Factorization of 899...993

Table of contents 目次

About 899...993 899...993 について
Prime numbers of the form 899...993 899...993 の形の素数
Factor table of 899...993 899...993 の素因数分解表
Related links 関連リンク

1. About 899...993 899...993 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

89w3 = { 83, 893, 8993, 89993, 899993, 8999993, 89999993, 899999993, 8999999993, 89999999993, … }

2. Prime numbers of the form 899...993 899...993 の形の素数

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

9×10¹-7 = 83 is prime. は素数です。
9×10⁶-7 = 8999993 is prime. は素数です。
9×10⁹-7 = 8999999993_<10> is prime. は素数です。
9×10¹⁰-7 = 89999999993_<11> is prime. は素数です。
9×10¹²-7 = 8(9)₁₁3_<13> is prime. は素数です。
9×10¹³-7 = 8(9)₁₂3_<14> is prime. は素数です。
9×10²³-7 = 8(9)₂₂3_<24> is prime. は素数です。
9×10⁶¹-7 = 8(9)₆₀3_<62> is prime. は素数です。
9×10¹⁹⁴-7 = 8(9)₁₉₃3_<195> is prime. は素数です。 (discovered by:発見: Makoto Kamada / November 29, 2004 2004 年 11 月 29 日) (certified by:証明: Makoto Kamada / PPSIQS / January 5, 2005 2005 年 1 月 5 日)
9×10²³³-7 = 8(9)₂₃₂3_<234> is prime. は素数です。 (discovered by:発見: Makoto Kamada / November 29, 2004 2004 年 11 月 29 日) (certified by:証明: Makoto Kamada / PPSIQS / January 5, 2005 2005 年 1 月 5 日)
9×10⁵⁴⁹-7 = 8(9)₅₄₈3_<550> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 1, 2006 2006 年 6 月 1 日)
9×10⁷⁶⁵-7 = 8(9)₇₆₄3_<766> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 1, 2006 2006 年 6 月 1 日)
9×10⁹⁷³-7 = 8(9)₉₇₂3_<974> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 1, 2006 2006 年 6 月 1 日)
9×10¹⁰⁶¹-7 = 8(9)₁₀₆₀3_<1062> 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 14, 2006 2006 年 9 月 14 日) [certificate証明]
9×10¹¹⁸⁶-7 = 8(9)₁₁₈₅3_<1187> 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 11, 2006 2006 年 9 月 11 日) [certificate証明]
9×10¹⁸⁵³-7 = 8(9)₁₈₅₂3_<1854> 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 / July 3, 2006 2006 年 7 月 3 日) [certificate証明]
9×10³⁷¹³-7 = 8(9)₃₇₁₂3_<3714> 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 4.0.2 - LX64 / April 15, 2013 2013 年 4 月 15 日) [certificate証明]
9×10⁶⁷⁸⁹-7 = 8(9)₆₇₈₈3_<6790> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 25, 2004 2004 年 12 月 25 日)
9×10⁷²⁵⁴-7 = 8(9)₇₂₅₃3_<7255> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 29, 2004 2004 年 12 月 29 日)
9×10⁷⁷⁶⁵-7 = 8(9)₇₇₆₄3_<7766> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 29, 2004 2004 年 12 月 29 日)
9×10⁹⁰²⁵-7 = 8(9)₉₀₂₄3_<9026> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / January 8, 2005 2005 年 1 月 8 日)
9×10¹⁰⁸⁵⁵-7 = 8(9)₁₀₈₅₄3_<10856> is PRP. はおそらく素数です。 (Sinkiti Sibata / PFGW / November 4, 2007 2007 年 11 月 4 日)
9×10²³⁶⁴⁰-7 = 8(9)₂₃₆₃₉3_<23641> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
9×10³¹⁴⁴⁰-7 = 8(9)₃₁₄₃₉3_<31441> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
9×10³¹⁸³⁹-7 = 8(9)₃₁₈₃₈3_<31840> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
9×10³²²⁸⁷-7 = 8(9)₃₂₂₈₆3_<32288> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
9×10¹²⁰³⁴²-7 = 8(9)₁₂₀₃₄₁3_<120343> is PRP. はおそらく素数です。 (Bob Price / September 8, 2015 2015 年 9 月 8 日)
9×10¹³²¹⁴⁸-7 = 8(9)₁₃₂₁₄₇3_<132149> is PRP. はおそらく素数です。 (Bob Price / September 8, 2015 2015 年 9 月 8 日)

2.3. Range of search 捜索範囲

n≤100000 / Completed 終了 / Dmitry Domanov / March 8, 2010 2010 年 3 月 8 日
n≤200000 / Completed 終了 / Bob Price / September 8, 2015 2015 年 9 月 8 日
n≤300000 / Completed 終了 / Bob Price / October 19, 2023 2023 年 10 月 19 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。

9×10^13k+5-7 = 53×(9×10⁵-753+81×10⁵×10¹³-19×53×k-1Σm=010^13m)
9×10^15k+4-7 = 31×(9×10⁴-731+81×10⁴×10¹⁵-19×31×k-1Σm=010^15m)
9×10^16k+3-7 = 17×(9×10³-717+81×10³×10¹⁶-19×17×k-1Σm=010^16m)
9×10^18k+2-7 = 19×(9×10²-719+81×10²×10¹⁸-19×19×k-1Σm=010^18m)
9×10^22k+3-7 = 23×(9×10³-723+81×10³×10²²-19×23×k-1Σm=010^22m)
9×10^26k+20-7 = 859×(9×10²⁰-7859+81×10²⁰×10²⁶-19×859×k-1Σm=010^26m)
9×10^28k+22-7 = 29×(9×10²²-729+81×10²²×10²⁸-19×29×k-1Σm=010^28m)
9×10^28k+22-7 = 281×(9×10²²-7281+81×10²²×10²⁸-19×281×k-1Σm=010^28m)
9×10^32k+27-7 = 449×(9×10²⁷-7449+81×10²⁷×10³²-19×449×k-1Σm=010^32m)
9×10^41k+1-7 = 83×(9×10¹-783+81×10×10⁴¹-19×83×k-1Σm=010^41m)

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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 31.06%. 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 31.06% です。

3. Factor table of 899...993 899...993 の素因数分解表

3.2. Range of factorization 分解範囲

n≤100 / Completed 終了 / November 29, 2004 2004 年 11 月 29 日
n≤150 / Completed 終了 / October 31, 2007 2007 年 10 月 31 日
n≤200 / Completed 終了 / March 28, 2021 2021 年 3 月 28 日
n≤300 / Remaining 49 残り 49

3.3. Terms that have not been factored yet まだ分解されていない項

n=207, 210, 211, 213, 216, 217, 218, 224, 227, 228, 236, 239, 242, 244, 246, 249, 250, 252, 253, 254, 257, 259, 260, 261, 262, 264, 267, 268, 269, 270, 271, 272, 274, 276, 277, 278, 280, 282, 283, 284, 285, 286, 289, 291, 292, 294, 295, 296, 298 (49/300)

3.4. Factor table 素因数分解表

9×10¹-7 = 83 = definitely prime number 素数

9×10²-7 = 893 = 19 × 47

9×10³-7 = 8993 = 17 × 23²

9×10⁴-7 = 89993 = 31 × 2903

9×10⁵-7 = 899993 = 53 × 16981

9×10⁶-7 = 8999993 = definitely prime number 素数

9×10⁷-7 = 89999993 = 379 × 237467

9×10⁸-7 = 899999993 = 1811 × 496963

9×10⁹-7 = 8999999993_<10> = definitely prime number 素数

9×10¹⁰-7 = 89999999993_<11> = definitely prime number 素数

9×10¹¹-7 = 899999999993_<12> = 313 × 2875399361_<10>

9×10¹²-7 = 8999999999993_<13> = definitely prime number 素数

9×10¹³-7 = 89999999999993_<14> = definitely prime number 素数

9×10¹⁴-7 = 899999999999993_<15> = 3313 × 271657108361_<12>

9×10¹⁵-7 = 8999999999999993_<16> = 317 × 3701 × 7671215129_<10>

9×10¹⁶-7 = 89999999999999993_<17> = 1867 × 3217 × 14984668187_<11>

9×10¹⁷-7 = 899999999999999993_<18> = 269 × 23747 × 140890424351_<12>

9×10¹⁸-7 = 8999999999999999993_<19> = 53 × 13415189 × 12658138529_<11>

9×10¹⁹-7 = 89999999999999999993_<20> = 17 × 31 × 22963 × 1020847 × 7285219

9×10²⁰-7 = 899999999999999999993_<21> = 19² × 859 × 4621 × 8269 × 75954443

9×10²¹-7 = 8999999999999999999993_<22> = 24049 × 393929 × 452443 × 2099731

9×10²²-7 = 89999999999999999999993_<23> = 29 × 281 × 523 × 2557231 × 8257841489_<10>

9×10²³-7 = 899999999999999999999993_<24> = definitely prime number 素数

9×10²⁴-7 = 8999999999999999999999993_<25> = 227 × 1951 × 63317 × 320951236598777_<15>

9×10²⁵-7 = 89999999999999999999999993_<26> = 23 × 3913043478260869565217391_<25>

9×10²⁶-7 = 899999999999999999999999993_<27> = 113 × 337 × 787 × 30030283538930108419_<20>

9×10²⁷-7 = 8999999999999999999999999993_<28> = 449 × 4096397 × 4893213091857087581_<19>

9×10²⁸-7 = 89999999999999999999999999993_<29> = 6247 × 177892207 × 80986770372427217_<17>

9×10²⁹-7 = 899999999999999999999999999993_<30> = 311 × 373 × 6967 × 428083 × 2601354241140871_<16>

9×10³⁰-7 = 8999999999999999999999999999993_<31> = 16631 × 541158078287535325596777103_<27>

9×10³¹-7 = 89999999999999999999999999999993_<32> = 53 × 40213357 × 42227591383310023366633_<23>

9×10³²-7 = 899999999999999999999999999999993_<33> = 109 × 34306163 × 140914869181_<12> × 1707996761659_<13>

9×10³³-7 = 8999999999999999999999999999999993_<34> = 962067047 × 3046158667_<10> × 3071034173656957_<16>

9×10³⁴-7 = 89999999999999999999999999999999993_<35> = 31 × 389 × 7463305415042706692097188821627_<31>

9×10³⁵-7 = 899999999999999999999999999999999993_<36> = 17 × 1676887 × 12045008363_<11> × 2621094531232243709_<19>

9×10³⁶-7 = 8999999999999999999999999999999999993_<37> = 578509 × 15557234200332233379255983917277_<32>

9×10³⁷-7 = 89999999999999999999999999999999999993_<38> = 13627 × 22961 × 19819511 × 14513044264682099118029_<23>

9×10³⁸-7 = 899999999999999999999999999999999999993_<39> = 19 × 59 × 383 × 56989 × 1216373 × 30239897518043332553383_<23>

9×10³⁹-7 = 8999999999999999999999999999999999999993_<40> = 10343147 × 6519673271990959_<16> × 133463951944204741_<18>

9×10⁴⁰-7 = 89999999999999999999999999999999999999993_<41> = 3178728147256931_<16> × 28313210765653266304553203_<26>

9×10⁴¹-7 = 899999999999999999999999999999999999999993_<42> = 1519153 × 592435389983760687699000693149406281_<36>

9×10⁴²-7 = 8999999999999999999999999999999999999999993_<43> = 83 × 50207 × 503527689989_<12> × 4289204835102465899374777_<25>

9×10⁴³-7 = 89999999999999999999999999999999999999999993_<44> = 3626823462259554793_<19> × 24815103612440213368896401_<26>

9×10⁴⁴-7 = 899999999999999999999999999999999999999999993_<45> = 53 × 233 × 2269 × 32120050759673104964293031794103622353_<38>

9×10⁴⁵-7 = 8999999999999999999999999999999999999999999993_<46> = 26227 × 57367 × 16810357 × 885199967 × 12266713841_<11> × 32770660463_<11>

9×10⁴⁶-7 = 89999999999999999999999999999999999999999999993_<47> = 131 × 859 × 958577 × 834355331834150144176536910168297721_<36>

9×10⁴⁷-7 = 899999999999999999999999999999999999999999999993_<48> = 23 × 6329 × 1294713809_<10> × 4775356485451602167308132609781431_<34>

9×10⁴⁸-7 = 8999999999999999999999999999999999999999999999993_<49> = 47 × 457 × 2454698263_<10> × 170698748147353661187216091658935609_<36>

9×10⁴⁹-7 = 89999999999999999999999999999999999999999999999993_<50> = 31 × 97 × 4297 × 61141 × 235427459 × 6051217595279_<13> × 79967092297671167_<17>

9×10⁵⁰-7 = 899999999999999999999999999999999999999999999999993_<51> = 29 × 281 × 110442999140998895570008590011044299914099889557_<48>

9×10⁵¹-7 = 8(9)₅₀3_<52> = 17² × 303053 × 102760469330812520066122479952203137078458429_<45>

9×10⁵²-7 = 8(9)₅₁3_<53> = 617 × 3361 × 13461960683_<11> × 1384640841470659_<16> × 2328323800825706481137_<22>

9×10⁵³-7 = 8(9)₅₂3_<54> = 257 × 2731 × 2730271 × 1107026068697_<13> × 194441495124557_<15> × 2181901445423281_<16>

9×10⁵⁴-7 = 8(9)₅₃3_<55> = 1156997 × 1469179 × 5294629371545575527506732661455484247697311_<43>

9×10⁵⁵-7 = 8(9)₅₄3_<56> = 1595289607_<10> × 76474336411677317_<17> × 737712693767839975691599501747_<30>

9×10⁵⁶-7 = 8(9)₅₅3_<57> = 19 × 38064163680249424816411_<23> × 1244436143416699013384483692272377_<34>

9×10⁵⁷-7 = 8(9)₅₆3_<58> = 53 × 14667123451153_<14> × 44590576184581379839_<20> × 259644189592931992527643_<24>

9×10⁵⁸-7 = 8(9)₅₇3_<59> = 4231 × 24419 × 41515165640477_<14> × 20982867305985629592625867628978277881_<38>

9×10⁵⁹-7 = 8(9)₅₈3_<60> = 61 × 181 × 199 × 449 × 593 × 1538437965218539798708007408281349027216862982511_<49>

9×10⁶⁰-7 = 8(9)₅₉3_<61> = 931990420483693_<15> × 9656751616963076551941680487833418652305879101_<46>

9×10⁶¹-7 = 8(9)₆₀3_<62> = definitely prime number 素数

9×10⁶²-7 = 8(9)₆₁3_<63> = 6553 × 13250766851189015597542931_<26> × 10364809607688328974145571574517051_<35>

9×10⁶³-7 = 8(9)₆₂3_<64> = 2969 × 4615291 × 209897257 × 170019792081371_<15> × 3516986807500121_<16> × 5233066331801641_<16>

9×10⁶⁴-7 = 8(9)₆₃3_<65> = 31 × 193 × 19489 × 64411397793914660436341_<23> × 11983156385596497470624913966200779_<35>

9×10⁶⁵-7 = 8(9)₆₄3_<66> = 28477 × 3408318076147_<13> × 9272741572275731948360977948814948957874962223647_<49>

9×10⁶⁶-7 = 8(9)₆₅3_<67> = 101311949 × 88834536190790288715105066234586011172285314538761859176157_<59>

9×10⁶⁷-7 = 8(9)₆₆3_<68> = 17 × 3925889327117306563949989_<25> × 1348514236122437171783930286890948195647861_<43>

9×10⁶⁸-7 = 8(9)₆₇3_<69> = 2239 × 24107 × 16674209276110880749705056396529593117983203253812608899955541_<62>

9×10⁶⁹-7 = 8(9)₆₈3_<70> = 23 × 391304347826086956521739130434782608695652173913043478260869565217391_<69>

9×10⁷⁰-7 = 8(9)₆₉3_<71> = 53 × 2203 × 41721353 × 4667317181_<10> × 1109998406431_<13> × 3566186797560116503238928077107754269_<37>

9×10⁷¹-7 = 8(9)₇₀3_<72> = 587 × 3299 × 2086577 × 116162821 × 1917434452242125040485081748409927752483794566690933_<52>

9×10⁷²-7 = 8(9)₇₁3_<73> = 859 × 8419 × 1402709784884641_<16> × 887198930441398371296360402386507058010071975542313_<51>

9×10⁷³-7 = 8(9)₇₂3_<74> = 577 × 33037 × 313151771 × 62245170469_<11> × 12758621487819479_<17> × 18984615547684073234135295828317_<32>

9×10⁷⁴-7 = 8(9)₇₃3_<75> = 19 × 15334860677681731423_<20> × 3088937164037708421559949570368204959659123615233580189_<55>

9×10⁷⁵-7 = 8(9)₇₄3_<76> = 107981 × 34645789 × 8452984712082679_<16> × 284599822377750208940599462415807344841270317063_<48>

9×10⁷⁶-7 = 8(9)₇₅3_<77> = 197 × 51417547 × 62450111 × 20902061156533_<14> × 22231066131117421759_<20> × 306183871590184218075442931_<27>

9×10⁷⁷-7 = 8(9)₇₆3_<78> = 4787412431419_<13> × 9572930986839253860842860383569_<31> × 19637976601995850451812419925821163_<35> (Makoto Kamada / msieve 0.81 / 1 minutes)

9×10⁷⁸-7 = 8(9)₇₇3_<79> = 29 × 281 × 99623 × 687707 × 1603249 × 16547411 × 19199909 × 31647902285474629463385388915403499874414487_<44>

9×10⁷⁹-7 = 8(9)₇₈3_<80> = 31 × 3931 × 1961471469667_<13> × 1489556428853252065481506534061_<31> × 252777733809051042510627160716499_<33>

9×10⁸⁰-7 = 8(9)₇₉3_<81> = 223 × 557 × 136333 × 24991979 × 11251141385453_<14> × 16308863265043_<14> × 11589388958273519680856002091406734971_<38>

9×10⁸¹-7 = 8(9)₈₀3_<82> = 195760283 × 63078669271237_<14> × 728845375474101807285300781953461969406930066225944407957183_<60>

9×10⁸²-7 = 8(9)₈₁3_<83> = 3329 × 27035145689396215079603484529888855512165815560228296785821568038449984980474617_<80>

9×10⁸³-7 = 8(9)₈₂3_<84> = 17 × 53 × 83 × 123707 × 24154932913_<11> × 6837637450591_<13> × 42049390908982969_<17> × 14007922697293690593254196391394339_<35>

9×10⁸⁴-7 = 8(9)₈₃3_<85> = 2460043 × 17754601 × 462084737 × 445930595549615608997917209874756352721133615668023076371690323_<63>

9×10⁸⁵-7 = 8(9)₈₄3_<86> = 35281 × 89658182401_<11> × 178071489654670298983_<21> × 159778117883200444491118378129099058561979659252591_<51>

9×10⁸⁶-7 = 8(9)₈₅3_<87> = 653740973 × 19321136458939597512041299_<26> × 71253161142181477236070250973511702994228555432462959_<53>

9×10⁸⁷-7 = 8(9)₈₆3_<88> = 24213892169609_<14> × 2546150484433285848884197116341593_<34> × 145980160671059359421302969277919938950489_<42> (Makoto Kamada / msieve 0.83 / 9.5 minutes)

9×10⁸⁸-7 = 8(9)₈₇3_<89> = 5737 × 2730224921_<10> × 32428952447_<11> × 44010331139998721_<17> × 1354451509234875550609003_<25> × 2972406589748367709819669_<25>

9×10⁸⁹-7 = 8(9)₈₈3_<90> = 1433 × 4783101992794033_<16> × 131306636683864008664877819453723561118073999554515651299297780880066737_<72>

9×10⁹⁰-7 = 8(9)₈₉3_<91> = 400260503 × 22485356243106505065277450071060346416443692921657073918182729111295800275352174831_<83>

9×10⁹¹-7 = 8(9)₉₀3_<92> = 23 × 449 × 72843863 × 21709335236231_<14> × 47820557697466403_<17> × 1591998561797473609405739_<25> × 72388825562933445729016559_<26>

9×10⁹²-7 = 8(9)₉₁3_<93> = 19 × 2222921 × 2592719 × 28489831 × 3405203237224919964164302378007_<31> × 84718160814355196926074187190089269343909_<41> (Makoto Kamada / msieve 0.83 / 4.3 minutes)

9×10⁹³-7 = 8(9)₉₂3_<94> = 3038766889_<10> × 85610088419_<11> × 34595545127810416261578469644387860475288120433778789515166544632779921723_<74>

9×10⁹⁴-7 = 8(9)₉₃3_<95> = 31 × 47 × 317 × 569 × 3727 × 8537 × 6928517 × 763440435724467257952628446906247_<33> × 2034844887234688044040269293005960665313_<40> (Makoto Kamada / msieve 0.83 / 4.7 minutes)

9×10⁹⁵-7 = 8(9)₉₄3_<96> = 1194573351918499376609_<22> × 753407062491883834740246764193083836545273035497250653710655350316236317977_<75>

9×10⁹⁶-7 = 8(9)₉₅3_<97> = 53 × 59 × 367 × 1291 × 6074664843579651527512711558479908510741720836416093561242761926313722830075197756377347_<88>

9×10⁹⁷-7 = 8(9)₉₆3_<98> = 179 × 7216035925321271_<16> × 69677216312777739656044295307979533123700507474608057068550974780959397438380277_<80>

9×10⁹⁸-7 = 8(9)₉₇3_<99> = 859 × 20865827 × 50212719510705002347050467277299825456184999045640036446817653141163429602617765772232201_<89>

9×10⁹⁹-7 = 8(9)₉₈3_<100> = 17 × 1987 × 14543 × 262027 × 290516931203304609450113_<24> × 240671255931226803033040927898839013903307752914346444123063719_<63>

9×10¹⁰⁰-7 = 8(9)₉₉3_<101> = 275573 × 29016007 × 633438539 × 146026016625925851960851_<24> × 121683999812110022401627219316059813295878908746202034867_<57>

9×10¹⁰¹-7 = 8(9)₁₀₀3_<102> = 1151 × 1579 × 495205039646665701933885725384595491763364621121375305445219593172553095609237004581747072375317_<96>

9×10¹⁰²-7 = 8(9)₁₀₁3_<103> = 153757 × 6203345868991_<13> × 9435862781643766392765431242711860011853071767563210891048721721836926586677604249139_<85>

9×10¹⁰³-7 = 8(9)₁₀₂3_<104> = 8969263 × 22129553 × 3138341068996635669510657500009591_<34> × 144481741911394492878214372456463812416287949515103488657_<57> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 1.16 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / October 28, 2007 2007 年 10 月 28 日)

9×10¹⁰⁴-7 = 8(9)₁₀₃3_<105> = 149 × 55001 × 61379 × 30483828623351_<14> × 32825864633489_<14> × 313678532475953_<15> × 5700269168653034105761773345654567533050804427789849_<52>

9×10¹⁰⁵-7 = 8(9)₁₀₄3_<106> = 349 × 3718002955578853001_<19> × 6935972328195994366867601230695622408433022905199687749554476469033858069752030913957_<85>

9×10¹⁰⁶-7 = 8(9)₁₀₅3_<107> = 29 × 281 × 21155789 × 26583757 × 367077182621_<12> × 29842828862698429679_<20> × 1792648855350778106226341288212621000032004613815105849951_<58>

9×10¹⁰⁷-7 = 8(9)₁₀₆3_<108> = 229346090476450181550249720633629_<33> × 3924200312856059802459172311645063058914298932835598068216843393357783672717_<76> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1313680099 for P33 / October 20, 2007 2007 年 10 月 20 日)

9×10¹⁰⁸-7 = 8(9)₁₀₇3_<109> = 134885793285601424333_<21> × 66723112796199255391367082753863720943876137047685460137756116714844525365672978998733021_<89>

9×10¹⁰⁹-7 = 8(9)₁₀₈3_<110> = 31² × 53 × 33889 × 26164060541_<11> × 13546917651611965549_<20> × 535200556128305490027165361453_<30> × 274866812455110095849889444659599825151057_<42> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2718962488 for P30 / October 20, 2007 2007 年 10 月 20 日)

9×10¹¹⁰-7 = 8(9)₁₀₉3_<111> = 19 × 41551595117_<11> × 41281949109330068117018801413_<29> × 27614743514922133541815936402538216668321370424896711617313719193012707_<71> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 1.60 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / October 28, 2007 2007 年 10 月 28 日)

9×10¹¹¹-7 = 8(9)₁₁₀3_<112> = 263 × 2273 × 30709243 × 15081727006323373636683367_<26> × 32506270040987637556622159708982578295394684865809958591379888244283291147_<74>

9×10¹¹²-7 = 8(9)₁₁₁3_<113> = 15149 × 73453 × 75516953 × 1071037180065325997386223485620247257953372676977259499895914366620144365351171155661589700049273_<97>

9×10¹¹³-7 = 8(9)₁₁₂3_<114> = 23 × 6988483 × 5599274518176361830196040119648035327490274697857081118475491250638962766995728357019996172709224342517477_<106>

9×10¹¹⁴-7 = 8(9)₁₁₃3_<115> = 15273767989713770811037_<23> × 232741247748956358607337_<24> × 2648289886635648530766401_<25> × 955999003944617666214740280660713563539945797_<45>

9×10¹¹⁵-7 = 8(9)₁₁₄3_<116> = 17 × 509 × 1741 × 3079 × 47681 × 5427249593_<10> × 148651844507_<12> × 50439630145140012356441776917545429269823969657927910498987184071213433369264909_<80>

9×10¹¹⁶-7 = 8(9)₁₁₅3_<117> = 867848053 × 8221001536282820042554959373_<28> × 126146175062235775566651327911035316108784424212762468419631710947788602532706697_<81>

9×10¹¹⁷-7 = 8(9)₁₁₆3_<118> = 192335013307_<12> × 1111873976141_<13> × 6876114528185803_<16> × 432493409946666533034050450858960849_<36> × 14151614711419740654283488076476618603054437_<44> (Makoto Kamada / Msieve 1.28 for P36 x P44 / 12 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / October 28, 2007 2007 年 10 月 28 日)

9×10¹¹⁸-7 = 8(9)₁₁₇3_<119> = 14831 × 29251 × 11591783009_<11> × 15310381321_<11> × 6287652139412027_<16> × 185911647667040247363626898402204883489295784715746022479797536976854416751_<75>

9×10¹¹⁹-7 = 8(9)₁₁₈3_<120> = 61 × 823 × 1004981 × 1446682233738538319_<19> × 45567990874948473844291875103339917072403_<41> × 270596365668481699029128282701225154281973286874043_<51> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2.11 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / October 28, 2007 2007 年 10 月 28 日)

9×10¹²⁰-7 = 8(9)₁₁₉3_<121> = 20354029401725849662526304753223971301497103511422609997_<56> × 442172889817918611600780346173978409068598975005735222119428696669_<66> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / October 28, 2007 2007 年 10 月 28 日)

9×10¹²¹-7 = 8(9)₁₂₀3_<122> = 479 × 187891440501043841336116910229645093945720250521920668058455114822546972860125260960334029227557411273486430062630480167_<120>

9×10¹²²-7 = 8(9)₁₂₁3_<123> = 53 × 4483 × 916879 × 2468335253078521_<16> × 21496643135387952418448986201888231937_<38> × 77859405334185056592558073314508609031087592802266287870129_<59> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2.78 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / October 28, 2007 2007 年 10 月 28 日)

9×10¹²³-7 = 8(9)₁₂₂3_<124> = 283 × 449 × 18553 × 335087805245091568482853093222231_<33> × 11392970303565490307790042441076114728020253883982388272289002974166360045042039653_<83> (Robert Backstrom / GMP-ECM 6.0.1 B1=226000, sigma=4254552781 for P33 / October 28, 2007 2007 年 10 月 28 日)

9×10¹²⁴-7 = 8(9)₁₂₃3_<125> = 31 × 83 × 859 × 514997239710717504843060243797163586321_<39> × 79068710858248681348102914984733040362741538735234491408794076224567905858038519_<80> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / October 28, 2007 2007 年 10 月 28 日)

9×10¹²⁵-7 = 8(9)₁₂₄3_<126> = 3947 × 6271 × 25471265971155677_<17> × 1427539228774468658751300436716796405108840460052646950466256970887892354170913842793876805033960215257_<103>

9×10¹²⁶-7 = 8(9)₁₂₅3_<127> = 3677 × 59222213 × 41329889829588424255804826541199422267006803659109803054115055195001946595585602838886274959316159376530032937660393_<116>

9×10¹²⁷-7 = 8(9)₁₂₆3_<128> = 16927 × 2815289 × 34549727 × 18928495665651195086151678397725759673977330546366127_<53> × 2887877797068484257309586094965034801453924030197429437839_<58> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 4.41 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / October 28, 2007 2007 年 10 月 28 日)

9×10¹²⁸-7 = 8(9)₁₂₇3_<129> = 19 × 66612701 × 711101942145111019404068618274937972375094369054808015476934662244540706244120337540907986111663916054561110611149382047_<120>

9×10¹²⁹-7 = 8(9)₁₂₈3_<130> = 1045571 × 838081845193_<12> × 1049171226970903_<16> × 343667900375662241_<18> × 87159316066813584377999_<23> × 326816061765706342325106563410532398059764756204215248403_<57>

9×10¹³⁰-7 = 8(9)₁₂₉3_<131> = 2424152785551971_<16> × 37126372783267998055843159178235622465202870961889271394375011300773037140602920337986974471215514460301932358538483_<116>

9×10¹³¹-7 = 8(9)₁₃₀3_<132> = 17 × 15807203 × 16332241 × 29548166606333_<14> × 6940044233644260805865391929265730365559559192127918756730817212365746010803798216745229167635247471631_<103>

9×10¹³²-7 = 8(9)₁₃₁3_<133> = 87359 × 453683 × 227081811124422167203942227581830789744857547422644471095022036000911125598887487270340241668613617124449321596453861290269_<123>

9×10¹³³-7 = 8(9)₁₃₂3_<134> = 264101 × 534617 × 182955127132944612210518087078849494903_<39> × 3484055901363921062151806188107621607898929991774539197434850631713521731052250641243_<85> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 6.85 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / October 28, 2007 2007 年 10 月 28 日)

9×10¹³⁴-7 = 8(9)₁₃₃3_<135> = 29 × 281 × 1093 × 45587 × 136753 × 38335721 × 422801499246408347784437788429319191683918585807111678844840089751748325423028958440969058106442511184501944579_<111>

9×10¹³⁵-7 = 8(9)₁₃₄3_<136> = 23 × 53 × 661 × 1110971 × 11332367 × 887184592663736351258794588647849201608579898071048711818340124356551553119117860137528284345310237225304875811724811_<117>

9×10¹³⁶-7 = 8(9)₁₃₅3_<137> = 5189 × 1932439 × 121773261717971_<15> × 73705705266237112903061904785478879040191055453335729064388835136829403264289003861332547456910848959029601202673_<113>

9×10¹³⁷-7 = 8(9)₁₃₆3_<138> = 227 × 2521 × 221091843902924979644001926922716807503_<39> × 7113299338479217992920918313593338363891253403625902931023690166695268837106428754985186805093_<94> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 13.09 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / October 29, 2007 2007 年 10 月 29 日)

9×10¹³⁸-7 = 8(9)₁₃₇3_<139> = 113 × 1039 × 21012038995387387919_<20> × 8324111480329451493669984302302012442668075809611357389_<55> × 438270694932342412379485394874876095508458992349269934992589_<60> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 6.25 hours on Core 2 Quad Q6600 / October 29, 2007 2007 年 10 月 29 日)

9×10¹³⁹-7 = 8(9)₁₃₈3_<140> = 31 × 34319 × 95880034599375142177521603584056943225357_<41> × 882303513756038409718500891576339947944242061119473046440639355414422699311396515924957852941_<93> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 6.16 hours on Core 2 Quad Q6600 / October 29, 2007 2007 年 10 月 29 日)

9×10¹⁴⁰-7 = 8(9)₁₃₉3_<141> = 47 × 109 × 167 × 617 × 153337616869490449763658859895879_<33> × 11119053224090329768606633153477332542273472771580149117582678104067239138069306589653736225297573611_<101> (Robert Backstrom / GMP-ECM 6.0.1 B1=690500, sigma=3998297514 for P33 / October 29, 2007 2007 年 10 月 29 日)

9×10¹⁴¹-7 = 8(9)₁₄₀3_<142> = 2467639565737_<13> × 53727058137272382231521263461791395461691665958866250660772681_<62> × 67884046657300958448660911774042029705347021611364740350454114167369_<68> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.28 / October 30, 2007 2007 年 10 月 30 日)

9×10¹⁴²-7 = 8(9)₁₄₁3_<143> = 1009 × 1104997769_<10> × 4632016416848161505913411911_<28> × 17426888481989185445727912461939386208627868426094724708353318363551372222498559470563406941300809238903_<104>

9×10¹⁴³-7 = 8(9)₁₄₂3_<144> = 1777 × 1725179 × 133421887 × 156872632499525723095280260098133461577_<39> × 14026414070177028542787457357907396822775755157120560213926799915579235133672913797156429_<89> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 9.59 hours on Core 2 Quad Q6600 / October 30, 2007 2007 年 10 月 30 日)

9×10¹⁴⁴-7 = 8(9)₁₄₃3_<145> = 30380069764762946805547503800941_<32> × 5793759319832245415885975057146558926953_<40> × 51132060310818176689028811056072205332653270314035794978186101297841513141_<74> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=578800379 for P32 / October 22, 2007 2007 年 10 月 22 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 8.87 hours on Core 2 Quad Q6600 / October 30, 2007 2007 年 10 月 30 日)

9×10¹⁴⁵-7 = 8(9)₁₄₄3_<146> = 97 × 3307 × 3767 × 88689612345000909646591931059_<29> × 839785174596700619416492075514766572936766799231731694119293012984478206119418982501449042954689673043155839_<108> (Robert Backstrom / GMP-ECM 6.0.1 B1=226000, sigma=1550273985 for P29 / October 29, 2007 2007 年 10 月 29 日)

9×10¹⁴⁶-7 = 8(9)₁₄₅3_<147> = 19 × 307 × 2243 × 17371526793899_<14> × 28598478520519_<14> × 64299853807288749095977974116352073454267827_<44> × 2153427995281495420234041605616327252058426335937525315582533212837981_<70> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 10.37 hours on Core 2 Quad Q6600 / October 30, 2007 2007 年 10 月 30 日)

9×10¹⁴⁷-7 = 8(9)₁₄₆3_<148> = 17 × 2029 × 744027979 × 606721972442519377_<18> × 578006271211006103445168626846863596682660958592932126625470299729097430772395542470494910326825803676709393711920247_<117>

9×10¹⁴⁸-7 = 8(9)₁₄₇3_<149> = 53 × 839 × 3833 × 5333122741489_<13> × 380397540317863012963011373_<27> × 185048077381378285528736195447051909587258335893_<48> × 1406572115111896750750738223467919885903244947129739803_<55> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 30.10 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / October 31, 2007 2007 年 10 月 31 日)

9×10¹⁴⁹-7 = 8(9)₁₄₈3_<150> = 35794409962129142828512220689799871821_<38> × 123028439265110134626156384131454479013793_<42> × 204372184460583650412981392697490828081020379007054396748321776875537981_<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 12.84 hours on Core 2 Quad Q6600 / October 29, 2007 2007 年 10 月 29 日)

9×10¹⁵⁰-7 = 8(9)₁₄₉3_<151> = 859 × 352963277 × 18139634852382632412042997_<26> × 55504280314514112186236174411054189440309_<41> × 29482533885016913889484106257918099812603456906714576053691076225565509087_<74> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 12.99 hours on Core 2 Quad Q6600 / October 31, 2007 2007 年 10 月 31 日)

9×10¹⁵¹-7 = 8(9)₁₅₀3_<152> = 90997 × 1567079 × 655276266581_<12> × 963163697811673343987868577874569117461268078514734619814169842532563771456880425444817362835048257153449785312467072290576114231_<129>

9×10¹⁵²-7 = 8(9)₁₅₁3_<153> = 27487 × 2387449 × 5618769997_<10> × 75820868126956676281536230696860571433120407_<44> × 32192229601894986931087007258474395061004652068487123300133829248970334366365297350334109_<89> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 37.53 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 1, 2007 2007 年 11 月 1 日)

9×10¹⁵³-7 = 8(9)₁₅₂3_<154> = 235483 × 15771126802857831503737789_<26> × 2469438507084583723424410362013_<31> × 29916323560200857306637278521712341_<35> × 32803016936544339453376593485631195739277624165372655627383_<59> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=2936328627 for P31 / October 30, 2007 2007 年 10 月 30 日) (Jo Yeong Uk / Msieve v. 1.28 for P35 x P59 / 1.42 hours on Core 2 Quad Q6600 / October 31, 2007 2007 年 10 月 31 日)

9×10¹⁵⁴-7 = 8(9)₁₅₃3_<155> = 31 × 59 × 3116155837_<10> × 3792154237087773328323098510929643_<34> × 13515254733080096925398066307959108515533417271_<47> × 308105468835983009135964692963347948427570307230290780677274397_<63> (Robert Backstrom / GMP-ECM 6.0.1 B1=1030000, sigma=1277051764 for P34, GGNFS-0.77.1-20060513-athlon-xp gnfs for P47 x P63 / 15.47 hours on Cygwin on AMD 64 3200+ / November 1, 2007 2007 年 11 月 1 日)

9×10¹⁵⁵-7 = 8(9)₁₅₄3_<156> = 449 × 889001 × 392454196502293_<15> × 5745197219293534564290482940434600173511654661178231708789916857339132144601793786666361428268813939928088595947487494143849747067149_<133>

9×10¹⁵⁶-7 = 8(9)₁₅₅3_<157> = 1683043 × 1587868814184539_<16> × 3367694427687296260583100430280362964295561507388352974134863965811500981423614721410604471883435025863666523126213907931758652262395209_<136>

9×10¹⁵⁷-7 = 8(9)₁₅₆3_<158> = 23 × 64057787 × 8547312778918799179387612593474476828728823510172134540253167241939987973_<73> × 7146824962215572093535969278319248184705372720242480746696150650147917691641_<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 37.30 hours on Msieve 1.28 / October 31, 2007 2007 年 10 月 31 日)

9×10¹⁵⁸-7 = 8(9)₁₅₇3_<159> = 199 × 6421 × 13103 × 8523801288669106552991843_<25> × 6306417307313970197809245310868775352913674246951445466422716802566492004315636870863362894640283909949213143762982427939823_<124>

9×10¹⁵⁹-7 = 8(9)₁₅₈3_<160> = 18104666690449826252281753693_<29> × 22392329597836817510288640646341074175512979619336814351_<56> × 22199985850784836127380389132731731977501124190563051137404670084573603137251_<77> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 59.23 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 2, 2007 2007 年 11 月 2 日)

9×10¹⁶⁰-7 = 8(9)₁₅₉3_<161> = 619 × 31247 × 201823 × 44832592826645189491277561661890927333335849_<44> × 58928729369518409469720209631759471783420671_<44> × 8726738097012509717654043907256703264726239277870739541104253_<61> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.28 / November 2, 2007 2007 年 11 月 2 日)

9×10¹⁶¹-7 = 8(9)₁₆₀3_<162> = 53 × 710382599 × 3193863019_<10> × 14169121763_<11> × 637003641965194182950788890954509239897_<39> × 829226536019218470577471928756725407087718463007725782007729866451066972588969963334914455291_<93> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 72.73 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 4, 2007 2007 年 11 月 4 日)

9×10¹⁶²-7 = 8(9)₁₆₁3_<163> = 29 × 281 × 106876054067_<12> × 152750521995337087_<18> × 67651133495946255417864949522676555857026289347396681034462798066358356607523483217492809572137338637499398298500262908602463817833_<131>

9×10¹⁶³-7 = 8(9)₁₆₂3_<164> = 17 × 7192250773_<10> × 9013613223467_<13> × 25920613065189923_<17> × 3150536960730125128921763452780254558726841743770021618219961721828962470357835320722259465108199647406218744914989315887653_<124>

9×10¹⁶⁴-7 = 8(9)₁₆₃3_<165> = 19 × 1847353 × 5195304037384876588643582502770703788863_<40> × 44521045988937219971985542168110282187182538753337627749_<56> × 110856890051938744122912238100452821884732080214861054731598977_<63> (Robert Backstrom / GMP-ECM 6.0.1 B1=141500, sigma=2371525520 for P40, GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.29 / November 6, 2007 2007 年 11 月 6 日)

9×10¹⁶⁵-7 = 8(9)₁₆₄3_<166> = 83 × 3391 × 5882321 × 1963931828123_<13> × 76471335051147697_<17> × 259614078290227987469021383_<27> × 139423052398459153337677410997022971547928633169768746347640708337313693782504396296367451593083457_<99>

9×10¹⁶⁶-7 = 8(9)₁₆₅3_<167> = 42709 × 1578482099_<10> × 326236852168633890020751838911718198217_<39> × 4092139473970466337231565660348581447470351547418909019180227591362356350317132972423887166170348215102482040007519_<115> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 124.14 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 7, 2007 2007 年 11 月 7 日)

9×10¹⁶⁷-7 = 8(9)₁₆₆3_<168> = 4102069211_<10> × 1475840225808026944863592821406727235005191165802606042142091249608358711_<73> × 148662072304606973843025284582176600459246392524700966245732210436802333527066765202333_<87> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.33 / January 27, 2008 2008 年 1 月 27 日)

9×10¹⁶⁸-7 = 8(9)₁₆₇3_<169> = 11369 × 646974011 × 57572701889099_<14> × 5558386317692349989_<19> × 49210457799346902131698308801292711620150749_<44> × 77698147296321048398209905863232249781232086869460260825621557916054516169171993_<80> (Robert Backstrom / GMP-ECM 6.1.3 B1=1586000, sigma=2359037686 for P44 / February 11, 2008 2008 年 2 月 11 日)

9×10¹⁶⁹-7 = 8(9)₁₆₈3_<170> = 31 × 499 × 34493149577_<11> × 998601279007657794155352289231_<30> × 168909976039395744416817759101263773883251916332855772388288330175279034030465755378771075571923248100895582334666758448039131_<126> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1164744747 for P30 / October 24, 2007 2007 年 10 月 24 日)

9×10¹⁷⁰-7 = 8(9)₁₆₉3_<171> = 4153 × 7523 × 98899 × 13495865681_<11> × 1229628762217_<13> × 17551848263811700308379709724898741112272604074035145853754506241391337238338312466219663795813981932340712670682553891685621262885475889_<137>

9×10¹⁷¹-7 = 8(9)₁₇₀3_<172> = 348827 × 1244911 × 14434703429_<11> × 295943798048527087_<18> × 4851510812226669980147389843090984419632343581457889655417604387714774941345657685885904675714457453463732257400553951728383159294303_<133>

9×10¹⁷²-7 = 8(9)₁₇₁3_<173> = 13195477 × 1856389490999279253223_<22> × 1230572333966178569213783745709380647003_<40> × 2985665619912987071009965308740715306903703470898269719229303606605231543658298741768182276250657874540761_<106> (Sinkiti Sibata / Msieve 1.40 snfs / May 13, 2010 2010 年 5 月 13 日)

9×10¹⁷³-7 = 8(9)₁₇₂3_<174> = 317 × 31815104256736732410487_<23> × 1143831950766122847147685783_<28> × 32933203402548031161720747926069273_<35> × 2368938010738226751172660755825073523676287922290421869222162020029734816560986221793413_<88> (Robert Backstrom / GMP-ECM 6.1.3 B1=2282000, sigma=3215918255 for P35 / February 10, 2008 2008 年 2 月 10 日)

9×10¹⁷⁴-7 = 8(9)₁₇₃3_<175> = 53 × 197 × 7436921 × 5931924217_<10> × 1741197521996180430496807_<25> × 278427057302514025989131353_<27> × 40304373398627470597587458659167052742345161887266956394465899657898964937941641047724930568377141640559_<104>

9×10¹⁷⁵-7 = 8(9)₁₇₄3_<176> = 28111 × 3837401 × 21374582844451_<14> × 6871684579286135803_<19> × 251708125395634031980166970606249136674893651112787_<51> × 22566849394309859194946786232536651024766683710075427312106529413911041167911179333_<83> (Warut Roonguthai / Msieve 1.47 snfs / September 26, 2011 2011 年 9 月 26 日)

9×10¹⁷⁶-7 = 8(9)₁₇₅3_<177> = 131 × 859 × 4218701 × 3842326693_<10> × 5266803491_<10> × 1425412813104737_<16> × 6570577352524454280361407329198116089534862000482006847_<55> × 10002618626491237257044328548099948893728032266318767226567438548309828853181_<77> (Warut Roonguthai / Msieve 1.48 snfs / October 20, 2011 2011 年 10 月 20 日)

9×10¹⁷⁷-7 = 8(9)₁₇₆3_<178> = 256408211102806553939_<21> × 305398083771533035043258313436922481348866163347550983513663_<60> × 114932875645115465637330837941543017125838642645103637831465181873242210223610362729436008275705149_<99> (Robert Backstrom / Msieve 1.44 snfs / January 13, 2012 2012 年 1 月 13 日)

9×10¹⁷⁸-7 = 8(9)₁₇₇3_<179> = 3257 × 392492437 × 70403371649890161048146013166635871526439145455491501245844474127818963611181071610568931995045289197115706250942762177314828254968033727876418147210149639583247930877_<167>

9×10¹⁷⁹-7 = 8(9)₁₇₈3_<180> = 17 × 23 × 61 × 415999 × 390502486328174744753_<21> × 37457574674179057991882902961495853146207127601_<47> × 6201263321946707140413050056613102802441776271168702241656281439550588769801915267842062196313638178869_<103> (Dmitry Domanov / Msieve 1.50 snfs / May 13, 2013 2013 年 5 月 13 日)

9×10¹⁸⁰-7 = 8(9)₁₇₉3_<181> = 10891 × 5486819574558925029152624668200693996930258823313386814434120700542015883423_<76> × 150610091392044818382883472006373182746590680311053182451698963556980981251397542935784243994273255701_<102> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.36 snfs / 35.61 hours, 3.82 hours / September 24, 2008 2008 年 9 月 24 日)

9×10¹⁸¹-7 = 8(9)₁₈₀3_<182> = 3613 × 3761 × 17011 × 2340581 × 730684027 × 15300750882422633_<17> × 979400478501517858241_<21> × 16940272774462961564775996098870506033529998386074873_<53> × 896797988999442350354441292775914106811664777578919757946243069497_<66> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P53 x P66 / 38.34 hours on Core 2 Quad Q6600 / December 25, 2007 2007 年 12 月 25 日)

9×10¹⁸²-7 = 8(9)₁₈₁3_<183> = 19 × 202823 × 233545608992232532540039448448309999099551929774392346762292348760404781249505337425398396372050610890439343404684976815408405098871533566861642650825700500592038118795309469989_<177>

9×10¹⁸³-7 = 8(9)₁₈₂3_<184> = 5095805838797_<13> × 53788217895048934897759774462957_<32> × 2977363295566134355716987326447671187290847_<43> × 11028352820741991810400348173207780872206580956330420554196387180105586020050881417161266972915311_<98> (Makoto Kamada / GMP-ECM 6.1.3 B1=50000, sigma=3272108598 for P32 / October 13, 2007 2007 年 10 月 13 日) (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.1] [ECM] B1=11000000, sigma=916485008 for P43 / February 28, 2011 2011 年 2 月 28 日)

9×10¹⁸⁴-7 = 8(9)₁₈₃3_<185> = 31 × 311 × 22091 × 37100458201_<11> × 1275537910469_<13> × 282209150413571_<15> × 480434327015263_<15> × 14873984820428774119490711269_<29> × 593474640229445793717454630072648349617_<39> × 7461012807353624814862644671648910980191120545663272451503_<58> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P39 x P58 / 8.00 hours on Cygwin on AMD 64 3400+ / October 29, 2007 2007 年 10 月 29 日)

9×10¹⁸⁵-7 = 8(9)₁₈₄3_<186> = 3599750111_<10> × 3801247698075277_<16> × 511429239641393594286116552718821379525492217943216215358353_<60> × 128605171074271089706265876284348082856864372238484502708779354735407583514883437244255130318364103123_<102> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / October 15, 2014 2014 年 10 月 15 日)

9×10¹⁸⁶-7 = 8(9)₁₈₅3_<187> = 47 × 309805571 × 156017926876754387969365267_<27> × 2455524626025464022288068323784527_<34> × 1613379861317499642941797679884392489924869887710630236149338813585946718446408151377883594843543655814671126354176321_<118> (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.1] [ECM] B1=3000000, sigma=4163344250 for P34 / February 28, 2011 2011 年 2 月 28 日)

9×10¹⁸⁷-7 = 8(9)₁₈₆3_<188> = 53 × 449 × 1997 × 10391 × 54507041 × 353567687176836296397725275871337713846069593916198460906478598412494543249_<75> × 9457137756301415333768460326947672411400990031196972465095958693650838326356622936589160504783_<94> (LegionMammal978 / Msieve 1.53 snfs for P75 x P94 / July 14, 2017 2017 年 7 月 14 日)

9×10¹⁸⁸-7 = 8(9)₁₈₇3_<189> = 6689591 × 2889983980206166400633343347830421444067318005274107662508507_<61> × 46552982294567003262611165131940242875979617104663519183548141215584144647077930746442394215984131576858766423362881560989_<122> (matsui / Msieve 1.42 snfs / 288.28 hours / July 29, 2009 2009 年 7 月 29 日)

9×10¹⁸⁹-7 = 8(9)₁₈₈3_<190> = 229 × 857 × 111509 × 4417356837034719126053932314339876647693_<40> × 2521535447519712965500829712864415465809253_<43> × 36922297982483569405858068032116807465473204184283136830835962230083619343236636136201293780492921_<98> (matsui / Msieve 1.46 snfs / June 28, 2010 2010 年 6 月 28 日)

9×10¹⁹⁰-7 = 8(9)₁₈₉3_<191> = 29 × 281 × 401 × 727 × 214759 × 460700651766474898382043837818032330300809931640616466179041587072833751773017369_<81> × 382903387432799448414203860928239815011297816502034521950062446735854912628115242060075120769421_<96> (Kenji Ibusuki / Msieve v. 1.49 (SVN unknown) + GGNFS-0.77.1-VC8 with factMsieve.pl (decomposed + modified) snfs (without procrels.exe, matbuild.exe for "finalFF" calculation) / March 29, 2018 2018 年 3 月 29 日)

9×10¹⁹¹-7 = 8(9)₁₉₀3_<192> = 2694899 × 72275153 × 550854319189_<12> × 8388305470467760275118598470006215155634808322340793006782619203654349809033325076696383639330216355087681736024118375029382122889286338655336901330915612601852677671_<166>

9×10¹⁹²-7 = 8(9)₁₉₁3_<193> = 3469 × 42192949 × 667341094121537947_<18> × 7326564598429775364823_<22> × 12576218572910826994744471544154008911772696731264776763783641942128187748861284675431656667575547830909551595226118457123897290098155673516813_<143>

9×10¹⁹³-7 = 8(9)₁₉₂3_<194> = 511279 × 3106268111770496829983_<22> × 25313282195995488001015974270922753793617_<41> × 2238706474418559773565349675671260600341989139293305774021353476716466289221789053537675178434163005204076311296379271668194297_<127> (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.1] [ECM] B1=11000000, sigma=1287001053 for P41 / March 1, 2011 2011 年 3 月 1 日)

9×10¹⁹⁴-7 = 8(9)₁₉₃3_<195> = definitely prime number 素数

9×10¹⁹⁵-7 = 8(9)₁₉₄3_<196> = 17 × 439 × 119183 × 1271399 × 242885213 × 461827684596426570878380861037770727_<36> × 90273726781308008410859820613528673953162767949_<47> × 785941965246821725517634354985618196758423193048763238517231673375963788322474444838897417_<90> (matsui / October 21, 2008 2008 年 10 月 21 日) (Wataru Sakai / GMP-ECM 6.2.1 B1=11000000, sigma=1202030130 for P47 / August 17, 2009 2009 年 8 月 17 日)

9×10¹⁹⁶-7 = 8(9)₁₉₅3_<197> = 731413 × 15089069 × 101668669 × 13688355513133121_<17> × 20476877778258297685878989_<26> × 23222917624869682986808856353387_<32> × 12322489474660531695741954992123566822217378113251020935855509359836204616518712285683147287205008714067_<104> (Robert Backstrom / GMP-ECM 6.1.3 B1=696000, sigma=3337125325 for P32 / February 7, 2008 2008 年 2 月 7 日)

9×10¹⁹⁷-7 = 8(9)₁₉₆3_<198> = 104572749495411191273052631155941_<33> × 6705490534549797571934956800003022448129_<40> × 1283492776237749514056214634480831887204643584599589999215158576194203115091542292412887604724010842076711482471179351071298437_<127> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=2707934202 for P33 / October 29, 2007 2007 年 10 月 29 日) (Bob Backstrom / GMP-ECM 7.0.4 B1=35470000, sigma=1:3518309644 for P40 x P127 / March 28, 2021 2021 年 3 月 28 日)

9×10¹⁹⁸-7 = 8(9)₁₉₇3_<199> = 7541 × 1511118722439549589_<19> × 71998412045036748034474957_<26> × 4417115504705009301556717078603793892803_<40> × 50211444026482936981708622911020529833217_<41> × 49459599680436889739968648765959533378468882314170304438562372871450551_<71> (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.1] [ECM] B1=11000000, sigma=3970191681 for P40 / March 2, 2011 2011 年 3 月 2 日) (Dmitry Domanov / Msieve 1.40 gnfs for P41 x P71 / March 4, 2011 2011 年 3 月 4 日)

9×10¹⁹⁹-7 = 8(9)₁₉₈3_<200> = 31 × 743 × 6841 × 12697 × 316339 × 413089877 × 107105780766623_<15> × 13919023264892149_<17> × 19620579832179617602901623499857_<32> × 6427503805579223317744356595461437807_<37> × 1831041340434809452833718361805463604259680227651236173580827772015915361667_<76> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3694671248 for P32 / July 13, 2008 2008 年 7 月 13 日) (Serge Batalov / pol51+Msieve 1.36 gnfs for P37 x P76 / 12.00 hours on Opteron-2.8GHz; Linux x86_64 / July 17, 2008 2008 年 7 月 17 日)

9×10²⁰⁰-7 = 8(9)₁₉₉3_<201> = 19 × 53 × 457 × 8017 × 15934453357_<11> × 256144718010248113_<18> × 53233625480766077029_<20> × 17802940180354513744305268037686386634555232996219_<50> × 63064448745252440797528276587900110400369626444298621672290454824179477424400635508926027260781_<95> (Eric Jeancolas / cado-nfs-3.0.0 for P50 x P95 / May 18, 2020 2020 年 5 月 18 日)

9×10²⁰¹-7 = 8(9)₂₀₀3_<202> = 23 × 18473551492149938551253025419884040839_<38> × 21181869008369393932549895281176206440602071314901233547773826044115463753440350314470194147359203649884780565101875411593097870658027727125274244341497672422820569_<164> (Serge Batalov / GMP-ECM B1=3000000, sigma=1318125982 for P38 / January 20, 2013 2013 年 1 月 20 日)

9×10²⁰²-7 = 8(9)₂₀₁3_<203> = 859 × 449077220849490881_<18> × 233307295464234642614860113594967602499067134144009061548835067901794581622064472898086197444009370446912402852933687141515343006234511057589952261113915346369987332921783098457430267_<183>

9×10²⁰³-7 = 8(9)₂₀₂3_<204> = 654413 × 9116851 × 5700733195303605079093859_<25> × 3714817616108249415967179294405421727505728607106415503_<55> × 7123239101368569534914712010464454782135910096872760936314670940929557069879893687344516616127185996532235960043_<112> (Bob Backstrom / Msieve 1.54 snfs for P55 x P112 / February 26, 2022 2022 年 2 月 26 日)

9×10²⁰⁴-7 = 8(9)₂₀₃3_<205> = 467 × 877 × 852778217 × 64581526709789287365178051_<26> × 2053558833372212002058214069709_<31> × 194300751306947597754669850807502619790461622467210252600373615313385133534873580749349428852405670208521593826794916118650290102368209_<135> (Serge Batalov / GMP-ECM B1=3000000, sigma=260029717 for P31 / January 20, 2013 2013 年 1 月 20 日)

9×10²⁰⁵-7 = 8(9)₂₀₄3_<206> = 487 × 54516555087497_<14> × 288387721007212781599532200336102769015876043001_<48> × 7791132857078085768169330855649104435741331285915869596287304819131_<67> × 1508716945281805196990812250228695900528766934893279483663618496625218050477_<76> (Bob Backstrom / GMP-ECM 7.0.4 B1=48140000, sigma=1:3893305144 for P48, CADO for P67 x P76 / June 16, 2021 2021 年 6 月 16 日)

9×10²⁰⁶-7 = 8(9)₂₀₅3_<207> = 83 × 7027 × 37686926380823333777918743310476873583491907229979313936382475630190942709927412913260003240096639_<98> × 40945270467815697869802124945169170798638693085688843670705022093262292444277082489807139091402929789007_<104> (Serge Batalov / for P98 x P104 / December 15, 2014 2014 年 12 月 15 日)

9×10²⁰⁷-7 = 8(9)₂₀₆3_<208> = 106087 × 987451559 × 87337438049_<11> × 9941256980359_<13> × 158839581926397451_<18> × [622965588094753312963845339296698286706190518658460617232166441475927651257876166037983624292177021275491411422242555658903456189928901891116539364247181_<153>] Free to factor

9×10²⁰⁸-7 = 8(9)₂₀₇3_<209> = 574536111103_<12> × 1391105121913153482463639567447_<31> × 2636581926170702349059315753735431199_<37> × 14862841014106460425611150481332954439674343702681_<50> × 2873572286012483740353684853340786764135524135911421440338673549038381281922241767_<82> (Serge Batalov / GMP-ECM B1=3000000, sigma=1022288973 for P31 / January 20, 2013 2013 年 1 月 20 日) (Serge Batalov / GMP-ECM B1=3000000, sigma=2710756109 for P37 / January 20, 2013 2013 年 1 月 20 日) (Warut Roonguthai / Msieve 1.49 gnfs for P50 x P82 / January 25, 2013 2013 年 1 月 25 日)

9×10²⁰⁹-7 = 8(9)₂₀₈3_<210> = 1373 × 26600975179_<11> × 5389967025922824815570077202781153975800589462598781_<52> × 90411464377991804146315798803470592261583141068440557_<53> × 50566722132934450081376991972342552489576820047364263940220999663491818394985128615656559487_<92> (Bob Backstrom / Msieve 1.54 snfs for P52 x P53 x P92 / June 4, 2021 2021 年 6 月 4 日)

9×10²¹⁰-7 = 8(9)₂₀₉3_<211> = 563 × 25733 × 3357259 × 1241848757_<10> × 4162592938604101_<16> × [35795315755051556143482384255076882151591632985808593329074383552827847631716757686285387141751565124018657731300629295771004647245841545400949258434709664405781931442660109_<173>] Free to factor

9×10²¹¹-7 = 8(9)₂₁₀3_<212> = 17 × 3135735106303_<13> × [1688317880045848238737635477282196614078397543752708702777136968593143423264069517896376610156697713496264837758958701380734994977786389904428030201437542571489121827819183770213442415086421264667543_<199>] Free to factor

9×10²¹²-7 = 8(9)₂₁₁3_<213> = 59 × 1123 × 16043351717686627_<17> × 4491866070251411837471_<22> × 26037552998772984893743417633843_<32> × 7239168261249652601175641354803299067820557189900761721873245280224416814877258075052436615024860628213110140325413976892595629907245076079_<139> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=3170107370 for P32 / January 13, 2013 2013 年 1 月 13 日)

9×10²¹³-7 = 8(9)₂₁₂3_<214> = 53 × 4818742547441126957931019187_<28> × [35239757900095959189948510121644992116968106544620591121962414716741988948045348661040205002875883304243208249247186434316103019572593354993882186446599258791675338600776772573266508663_<185>] Free to factor

9×10²¹⁴-7 = 8(9)₂₁₃3_<215> = 31 × 1297 × 1365548820189078960598033793408349753834010789_<46> × 1639206275960755860192544465573038834070961355795909686010053192608450465373283185320044727810581013038497195864238647789104925497599717543912785743473449977395341291_<166> (Bob Backstrom / Msieve 1.53 snfs for P46 x P166 / September 20, 2017 2017 年 9 月 20 日)

9×10²¹⁵-7 = 8(9)₂₁₄3_<216> = 373 × 42594493 × 14335460384943499349502089131521786287516756150655932271224609427569567874796671702437_<86> × 3951559989821888270290522080066971457437905189009643822349277214829334916058407242048141854127861827207903071614799254501_<121> (Bob Backstrom / Msieve 1.54 snfs for P86 x P121 / March 23, 2020 2020 年 3 月 23 日)

9×10²¹⁶-7 = 8(9)₂₁₅3_<217> = 1531 × 2719 × 146241356685573643172218848457_<30> × [14783862129692949317475018927888153338416155864428159314036374204089970313827218283780018028017965573796400445589115191836812060879045701282325824746667677037394466961431203022008541_<182>] (Serge Batalov / GMP-ECM B1=3000000, sigma=614155650 for P30 / January 20, 2013 2013 年 1 月 20 日) Free to factor

9×10²¹⁷-7 = 8(9)₂₁₆3_<218> = 262957 × 73421239 × [4661611366472302138577489377779168246777410017014068428533764991254956557348592633526301994108867795835218676096295042181118439943632336511685406302943971788113412131260248527227757461561414940773696784491_<205>] Free to factor

9×10²¹⁸-7 = 8(9)₂₁₇3_<219> = 19 × 29 × 281 × 726187128727188163349259374603_<30> × [8004533815769898690183447481208852476193163102671210019900458966591910211332399460647347159579945368023782391883683455350943416854607383776283068178709060861382977898123092802505255301_<184>] (Serge Batalov / January 20, 2013 2013 年 1 月 20 日) Free to factor

9×10²¹⁹-7 = 8(9)₂₁₈3_<220> = 449 × 1951 × 159701 × 63158037906822595224942243033760649763838484973833516166836119201083380410987212416522569156046352346313_<104> × 1018597565591349500214532370668571355360359614927805758715107854853459966226018788227829648291875854188339_<106> (Bob Backstrom / Msieve 1.54 snfs for P104 x P106 / March 15, 2020 2020 年 3 月 15 日)

9×10²²⁰-7 = 8(9)₂₁₉3_<221> = 75260651973370570125976289397269369_<35> × 15682630947055255008118917819750016811_<38> × 76252767537303327632880725241381302650389068242261095290287948360901508705233306302893861720141730092561206313306572852874043101202638033969041441027_<149> (Serge Batalov / January 20, 2013 2013 年 1 月 20 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3310117485 for P38 / January 28, 2013 2013 年 1 月 28 日)

9×10²²¹-7 = 8(9)₂₂₀3_<222> = 349 × 3637 × 78598523475414291157_<20> × 2620589780561013146805911_<25> × 3442392213553745374365612602200652128863904519091558208507880325456756735401634493662157955782855306496000471640731152129124313574316109108839108580376573332246883591846643_<172>

9×10²²²-7 = 8(9)₂₂₁3_<223> = 142132421 × 394730569 × 5939811127_<10> × 3671818914913_<13> × 35244181375973610034177786987262098510391419731055177820220071251346506124996929891_<83> × 208692709347936287369310605034290787099296506064770170447502303352003936832232696942652759914227181177_<102> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P83 x P102 / April 23, 2022 2022 年 4 月 23 日)

9×10²²³-7 = 8(9)₂₂₂3_<224> = 23 × 565914229 × 1981690873781_<13> × 2531570481161_<13> × 244555354268664638547136759_<27> × 1530560919151698721057534319_<28> × 47192818741997150986206081887459_<32> × 751925240918113249213728657273210872522801_<42> × 103767116895828891993244277717324878249617708403313419080441821_<63> (Serge Batalov / ECM for P32, Msieve 1.51 for P42 x P63 / January 20, 2013 2013 年 1 月 20 日)

9×10²²⁴-7 = 8(9)₂₂₃3_<225> = 75870953 × [11862247202826093406260496029356583935356657507649864369042524086919008385198483008378713787870833782725781762620010849211291704745029365849668449531667277198956496565951926292529896125069102532559463171630386664577681_<218>] Free to factor

9×10²²⁵-7 = 8(9)₂₂₄3_<226> = 4073 × 120693253343593563076388548628735920212208887624011467_<54> × 18308177119693579433081123023987034386650702014604952448966618748334513884121980859102097989911908693640166783401865769867575797018363992400224835267053472913414831211923_<170> (Bob Backstrom / Msieve 1.54 snfs for P54 x P170 / September 12, 2018 2018 年 9 月 12 日)

9×10²²⁶-7 = 8(9)₂₂₅3_<227> = 53 × 925063 × 7571494175648054779994833698583367_<34> × 242445281659127182367148236133057354076074365144420882219008029786914073838350984716405748566549369393481094361937065933294704293382288096058985007459491546992328429171120216387174790661_<186> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1433781751 for P34 / January 21, 2013 2013 年 1 月 21 日)

9×10²²⁷-7 = 8(9)₂₂₆3_<228> = 17 × 1087 × 48523 × 144169 × 56042137793_<11> × [124230954042644334296276040324436885628779762573283296242939903571000824579597929200035093975464582165172428645068117512519399521148672648062380477415958546762533166825043665838430487190857531537796718237_<204>] Free to factor

9×10²²⁸-7 = 8(9)₂₂₇3_<229> = 617 × 691 × 859 × 16606425449161255957_<20> × [1479823684976212208026497411548332854698756329227171402021602130542792274780536900423023843555071909564888213390814799535682546773909325656271770147697868404556143892351712405416242197398525345487736813_<202>] Free to factor

9×10²²⁹-7 = 8(9)₂₂₈3_<230> = 31 × 1019 × 24989 × 217790949503_<12> × 523501494985859812235665886784086975387850778477156226153562698642599259059837346520436128686009555779653402682569207051077552790874935287432531040471167420974552743664951178172633521953376911719225081747877111_<210>

9×10²³⁰-7 = 8(9)₂₂₉3_<231> = 51237427786340924800239379315294597942435524037389830309662907605385003608714689353423882260715576183142758981623_<113> × 17565284575817944220187662032055297125230805776180803212134090784297624398948378125807152313972935318264056805958370191_<119> (matsui / Msieve 1.52 snfs / March 29, 2013 2013 年 3 月 29 日)

9×10²³¹-7 = 8(9)₂₃₀3_<232> = 134489753158520949524261_<24> × 8172223397499257517575047073_<28> × 8188664594115595503580423196854750405631594703283051003754763393464283809901576925519295020997320716288677629674434349693395532796350581759007875765177277807975844334988284475890981_<181> (Serge Batalov / GMP-ECM B1=3000000, sigma=3965648295 for P28 / January 20, 2013 2013 年 1 月 20 日)

9×10²³²-7 = 8(9)₂₃₁3_<233> = 47 × 3221 × 223747 × 542947 × 2633583264182581_<16> × 1858198966356605741206616791354209768199094689953502342873434279871048621826631208216027617054133913688814012039136810855527192384379385000987247967633826627273845449746119709407234992737858069482813591_<202>

9×10²³³-7 = 8(9)₂₃₂3_<234> = definitely prime number 素数

9×10²³⁴-7 = 8(9)₂₃₃3_<235> = 2383 × 6271518960001_<13> × 602206900333626995406275540737996308679568146311954470692175641215152506020685807126707596458165635021202709612559559787631897839483212375735925250679881344269463450432164499513498710750969983922484312225102190318687671_<219>

9×10²³⁵-7 = 8(9)₂₃₄3_<236> = 556054699 × 143766339316507_<15> × 19379109037590456317_<20> × 776438272066673328185940224749_<30> × 182308333812625357482780802735163521_<36> × 601201381906764207791557996852690222334833_<42> × 682653854795073482299474970784742997784507541244272296778504446523147516112224673441929_<87> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=731035129 for P30 / January 13, 2013 2013 年 1 月 13 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2987282525 for P42 / January 21, 2013 2013 年 1 月 21 日) (Warut Roonguthai / GMP-ECM 6.3 B1=3000000, sigma=473056303 for P36 / January 22, 2013 2013 年 1 月 22 日)

9×10²³⁶-7 = 8(9)₂₃₅3_<237> = 19 × 215078117 × [220238217227053270823309379506198573178732176889160597158140551568208024377340169165752827133819574274176758518712626876083255589263044611049756156124525921117204812465514809354495824270309436601488134510778949359961838276745991_<228>] Free to factor

9×10²³⁷-7 = 8(9)₂₃₆3_<238> = 2832991279_<10> × 3176854114135096848633821720988079328287971055204932030431428659544419303523030718090678598237929838682006052161941724071223305731891735908164085809739621157513630312873264584447737722809982571781859692763282946908076239086791767_<229>

9×10²³⁸-7 = 8(9)₂₃₇3_<239> = 61210468733265087121_<20> × 630639403128246855206939_<24> × 2331501513438456320884919109581828161802831311815699495444459651870522301428310421525893970024356669694710027426565500923380969738771147768402315271138490072338677134785084677903747342944002595147_<196>

9×10²³⁹-7 = 8(9)₂₃₈3_<240> = 53 × 61 × 181 × 1097 × 70487429431_<11> × [19890235701114469437485055147036442767058576937793951397755243149536659778873586871806064463546074587897849271216080361693384766514478354600872426776714641183888058533408690040719442113843963065364036046456243691866509563_<221>] Free to factor

9×10²⁴⁰-7 = 8(9)₂₃₉3_<241> = 1493 × 727600073 × 8284951449288015589655214253531188170680080862743993548042677439169697347318322791612201327449841538844477934667438681715446795063023864783035511847797140937014668798637974378182858190916662429236269624721312497766627421381366637_<229>

9×10²⁴¹-7 = 8(9)₂₄₀3_<242> = 97 × 428977 × 7819153 × 333950511407755111267_<21> × 640348536377035300721_<21> × 17234896425085743278671_<23> × 151865262155527239664587101_<27> × 26366598223416408664066590830488778680400386657_<47> × 18743785203443202798774284905711376437130006465216403601267394610637495193282374848223443281_<92> (Serge Batalov / GMP-ECM B1=3000000, sigma=3036460514 for P27 / January 20, 2013 2013 年 1 月 20 日) (Erik Branger / GGNFS, Msieve gnfs for P47 x P92 / May 14, 2014 2014 年 5 月 14 日)

9×10²⁴²-7 = 8(9)₂₄₁3_<243> = 13753601 × 23996081019929_<14> × [2727003961102287588138034269608582625495782167332837466984393061079851441565226163715120465722327507738881539880506919806528878019814939700394044154052656299652472553377429536588989142706646857168399660997815752019767771617_<223>] Free to factor

9×10²⁴³-7 = 8(9)₂₄₂3_<244> = 17 × 15497078775043_<14> × 54752784416363113_<17> × 623932398575173364004302545824353773067706690871848245274022936070149459108138501135970645090176628692013836732107135993851745228732273889809771535846187888746639281898560720878763440044119949690751119329285737131_<213>

9×10²⁴⁴-7 = 8(9)₂₄₃3_<245> = 31 × 159638243413260087892132991119_<30> × 6195053198794057032257850600279149_<34> × [2935613222040072107797581651663263843388960138131903713499021375072598111904917739042289432345457880040784198202743678822594851809696777932275399609799260999368273188632856566810413_<181>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=3768350025 for P30, B1=1e6, sigma=1172650598 for P34 / January 14, 2013 2013 年 1 月 14 日) Free to factor

9×10²⁴⁵-7 = 8(9)₂₄₄3_<246> = 23 × 1860904349_<10> × 21027644329831535931444004080554846867932822156731037778926141099441930765664844332980906969250937174777683975089309841698955025937090295034171371424771802665631514551782889738085782907601817290675663378996586249955425395114192125659259_<236>

9×10²⁴⁶-7 = 8(9)₂₄₅3_<247> = 29 × 281 × 68455272871_<11> × 1558492461493855183749184811137_<31> × [10352055215854388530080700415950825894651320495185249791532003376327943732655344147005599022003218723987383107692414575227948525517134886787393056269647335492933120773242470223656928504378627327279115491_<203>] (Serge Batalov / GMP-ECM B1=3000000, sigma=2911317418 for P31 / January 20, 2013 2013 年 1 月 20 日) Free to factor

9×10²⁴⁷-7 = 8(9)₂₄₆3_<248> = 83 × 89783 × 824009388679363_<15> × 14656765662384274914891948552588274083272069694930399633989650930567223888023179993194374467143672716303900791256591970756053099286090589682133511559625649623249859388218484551875662607436975908515045859964107926058857607228999_<227>

9×10²⁴⁸-7 = 8(9)₂₄₇3_<249> = 109 × 54937567 × 36485895258851_<14> × 4119282552375161508539024549658966967773023986781993109872276626822014849290001680770911185266416258735695984132533871652559010686460704806581967657102448575344845705262253694522612684671364550694425825820343318101087004586881_<226>

9×10²⁴⁹-7 = 8(9)₂₄₈3_<250> = 52859 × 192408197 × 22097578747091_<14> × 7447766937104939_<16> × 937809330181667357223217916713939668971_<39> × [5733432177420291334673646862167762084439087066950690364893303063295632113028266269161472739983721751603548072432556869419339663476577187625578436633189530331747134632429_<169>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=56793237 for P39 / January 28, 2013 2013 年 1 月 28 日) Free to factor

9×10²⁵⁰-7 = 8(9)₂₄₉3_<251> = 113 × 227 × 541 × 9679 × [670055002346138812001188130600818579517754106596023863482960051225560197481805411507440327796370627319125614378999622117783596823012376481367639774927452921730442491652288141815246986178535862382411327236085383012391536461234711239231547537_<240>] Free to factor

9×10²⁵¹-7 = 8(9)₂₅₀3_<252> = 449 × 2004454342984409799554565701559020044543429844097995545657015590200445434298440979955456570155902004454342984409799554565701559020044543429844097995545657015590200445434298440979955456570155902004454342984409799554565701559020044543429844097995545657_<250>

9×10²⁵²-7 = 8(9)₂₅₁3_<253> = 53 × 149 × 317 × 16661 × 3637607287_<10> × [59320422236549840731139387729050121677297835649227773756269704657926281187394032427478868097657592575460219181592671936663910710016839859075313244875442147696598510059967281061068681583900511648405463065449264078877171382957420531751_<233>] Free to factor

9×10²⁵³-7 = 8(9)₂₅₂3_<254> = 23581721 × 3532033069_<10> × 436269692202961_<15> × 5879285761271850312491120291689412580764911_<43> × [421272042752509802441893659456778983888229528062893585872628293528615766275032087661538463634098432602147534842694981531412306585792199584646685991278881154233570178553213630802267_<180>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:3400662323 for P43 / March 31, 2019 2019 年 3 月 31 日) Free to factor

9×10²⁵⁴-7 = 8(9)₂₅₃3_<255> = 19 × 859 × 15447898484615697361_<20> × 4213508014433654812455105979676107_<34> × [847193301943542221283831182444153585079582542756988228598344397802742965930550207717351054913906032765040713913847891724035295078461121501504680416075648741912495209626989782331507945683995794074779_<198>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:2140075374 for P34 / March 31, 2019 2019 年 3 月 31 日) Free to factor

9×10²⁵⁵-7 = 8(9)₂₅₄3_<256> = 5857 × 12503 × 357611 × 2239816498651_<13> × 153436875352954825686014977631640104855749854784863753788837898728020535979557856134708099503755346223057699740380817819343281718250399956806973031151824218008983741032004927625639158178030207147227940917485616608262127886306834903_<231>

9×10²⁵⁶-7 = 8(9)₂₅₅3_<257> = 193 × 5563 × 14079661 × 302585341 × 287638273076120124293_<21> × 68405242224715283367504471798106629398849810279165350478691136336387549436338242956679561994624725077176501999214016675267173444597972098681297335697998769702776203442643742192143112466892901891461459056346128209239_<215>

9×10²⁵⁷-7 = 8(9)₂₅₆3_<258> = 199 × [4522613065326633165829145728643216080402010050251256281407035175879396984924623115577889447236180904522613065326633165829145728643216080402010050251256281407035175879396984924623115577889447236180904522613065326633165829145728643216080402010050251256281407_<256>] Free to factor

9×10²⁵⁸-7 = 8(9)₂₅₇3_<259> = 8852408201971_<13> × 2819312620168697_<16> × 306191666134557539211555992227_<30> × 1177726578539203481939276634648837573798889798787783529108339587882725288891122111972527881580330756292323284646634647161164079403379861880028573282234474956245763335636701812484245295099298361572850057_<202> (Erik Branger / GMP-ECM B1=3e6, sigma=3:561439047 for P30 x P202 / March 31, 2019 2019 年 3 月 31 日)

9×10²⁵⁹-7 = 8(9)₂₅₈3_<260> = 17 × 31 × 8934139199789_<13> × 1735838966976143_<16> × 5028129345683033942773_<22> × [2190096771187188259833272700597043827194412067975417305413043054559012757307762077351119855510229688224081757651761133482805123790430943580622612618943157420133583550875784129100322824985828021591449794001929_<208>] Free to factor

9×10²⁶⁰-7 = 8(9)₂₅₉3_<261> = 2560549716682411_<16> × [351487024109061035857157928137522248016271403343050034094032753076158984815643888483269597416496134440770005498358267290858505814607645832777800983579210478018590988562885339775926792588068624535616515973957131991767950347567335121161235547997163_<246>] Free to factor

9×10²⁶¹-7 = 8(9)₂₆₀3_<262> = 10867 × 71993 × 143443 × 6225119 × 425147167811_<12> × [30302346736555904965266823952263950867110207520976026112789719495769764354334789149149462548718116551662250135198604561393572501100169601325408132641634982201551234956145023134286827662319707425984358716233090780096655360323033869_<230>] Free to factor

9×10²⁶²-7 = 8(9)₂₆₁3_<263> = 2913654191923920531439453_<25> × [30889046562032788497359691451896031395661891445276639376761868005709916742681990263141088437292875424827745317681261159138132716727891768486661778314327131495081947868600396278056511616847379742249560652485719509864748868240656151258703181_<239>] Free to factor

9×10²⁶³-7 = 8(9)₂₆₂3_<264> = 56857 × 76436675096381_<14> × 3364855142549962093_<19> × 61544664498742261203732494676227068903302355169947688838416426336532205496390281381812403221718700402752469503444301866284278559411617187190024597500601231654244163368362534492280940217780466856199513521902471331518934867187753_<227>

9×10²⁶⁴-7 = 8(9)₂₆₃3_<265> = 283 × 2789951 × 28024501 × 36815239830739_<14> × [11048262283103462540015988193303072623124030843768426670843561468826897364800568508033009905430337796034424518603531589466903411164240423964274884578516296290265880432340107047724480845460939446602498188630191670240797508732164162212939_<236>] Free to factor

9×10²⁶⁵-7 = 8(9)₂₆₄3_<266> = 53 × 6464413 × 68845961 × 3815566950464414720324458404736271716689967336290879921377400241635636737962870479376811195693992017580040300643631795656089976646182459296895357121548367851513979008420446122312580748849064621948961838380039450627200731917204870602575585498026997617_<250>

9×10²⁶⁶-7 = 8(9)₂₆₅3_<267> = 54060125149_<11> × 719659028909_<12> × 38925985977503749703_<20> × 57174961009212295685687_<23> × 8220200635739513794295579_<25> × 1264476514511561286579333522427100068177948938020919894790789574753642032795045695638415189899702405729299055304234465952725949389650144608550842116680170761052748267036425289267_<178>

9×10²⁶⁷-7 = 8(9)₂₆₆3_<268> = 23 × 93383429 × 7316393671_<10> × 2443074319577_<13> × 130584692994641_<15> × [1795224803690244928531694821772889412252790417429182654917054472313743949288509720973751839854349431367911216306771630089063896749309007802642934444454512690895399598314122046120837369105721005643305176461677088400793077757_<223>] Free to factor

9×10²⁶⁸-7 = 8(9)₂₆₇3_<269> = 26443741097_<11> × 622080327936822032800931_<24> × 390913707853468698060515953681_<30> × [13995623322108420474682001283387016020740982845906248658567211351583732000797265123960481664913918216357304495477243594729216854569246834713374471490520587855398292838195650518310649804350864476255008687179_<206>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:1312574879 for P30 / March 31, 2019 2019 年 3 月 31 日) Free to factor

9×10²⁶⁹-7 = 8(9)₂₆₈3_<270> = 526469781839083_<15> × 2197221776008463_<16> × [778027891319306202981907269919341000332062058936433097374970924832194816099126258422111992642359804327085264546290443487687190067376310702588645546861962116774646747586216428332399910914098887097021267021306312894765023420251887605891409317_<240>] Free to factor

9×10²⁷⁰-7 = 8(9)₂₆₉3_<271> = 59 × 149705639 × 224576266276151_<15> × [4537205828768769066446030518014001176689798907630077512015365225690647080027978152330170603593708296064619267528322756761990788524588468484825452208161176187744658854156838088482441475415033811037951661626629702105633339389443368959055850250464443_<247>] Free to factor

9×10²⁷¹-7 = 8(9)₂₇₀3_<272> = 3989 × 5501 × 104884943 × 479519210469709591_<18> × [81548818100088329228616559961951919441065059446203209063198487475197327264435001473445894985127859242048394218048833528933161769206407481551764435197913202197927045638425854933973993667010279172630011339967837910904451309017982800005951649_<239>] Free to factor

9×10²⁷²-7 = 8(9)₂₇₁3_<273> = 19 × 197 × 27988913 × 368879241540239_<15> × [23289085425056323487319513679163817103988040221812221238221844547523890341070194860142273139175101124104323093421786236837825555773864043210742795268251686131265661328347355825654801461951268960315600453493956261681088731100496319261523325921513593_<248>] Free to factor

9×10²⁷³-7 = 8(9)₂₇₂3_<274> = 461 × 60319559 × 604289713 × 85899522425947_<14> × 6235158183612274725508548092385648454222442751357842293609236339554557794666243804580895423779743628366445720198833747080466753738766593548372047141463523332125577464608629683995412209492731693818488830773125548313939697241981114902415777137_<241>

9×10²⁷⁴-7 = 8(9)₂₇₃3_<275> = 29 × 31 × 281 × 48527 × 167572747 × 9019887460583_<13> × 9670835119631594825567927_<25> × 2070898730215501114405454516137_<31> × [242530133309447937329976108605277306513963234586414260514974905873398034965612086758015957671886013400634088298356811689701079673828410545111914401506971066299312001822681306701041470128439_<189>] (Erik Branger / GMP-ECM / March 31, 2019 2019 年 3 月 31 日) Free to factor

9×10²⁷⁵-7 = 8(9)₂₇₄3_<276> = 17 × 179 × 487266589 × 3233283491_<10> × 187728469162318981832523859830057589506371818569359462450960871073070941047510141538449911569851594555852242506606069739514077984519311122607923207241217155200879231350732989298666836560275120067290809395565109445759355196095454883131950486771014195314149_<255>

9×10²⁷⁶-7 = 8(9)₂₇₅3_<277> = 233 × 12097 × 21088768062725205053_<20> × 82861229895020358090362868738559_<32> × [1827285138982441227812339855605040233606561345716282063796017452951634742846909740305540818736678863177566967244113549444302514424681405195054724327003821021367542522803479145485859434340927530387466733546182014143565659_<220>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:3353975552 for P32 / March 31, 2019 2019 年 3 月 31 日) Free to factor

9×10²⁷⁷-7 = 8(9)₂₇₆3_<278> = 653 × 14051 × 14747 × 41446021961_<11> × [16048541194548222158111520517840971218042821968750577317935692114435897811977275255274879998596992434544859504041483660462849417601963542739598173488538467844248713693558403795719302911426752794023779776293246387079465184304079028240892438286177986062501893_<257>] Free to factor

9×10²⁷⁸-7 = 8(9)₂₇₇3_<279> = 47 × 53 × [361300682456844640706543556804496186270574066639903653151344841429144921718185467683661180248896025692492974708952228020875150541951023685266961059815335206744279405861099959855479727017262143717382577278201525491770373344038538739462063428342031312725812926535527900441589723_<276>] Free to factor

9×10²⁷⁹-7 = 8(9)₂₇₈3_<280> = 16747 × 537409685316773153400609064310025676240520690272884695766405923448975935988535260046575506060787006628052785573535558607511793156983340299755180032244581119006389204036543858601540574431241416373081745984355406938556159312115602794530363647220397683167134412133516450707589419_<276>

9×10²⁸⁰-7 = 8(9)₂₇₉3_<281> = 859 × 2129 × 4481 × 15959 × 886421 × 231302821 × 1392422883509887788721_<22> × 326348858699656401908831368987_<30> × 61723522264576616880765710182753689480709_<41> × [119665276409905618606929092305684746044414624940528149732169586677639367515697711601421530094616957143485297718998050458853401324586577352566580402934097706646019_<162>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:2589178780 for P30, B1=3e6, sigma=3:1535205533 for P41 / March 31, 2019 2019 年 3 月 31 日) Free to factor

9×10²⁸¹-7 = 8(9)₂₈₀3_<282> = 211273409019682711148060279496278317_<36> × 4259882983741479523845233616813241168609666206481915488516676888627285980660017453819851816616691670429873042828385836338593987576772333567581109520978052301047663472539832364854627813715315306158712583290438070397090424992374688604054923535106429_<247> (Erik Branger / GMP-ECM B1=3e6, sigma=3:3234356668 for P36 x P247 / March 31, 2019 2019 年 3 月 31 日)

9×10²⁸²-7 = 8(9)₂₈₁3_<283> = 13831 × 37848871657_<11> × [17192379583056893614358644779078996070124914264896915179430057675423032733982533555334325423681304905948834654146489039498876226913495037488021094023732229396302337989322515699541896823026247061046952680883152155893418940255471203798882453636202413037247085845436531879_<269>] Free to factor

9×10²⁸³-7 = 8(9)₂₈₂3_<284> = 449 × 523 × 98621 × [3886199375786764491039979949815838121933644390364921067751861439228694935082979720470443380092744732760257225165238106850449649073814989837670458404467699471680439698304433512865077597061869222475556166155393390252278153904910948642254401578252720032218655101741028473744679_<274>] Free to factor

9×10²⁸⁴-7 = 8(9)₂₈₃3_<285> = 1319 × 1047649 × 583630836216692597_<18> × 1351846042745917127_<19> × [825498801757700020673305504985970206806153512672532784259577990180748430330131057951386995753195820472147085137446387213290367414210173444483444213382298872863507229417685428660516482964895285124832236749345257261481121864836456105636738437_<240>] Free to factor

9×10²⁸⁵-7 = 8(9)₂₈₄3_<286> = 269 × 3838735139_<10> × 788930224133672478090039419_<27> × [11047486689019826985130244671239802538212778541967905635092793723735134217672907889710968047659761403706077425749872847207953981311215538950101875576996805052379196894238302002533553104247211816493164529811496094990786226409382608148836267119407117_<248>] Free to factor

9×10²⁸⁶-7 = 8(9)₂₈₅3_<287> = 1519417 × 445218509 × [133043088248905346370266033811386328806456618673081430346649157823637303325398893521757283270767146214537042413219318645292230812257554727761556975723685861168488816081548270908332095544716795867550456299171112828602562957409581144540458278534162210043484495187746465648581_<273>] Free to factor

9×10²⁸⁷-7 = 8(9)₂₈₆3_<288> = 1619 × 786179 × 483460057 × 49377615569_<11> × 103541686081_<12> × 7617376472509_<13> × 17961267096315090523724759_<26> × 440059243199459546986813069_<27> × 4751324988033151995598933268005639636852381125569253796216160203518873563752042679222385695650504692785531108335123892481042176831606643967986694274063967529475201908836861871676295719_<184>

9×10²⁸⁸-7 = 8(9)₂₈₇3_<289> = 83 × 311075565540967_<15> × 29883490468366121105386723530819736197041_<41> × 11664528669994133232928266351562341841918630387203147422115087157905144766991159283865953588477357962629709020534805869143810461727549116131693947974580067603940244277570116063450118672081056113174757620795589515408757511423603263893_<233> (Erik Branger / GMP-ECM B1=3e6, sigma=3:1890656892 for P41 x P233 / March 31, 2019 2019 年 3 月 31 日)

9×10²⁸⁹-7 = 8(9)₂₈₈3_<290> = 23 × 31 × 3713862871_<10> × 7698221743_<10> × [4415060905604893125659233858232977574449909831278214582885679475163591508619895706338156031975463432302833481913650956767178025453740378426318537715506217590788682945277034771050900264951624035836812536650142228911639402734557589956898233573438764675764755730947017337_<268>] Free to factor

9×10²⁹⁰-7 = 8(9)₂₈₉3_<291> = 19 × 13859 × 7429066847444811857_<19> × 460068763301241556286973361789028318635305485977073589529121240422343382271381107731997944537336956008147409844640941889904768386039814973371700054382451105942590724739369541417868310626403000343095844628898924477354185075046864197327124798820753083670706359840029969_<267>

9×10²⁹¹-7 = 8(9)₂₉₀3_<292> = 17 × 53 × 12037 × 706082387 × 5205636259545709738518167_<25> × 66259630942198167557944837_<26> × [3407385322040401802284517692565996212105103344440812159592700910106949479498294186806973199046191415170896846137705282462260262958327077551449421231475121531045442487649438378130715178317380781429718723215999186948812807000793_<226>] Free to factor

9×10²⁹²-7 = 8(9)₂₉₁3_<293> = 46690872694331602205746477431731722154484784931_<47> × [1927571596041858574711742605275945963328677726469559734438327954983076624255776973155902809305583915359379765335499342071206656936462004551029632958036688234002729336871331320268091684095207965051283843697490023266192197478039928158615997235889203_<247>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1:3936551490 for P47 / June 13, 2019 2019 年 6 月 13 日) Free to factor

9×10²⁹³-7 = 8(9)₂₉₂3_<294> = 18395917 × 10045053853_<11> × 16394799399521_<14> × 297072664444481204796105066107506578840634620329711944945836012995263061450274480365281024025126029420288059383797367625096086514848484543709438325690712523606220348237568383278632373130033754545475118765124045529667357696376228862546515655539822517556178401379233_<264>

9×10²⁹⁴-7 = 8(9)₂₉₃3_<295> = 284848981 × 72629805866029527230943661930448834790914999453_<47> × [435023738126056301123397544474885876762190433557321336981904139685288531464773537529283413963922848561981033943653895066281302859532971902147457756088218412973968880208876899611979225803369174981041666301976541253082081403182047382909898201_<240>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:1433992597 for P47 / March 31, 2019 2019 年 3 月 31 日) Free to factor

9×10²⁹⁵-7 = 8(9)₂₉₄3_<296> = 219503 × 140706637079331353716523239_<27> × [2913986032746433416051112522214093982770588011677348869525602527850317927109311357875388792296918801279593909345214737614754475429122250872766324406645462080658689119983058398330905356723608198478120281085885502726735244216074083014534231501071796347454757915906129_<265>] Free to factor

9×10²⁹⁶-7 = 8(9)₂₉₅3_<297> = 50849 × 35869065806860187581_<20> × [493446448022639538032855087697829860490914540004320593203703593285911450058186619820323886916477223585299136250104178461467056532894762866131019221263431403100097308582458529017658259491475211656955768611602244335455995822342196470091706055694841520186383113869533123285197_<273>] Free to factor

9×10²⁹⁷-7 = 8(9)₂₉₆3_<298> = 1099687 × 2160032873769263889859363327611122971_<37> × 3788899253810412043198614027916099084001214720620766332028911373020462658262317387060088875411728522265034311520075810251913171207863085541886352028068352056717532169182190944265806905082163724683206825802938421288328276681901876306648095603562958908720909_<256> (Erik Branger / GMP-ECM B1=3e6, sigma=3:2247565898 for P37 x P256 / March 31, 2019 2019 年 3 月 31 日)

9×10²⁹⁸-7 = 8(9)₂₉₇3_<299> = 419 × 12062193984038950942855862226938125303417_<41> × [17807468220326420829085071717128485129185608625092552570957550569504497904337960212143944082094404841812756353933884601025108553116946675824071840053306814149263449514348258772473073931367265791945368778045839455141012579215395718220632416052801413757988491_<257>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:2657400841 for P41 / March 31, 2019 2019 年 3 月 31 日) Free to factor

9×10²⁹⁹-7 = 8(9)₂₉₈3_<300> = 61 × 307 × 48058952314839536498104341325359107171463662092166390772681155550808992363966465531051423078976878304052971645218134244673466118438618038126768836439365621829444118118225022694505259785336679660383403641800608746729321300795642654990121215357505206386500774283120627970310247236610241896726651359_<296>

9×10³⁰⁰-7 = 8(9)₂₉₉3_<301> = 529003 × 102961043 × 165238575053718729792244995836767291177428843268601556914580276443633357351368013217981357397577331551608480901477407994847170429178697160504615424624351890180271024178002335477265307941297871401386784800906731639505277513236142190770194586273228514784938121954914216405103663905990878217_<288>

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4. Related links 関連リンク

A103092 - OEIS (The OEIS Foundation Inc.)