697143430783130514316308433627430203116460129610832877873579244420153257559702408173736517461769265947597961027517205224588134250945311367160050416606248536022219<271>
3×10276+7 = 3(0)2757<277> = 23 × 863 × 3503990729985156500420678576002843<34> × [43133994085101951622405032530299490227961527942381117944375875531887983023084270316530196273113677148810954620207173345939414501671903374921490516789548575813479841636145244026592935960597203793981797201874176108877693453247557732785519901<239>] (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=2747123316 for P34 / May 28, 2016 2016 年 5 月 28 日) Free to factor
3×10277+7 = 3(0)2767<278> = 37 × 364806217 × 9874017767<10> × 225740828026187947612124333<27> × 3496762666350801742445833973<28> × 285159027512783623910591663485945944972928526750331733774825613612168015963735840190648268498852865887721735062752860792657083883136181420071683051223236876154711565972693058517998261520074466073423931861<204>
3×10278+7 = 3(0)2777<279> = 17 × 4051 × 503778887191<12> × 190006664231657346644267<24> × 369398858104885345028116207<27> × 123198592240635516860765637170250283372621242182699122043619524367722198811529389640249034652346117508001208496250091935990078359327903850474176610278099922364360701997719264660039802682876664409651586705278515199<213>
3×10279+7 = 3(0)2787<280> = 73 × 521 × 823 × 144282384927075270011<21> × 10520540470064206663297<23> × 63140711633848032579269249078691081357882435202126243795083057991225888198540074806294445392285927533652507094788232809736980203034998026473652785749052107938057686777087912612671224375194200093208910133882787075144007197607484819<230>
3×10280+7 = 3(0)2797<281> = 37 × 6642553 × 215194278389<12> × 587186472265363<15> × [966001366259251064324049703237781909018819406467320154843963866630472607182259827416140397612756705101731087062006625522586932619602661929299493071362488370156162969706380384515752709115532730060107692968768173202733092593764604903044836220448541<246>] Free to factor
3×10281+7 = 3(0)2807<282> = 107 × 114941 × 12422929 × 188497973 × 29547136911037<14> × 352546505084740468508197458015742688191867299448690121890878855330922711968473005490701559185962728248199339772415451942883177756878046380314654783256072136556933670776903030077009008390787221450174806842262448372243313170914098619692165510272009<246>
3×10282+7 = 3(0)2817<283> = 1843489409<10> × 1411015904372601479<19> × 17250719192914733818653763<26> × 1438596712461100071114039104563708057<37> × 46473184152315097314126930022150605313886357963854355344460183777400844779762272939860087248120258175965879592802985089454574125075907740251917807833037496463797539727670461850446093716202367907<194> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2700844742 for P37 x P194 / August 18, 2016 2016 年 8 月 18 日)
3×10283+7 = 3(0)2827<284> = 37 × 905448581 × 4599938112171007<16> × [194672116004856139872267371403944512518539282031626150238770774136086555825098286332580856618481621896729270797248965130937799081484215242304434991363636410576947037928966314984780896745920351612162185185751888839503981060171974384665945778418853233723056833<258>] Free to factor
3×10284+7 = 3(0)2837<285> = 1301 × 1451848043<10> × 6380463141675209<16> × [24892618912750418467074266371643226652369935776851619341748239744395231279589260191014809993177011035455124453426989681963651680447219414638264245581202411188946719799051812482689044869202654105985714184463890414452010352219557032298949445302113198197231161<257>] Free to factor
3×10285+7 = 3(0)2847<286> = 199 × 647 × 114311 × 6729310166479<13> × 111225410998772796659<21> × [272333650878372694713618139852203602687674695852151204674941906684749652150406875418602610318863377208658138231059133218983641019657145107504911030827746624999413826756121566942773540535291840047037381335202998372260696676904530719204603297189<243>] Free to factor
3×10286+7 = 3(0)2857<287> = 19 × 37 × 1109 × [38479939766067619515486251758853913474007442020350757477614295041090162346865873039286735836496170604660946837397883859845798054710778359394941427118352750738494177343781064534706981672004689421992824773898287257881012330255365706934213412311271928755674187784671387727721076873941<281>] Free to factor
3×10287+7 = 3(0)2867<288> = 29 × 73 × 277 × 992371 × 1072084087<10> × 1124454553<10> × 1195220189<10> × 6824349744047017807963103219393087378507<40> × [52428400659218822652930178733613872592330711135932430857015848288249389397512516200115257087280942969879075645114550178071668552496486125957621667811114632789474773544323292326785905289134471765307504038666421<209>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=198430419 for P40 / May 29, 2016 2016 年 5 月 29 日) Free to factor
3×10288+7 = 3(0)2877<289> = 31 × 139 × 1599540426834935527651991<25> × 504453190959145816602697453002071635511849<42> × [862836813243802398143140376176915697408440196752694486022926187106200263659383009220767493865971440243521152605332999490066846395550217581321691945019542786404683783424087282030103421054901065081891860075739801412113797<219>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2813357601 for P42 / August 18, 2016 2016 年 8 月 18 日) Free to factor
3×10289+7 = 3(0)2887<290> = 37 × 44059 × 171513869 × [107296523580435316571409065941009188317022747956992407421342244372667549693524192098388513369330978665287578133766553098554898332557480508543250903934041969268109847872842511684952446578477710833800120296703022410480761759648719641600926318917057777026843185770643805081576741<276>] Free to factor
3×10290+7 = 3(0)2897<291> = 89 × 2441 × 133253728585989047269<21> × 10362966607931262445984029819259530929400614922123093203618749122401914124309838222544698580480763795115238950924728587117674797930012695478330378747752981216342841197347182888930971550463772325973655857614690363750933880420329837454387384864989703449299535170337947<266>
3×10291+7 = 3(0)2907<292> = 97 × 986137 × [31362614983056504068478638959524757695311547278896413140312607283011815478389281746877582482658120451656363716594907783928184044271718211002425595096994584376824160763342631268407960170398941557742823818137228146370453180064094521736273255104587055296022366311600396711989443678331263<284>] Free to factor
3×10292+7 = 3(0)2917<293> = 37 × 57649 × 22066258049088175241797<23> × 637380921499746273124268393665777953900497174114228289505552325288534892076395269423543410527003065992821747442390109345308498008737778189366253948648573218961879633862814189381136292330734770265776587779072827437874403079874251669305174913404164117075775577584687<264>
3×10293+7 = 3(0)2927<294> = 149 × 91099 × 35573705446289<14> × 415285962254304033125953<24> × 99265745061833633784662981<26> × 1083142479345357705806747893605689<34> × 13914257157477870757791107158641632253455435362317046017596686555167276077023497257300709853316392697975686131299114310784391290398713204125095464725608089333627178797443190455728899595893269<191> (Makoto Kamada / GMP-ECM 6.4.4 B1=25e4, sigma=820694423 for P34 x P191 / May 29, 2016 2016 年 5 月 29 日)
3×10294+7 = 3(0)2937<295> = 17 × 11549 × 4832462506098631133658654625059342021736433<43> × 3161982477193659420487258971220179921374004863731983590341137961805231982439385879964430302759999566464506759400696929532960326621362799827335650288728236575671226407362550329280549953816074629428501280585413097013018834113186003349647603593262963<247> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3489537725 for P43 x P247 / August 18, 2016 2016 年 8 月 18 日)
3×10295+7 = 3(0)2947<296> = 37 × 73 × 118203367 × [93965152518601871814446800885100069672900104190865451382686647761742438445996190686913947053386483542363123778626212652733546899796579156505499636968864079542432839244004842919646842812700673840424506760177748413630308068952116797750617120839772672536200016882514108984707756821101221<284>] Free to factor
3×10296+7 = 3(0)2957<297> = 5717 × 1133333 × 34243336633104945989779111896593444706229<41> × [1352133125818668237879743406426035578779844426010402960327403237626482148981761008414693107782982058163940260661738631423180993261471189249836824835389520313503174508647731002291304299386282504882873282586831123088437834485646816610675238705384803<247>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3534511075 for P41 / September 21, 2016 2016 年 9 月 21 日) Free to factor
3×10297+7 = 3(0)2967<298> = 3943 × 3044246551083349723<19> × 97389270416524855425591316294261<32> × 31417692299642771871271434525071454341<38> × [81682544988242208349179357567028421014104056162801945379884908030750163000376057753869296768074206618996666668604450691505403562163962797550193089286136517939439458774276494253043695897304592900628431932763<206>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2111234914 for P32, B1=1e6, sigma=123853991 for P38 / May 30, 2016 2016 年 5 月 30 日) Free to factor
3×10298+7 = 3(0)2977<299> = 23 × 37 × 756629 × [46591716611835023782019572903704446663269685315927380342730189392734421551312857585698097333602805327015463428881135692474567589228056620409670123828467010499764821321644270942206688902832616249800146772915059158613017959511764097056515654407550998994039799691090396023208135421880748908233<290>] Free to factor
3×10299+7 = 3(0)2987<300> = 229 × 983 × [1332699560653378171269662871434473383768607817615622792716352667842403834620869186653458133243302074124749563540893886018648909185409605209966815780939730883535385394501281612744161665341370992461362818570724144517940357252328892482241778354293735867831742238135642161283300830271826287054600701<295>] Free to factor
3×10300+7 = 3(0)2997<301> = 929 × 352911714248377<15> × [9150387091231088261572462447630301419516835213519689892656289900600420515361826198650483228522170346015852211369076681201000614911948503249487488297073763624757914297405012425854207471382166610983670508452369239144366457854045170620952793811880524852974981362955807729997271411549279<283>] Free to factor
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