Factorization of 399...991

Table of contents 目次

About 399...991 399...991 について
Prime numbers of the form 399...991 399...991 の形の素数
Factor table of 399...991 399...991 の素因数分解表
Related links 関連リンク

1. About 399...991 399...991 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

39w1 = { 31, 391, 3991, 39991, 399991, 3999991, 39999991, 399999991, 3999999991, 39999999991, … }

1.4. Algebraic factorization 代数的因数分解

4×10^2k-9 = (2×10^k-3)×(2×10^k+3)

2. Prime numbers of the form 399...991 399...991 の形の素数

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

4×10¹-9 = 31 is prime. は素数です。
4×10¹⁷-9 = 3(9)₁₆1_<18> is prime. は素数です。
4×10¹⁹-9 = 3(9)₁₈1_<20> is prime. は素数です。
4×10²⁹-9 = 3(9)₂₈1_<30> is prime. は素数です。
4×10⁴³-9 = 3(9)₄₂1_<44> is prime. は素数です。
4×10¹¹⁹-9 = 3(9)₁₁₈1_<120> is prime. は素数です。 (discovered by:発見: Makoto Kamada / November 24, 2004 2004 年 11 月 24 日) (certified by:証明: Makoto Kamada / PFGW / January 1, 2005 2005 年 1 月 1 日)
4×10¹⁷³-9 = 3(9)₁₇₂1_<174> is prime. は素数です。 (discovered by:発見: Makoto Kamada / November 24, 2004 2004 年 11 月 24 日) (certified by:証明: Makoto Kamada / PFGW / January 1, 2005 2005 年 1 月 1 日)
4×10⁹⁴⁹-9 = 3(9)₉₄₈1_<950> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 29, 2006 2006 年 5 月 29 日)
4×10¹⁶⁰⁹-9 = 3(9)₁₆₀₈1_<1610> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / August 11, 2006 2006 年 8 月 11 日) [certificate証明]
4×10⁵⁵⁷⁹-9 = 3(9)₅₅₇₈1_<5580> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 23, 2004 2004 年 12 月 23 日)
4×10¹⁹⁶⁷⁹-9 = 3(9)₁₉₆₇₈1_<19680> is PRP. はおそらく素数です。 (Sinkiti Sibata / PFGW / November 19, 2007 2007 年 11 月 19 日)
4×10³⁴¹⁴⁷-9 = 3(9)₃₄₁₄₆1_<34148> is PRP. はおそらく素数です。 (Erik Branger / srsieve, PFGW / November 22, 2013 2013 年 11 月 22 日)
4×10⁴³⁴⁹³-9 = 3(9)₄₃₄₉₂1_<43494> is PRP. はおそらく素数です。 (Erik Branger / srsieve, PFGW / November 22, 2013 2013 年 11 月 22 日)
4×10⁹⁷⁷⁹⁹-9 = 3(9)₉₇₇₉₈1_<97800> is PRP. はおそらく素数です。 (Erik Branger / srsieve, PFGW / November 22, 2013 2013 年 11 月 22 日)

2.3. Range of search 捜索範囲

n≤30000 / Completed 終了
n≤100000 / Completed 終了 / Erik Branger / November 22, 2013 2013 年 11 月 22 日
n≤200000 / Completed 終了 / Dylan Delgado / August 26, 2019 2019 年 8 月 26 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。

4×10^2k-9 = (2×10^k-3)×(2×10^k+3)
4×10^6k+3-9 = 13×(4×10³-913+36×10³×10⁶-19×13×k-1Σm=010^6m)
4×10^6k+4-9 = 7×(4×10⁴-97+36×10⁴×10⁶-19×7×k-1Σm=010^6m)
4×10^13k+5-9 = 53×(4×10⁵-953+36×10⁵×10¹³-19×53×k-1Σm=010^13m)
4×10^13k+7-9 = 79×(4×10⁷-979+36×10⁷×10¹³-19×79×k-1Σm=010^13m)
4×10^15k+1-9 = 31×(4×10¹-931+36×10×10¹⁵-19×31×k-1Σm=010^15m)
4×10^16k+2-9 = 17×(4×10²-917+36×10²×10¹⁶-19×17×k-1Σm=010^16m)
4×10^18k+12-9 = 19×(4×10¹²-919+36×10¹²×10¹⁸-19×19×k-1Σm=010^18m)
4×10^21k+20-9 = 43×(4×10²⁰-943+36×10²⁰×10²¹-19×43×k-1Σm=010^21m)
4×10^22k+2-9 = 23×(4×10²-923+36×10²×10²²-19×23×k-1Σm=010^22m)

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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 9.38%. 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 9.38% です。

3. Factor table of 399...991 399...991 の素因数分解表

3.2. Range of factorization 分解範囲

n≤100 / Completed 終了 / November 24, 2004 2004 年 11 月 24 日
n≤150 / Completed 終了 / November 19, 2007 2007 年 11 月 19 日
n≤200 / Completed 終了 / January 16, 2021 2021 年 1 月 16 日
n≤400 / Remaining 58 残り 58

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

n=209, 211, 213, 225, 235, 239, 243, 245, 247, 253, 259, 265, 267, 271, 279, 281, 283, 287, 289, 293, 299, 301, 303, 307, 309, 313, 315, 317, 319, 321, 323, 327, 329, 333, 335, 337, 341, 343, 345, 349, 351, 355, 357, 359, 361, 365, 367, 369, 373, 377, 379, 381, 385, 387, 389, 393, 395, 397 (58/400)

3.4. Factor table 素因数分解表

4×10¹-9 = 31 = definitely prime number 素数

4×10²-9 = 391 = 17 × 23

4×10³-9 = 3991 = 13 × 307

4×10⁴-9 = 39991 = 7 × 29 × 197

4×10⁵-9 = 399991 = 53 × 7547

4×10⁶-9 = 3999991 = 1997 × 2003

4×10⁷-9 = 39999991 = 79 × 506329

4×10⁸-9 = 399999991 = 83 × 241 × 19997

4×10⁹-9 = 3999999991_<10> = 13² × 23668639

4×10¹⁰-9 = 39999999991_<11> = 7 × 28571 × 200003

4×10¹¹-9 = 399999999991_<12> = 175961 × 2273231

4×10¹²-9 = 3999999999991_<13> = 19 × 105263 × 2000003

4×10¹³-9 = 39999999999991_<14> = 67 × 2551 × 234031723

4×10¹⁴-9 = 399999999999991_<15> = 59 × 257 × 1319 × 20000003

4×10¹⁵-9 = 3999999999999991_<16> = 13 × 89 × 1361 × 4243 × 598681

4×10¹⁶-9 = 39999999999999991_<17> = 7 × 31 × 223 × 743 × 4133 × 269179

4×10¹⁷-9 = 399999999999999991_<18> = definitely prime number 素数

4×10¹⁸-9 = 3999999999999999991_<19> = 17 × 53 × 211 × 233 × 2393 × 37735849

4×10¹⁹-9 = 39999999999999999991_<20> = definitely prime number 素数

4×10²⁰-9 = 399999999999999999991_<21> = 43 × 79 × 337 × 1123 × 1229 × 253164557

4×10²¹-9 = 3999999999999999999991_<22> = 13 × 347 × 2437 × 363857754541013_<15>

4×10²²-9 = 39999999999999999999991_<23> = 7³ × 47 × 1171 × 1733 × 336463 × 3633919

4×10²³-9 = 399999999999999999999991_<24> = 5717 × 69966765786251530523_<20>

4×10²⁴-9 = 3999999999999999999999991_<25> = 23 × 97 × 26161 × 34267 × 2000000000003_<13>

4×10²⁵-9 = 39999999999999999999999991_<26> = 369877 × 759263431 × 142432855693_<12>

4×10²⁶-9 = 399999999999999999999999991_<27> = 617 × 64879 × 499621 × 19999999999997_<14>

4×10²⁷-9 = 3999999999999999999999999991_<28> = 13 × 100197068443_<12> × 3070871358550249_<16>

4×10²⁸-9 = 39999999999999999999999999991_<29> = 7 × 8431 × 3388854059_<10> × 199999999999997_<15>

4×10²⁹-9 = 399999999999999999999999999991_<30> = definitely prime number 素数

4×10³⁰-9 = 3999999999999999999999999999991_<31> = 19 × 71 × 28169014084507_<14> × 105263157894737_<15>

4×10³¹-9 = 39999999999999999999999999999991_<32> = 31 × 53 × 59747 × 407480025252759604989271_<24>

4×10³²-9 = 399999999999999999999999999999991_<33> = 29 × 293 × 3067 × 767450903 × 20000000000000003_<17>

4×10³³-9 = 3999999999999999999999999999999991_<34> = 13 × 79 × 3894839337877312560856864654333_<31>

4×10³⁴-9 = 39999999999999999999999999999999991_<35> = 7 × 17 × 1680672268907563_<16> × 200000000000000003_<18>

4×10³⁵-9 = 399999999999999999999999999999999991_<36> = 445668752387_<12> × 897527587154364423044093_<24>

4×10³⁶-9 = 3999999999999999999999999999999999991_<37> = 107 × 1279 × 112957699 × 17705743103_<11> × 14614221098551_<14>

4×10³⁷-9 = 39999999999999999999999999999999999991_<38> = 317 × 126182965299684542586750788643533123_<36>

4×10³⁸-9 = 399999999999999999999999999999999999991_<39> = 241 × 21977 × 910042316967739_<15> × 82987551867219917_<17>

4×10³⁹-9 = 3999999999999999999999999999999999999991_<40> = 13 × 1493 × 2166811449521_<13> × 95112086615723827961719_<23>

4×10⁴⁰-9 = 39999999999999999999999999999999999999991_<41> = 7 × 173 × 331 × 431 × 2339 × 4877 × 81971 × 861381217 × 287456395901_<12>

4×10⁴¹-9 = 399999999999999999999999999999999999999991_<42> = 43 × 1184658156896449_<16> × 7852328983886332499055013_<25>

4×10⁴²-9 = 3999999999999999999999999999999999999999991_<43> = 11850947 × 50267717 × 39786967050841_<14> × 168762884518849_<15>

4×10⁴³-9 = 39999999999999999999999999999999999999999991_<44> = definitely prime number 素数

4×10⁴⁴-9 = 399999999999999999999999999999999999999999991_<45> = 53 × 377358490566037735849_<21> × 20000000000000000000003_<23>

4×10⁴⁵-9 = 3999999999999999999999999999999999999999999991_<46> = 13 × 22277 × 221071 × 45219253 × 1381671421343196669691329557_<28>

4×10⁴⁶-9 = 39999999999999999999999999999999999999999999991_<47> = 7 × 23² × 31 × 67 × 79 × 191 × 4372157 × 174456743 × 884907301 × 510655527299_<12>

4×10⁴⁷-9 = 399999999999999999999999999999999999999999999991_<48> = 35267 × 12227186849_<11> × 927608937918464402236039505790877_<33>

4×10⁴⁸-9 = 3999999999999999999999999999999999999999999999991_<49> = 19 × 211 × 11471 × 43490325653166523_<17> × 2000000000000000000000003_<25>

4×10⁴⁹-9 = 39999999999999999999999999999999999999999999999991_<50> = 83 × 2683 × 27525479 × 6525688527105038387100875841973862161_<37>

4×10⁵⁰-9 = 399999999999999999999999999999999999999999999999991_<51> = 17 × 61 × 181 × 20563 × 809707 × 1201200837522317_<16> × 106554713181350794099_<21>

4×10⁵¹-9 = 3(9)₅₀1_<52> = 13 × 9533 × 11478529 × 20778496481_<11> × 346549605163_<12> × 390500219882387917_<18>

4×10⁵²-9 = 3(9)₅₁1_<53> = 7 × 389 × 17209 × 3793020318169_<13> × 7532632618541_<13> × 29876158840183612897_<20>

4×10⁵³-9 = 3(9)₅₂1_<54> = 157 × 163 × 569 × 761 × 1237 × 1665067809413_<13> × 17525652127950822486483289769_<29>

4×10⁵⁴-9 = 3(9)₅₃1_<55> = 113 × 1433 × 6053 × 8860097 × 335676199 × 686898522953_<12> × 1997620911401736077_<19>

4×10⁵⁵-9 = 3(9)₅₄1_<56> = 1213 × 435439 × 27926295591401_<14> × 2711805491993242645187238684535013_<34>

4×10⁵⁶-9 = 3(9)₅₅1_<57> = 509 × 62658571 × 944220544009_<12> × 21181492106794667_<17> × 627092674117858723_<18>

4×10⁵⁷-9 = 3(9)₅₆1_<58> = 13 × 53 × 541999 × 15204376720919_<14> × 704488101605429696569025928135183199_<36>

4×10⁵⁸-9 = 3(9)₅₇1_<59> = 7 × 541 × 2659 × 139031879314767479609237_<24> × 28571428571428571428571428571_<29>

4×10⁵⁹-9 = 3(9)₅₈1_<60> = 79 × 89 × 14719049 × 1382642844254719_<16> × 2795459032091734897902450212049031_<34>

4×10⁶⁰-9 = 3(9)₅₉1_<61> = 29 × 199 × 5237 × 8837 × 1632417869_<10> × 606070113479_<12> × 24023856568681_<14> × 630121869948239_<15>

4×10⁶¹-9 = 3(9)₆₀1_<62> = 31 × 48079 × 51067383403_<11> × 525532120638669805503793461936388538314810453_<45>

4×10⁶²-9 = 3(9)₆₁1_<63> = 43 × 11827 × 8898053 × 723962431 × 3104695253724121_<16> × 39326649113872278841672877_<26>

4×10⁶³-9 = 3(9)₆₂1_<64> = 13 × 5879 × 397951 × 41150327719_<11> × 201555190323689_<15> × 15856827214779275189453215813_<29>

4×10⁶⁴-9 = 3(9)₆₃1_<65> = 7² × 227 × 599 × 2371 × 6883 × 13326490787_<11> × 1349249466612248603_<19> × 20459445058501213949971_<23>

4×10⁶⁵-9 = 3(9)₆₄1_<66> = 71 × 907 × 2917 × 5335216441_<10> × 399122198972580674414039835959554050436938872399_<48>

4×10⁶⁶-9 = 3(9)₆₅1_<67> = 17 × 19 × 6299 × 11813 × 376757 × 1241427542057_<13> × 1273584854099_<13> × 279392706425459492737396141_<27>

4×10⁶⁷-9 = 3(9)₆₆1_<68> = 3169 × 1035361 × 7119289 × 1099261249_<10> × 1557788195773317123427567075719367853357359_<43>

4×10⁶⁸-9 = 3(9)₆₇1_<69> = 23 × 47 × 241 × 10055497 × 3229088693532413_<16> × 25699991466148591_<17> × 1839927713575003331301821_<25>

4×10⁶⁹-9 = 3(9)₆₈1_<70> = 13 × 3859451384609369_<16> × 189256353195151619017207481_<27> × 421250662534968233939990563_<27>

4×10⁷⁰-9 = 3(9)₆₉1_<71> = 7 × 53 × 314663749 × 49300544393_<11> × 34750228004651_<14> × 200000000000000000000000000000000003_<36>

4×10⁷¹-9 = 3(9)₇₀1_<72> = 151 × 207997 × 1022933782794153551_<19> × 12450260872825111678178680692319362199954369403_<47>

4×10⁷²-9 = 3(9)₇₁1_<73> = 59 × 79 × 1613 × 120943 × 3547890075714688351659371161_<28> × 1239925604463732176069435833849969_<34>

4×10⁷³-9 = 3(9)₇₂1_<74> = 1031 × 38797284190106692531522793404461687681862269641125121241513094083414161_<71>

4×10⁷⁴-9 = 3(9)₇₃1_<75> = 8573 × 5049497107807891_<16> × 3960790465465279655633_<22> × 2332905633967106030561063804969089_<34>

4×10⁷⁵-9 = 3(9)₇₄1_<76> = 13 × 373 × 401 × 8443 × 26858801 × 3713923013_<10> × 2442570608687872717356988936002096246082203654401_<49>

4×10⁷⁶-9 = 3(9)₇₅1_<77> = 7 × 31 × 5653633 × 348331826708401_<15> × 2645922409342926726059_<22> × 35375483339650805066405972938109_<32>

4×10⁷⁷-9 = 3(9)₇₆1_<78> = 6909201596477648329_<19> × 172076998829363467934536230121_<30> × 336441300962383991893868484199_<30>

4×10⁷⁸-9 = 3(9)₇₇1_<79> = 211 × 2341 × 24024727 × 88033849 × 4860567927377_<13> × 17127126974796668443_<20> × 45993497522560350084477797_<26>

4×10⁷⁹-9 = 3(9)₇₈1_<80> = 67 × 55843 × 155464245025206671_<18> × 3651737033218895580218723_<25> × 18831565676508989772214639824667_<32>

4×10⁸⁰-9 = 3(9)₇₉1_<81> = 6770723 × 2359303200251_<13> × 9976145988074011_<16> × 1252019786340070350611_<22> × 2004782209874335297654727_<25>

4×10⁸¹-9 = 3(9)₈₀1_<82> = 13 × 719 × 769 × 556495182212521892868277729494091621088551878498180886811245042497450208637_<75>

4×10⁸²-9 = 3(9)₈₁1_<83> = 7 × 17 × 19603 × 260809 × 16954274587_<11> × 329615502427472542979_<21> × 11764705882352941176470588235294117647059_<41>

4×10⁸³-9 = 3(9)₈₂1_<84> = 43 × 53 × 173 × 4334590831_<10> × 234056903434069220367254497556350798823218530337710050465501450978683_<69>

4×10⁸⁴-9 = 3(9)₈₃1_<85> = 19 × 6337 × 98327 × 10311465629_<11> × 29391458183_<11> × 557414635291_<12> × 473476023375163705877_<21> × 4224078731047546560439_<22>

4×10⁸⁵-9 = 3(9)₈₄1_<86> = 79 × 643 × 1278163 × 124449733 × 5271060797_<10> × 11374658929_<11> × 1146546591356161409_<19> × 72013447150613939027878801921_<29>

4×10⁸⁶-9 = 3(9)₈₅1_<87> = 109 × 131 × 6263 × 8833091 × 23949661 × 2187467868975357653_<19> × 1459842158613772062977_<22> × 6620947236743160286544093_<25>

4×10⁸⁷-9 = 3(9)₈₆1_<88> = 13² × 1013 × 4853242517_<10> × 84485683303708399_<17> × 716034478303081832491184053_<27> × 79581989493293634276223487797_<29>

4×10⁸⁸-9 = 3(9)₈₇1_<89> = 7 × 29 × 419 × 1091 × 1201 × 218809 × 1115911 × 22068793 × 33872427605755993_<17> × 774778366537166689_<18> × 2537961573918528140906387_<25>

4×10⁸⁹-9 = 3(9)₈₈1_<90> = 107 × 479 × 6797351561328298574237479322906911_<34> × 1148156180270793396284227336382345195326385956160677_<52> (Makoto Kamada / GGNFS-0.54.5b)

4×10⁹⁰-9 = 3(9)₈₉1_<91> = 23 × 83 × 3769 × 5281 × 11125019 × 1137872495299_<13> × 126823666282673_<15> × 376099532000829380399_<21> × 174346928210271221879232893_<27>

4×10⁹¹-9 = 3(9)₉₀1_<92> = 31 × 723799 × 890306831 × 10009707608420736556767604383961_<32> × 200041094280928247178817127740041862433271929_<45> (Makoto Kamada / GGNFS-0.54.5b)

4×10⁹²-9 = 3(9)₉₁1_<93> = 601 × 647 × 10825259 × 734482643 × 6338564899_<10> × 4185387670524992598018391019_<28> × 4876798072509021078191981031219049_<34>

4×10⁹³-9 = 3(9)₉₂1_<94> = 13 × 12271757 × 25073207340424659020521047450035695158215103810506327032689150191965803454851029701151_<86>

4×10⁹⁴-9 = 3(9)₉₃1_<95> = 7 × 5443 × 40762871 × 176905403 × 987525370892477_<15> × 130400901777472032491_<21> × 1130547719902031482893713540224658938201_<40>

4×10⁹⁵-9 = 3(9)₉₄1_<96> = 63311 × 4783391 × 22339434383766054987787_<23> × 59125219091727708259291180183537020669016066641432440106136693_<62>

4×10⁹⁶-9 = 3(9)₉₅1_<97> = 53 × 6871 × 10949 × 1194151159441_<13> × 31600563093091571718561868639841689_<35> × 26584934299123232854555060648941702283057_<41>

4×10⁹⁷-9 = 3(9)₉₆1_<98> = 20748910387_<11> × 11947840377877_<14> × 26998259611105711237_<20> × 130854750156377789637493591_<27> × 45671999240020004544736419427_<29>

4×10⁹⁸-9 = 3(9)₉₇1_<99> = 17 × 79 × 241 × 311 × 2269 × 39317 × 161461 × 1089735593698011381725554998847_<31> × 253164556962025316455696202531645569620253164557_<48>

4×10⁹⁹-9 = 3(9)₉₈1_<100> = 13 × 26399 × 77773529 × 408808471 × 17465373185831_<14> × 95419353470123_<14> × 219969836350708990879865183829475893001854137377279_<51>

4×10¹⁰⁰-9 = 3(9)₉₉1_<101> = 7 × 71 × 6491 × 144311 × 237151 × 1153609 × 4383461 × 8988086730774101_<16> × 243852700434495407_<18> × 1790067864550241141_<19> × 18261123537479423831_<20>

4×10¹⁰¹-9 = 3(9)₁₀₀1_<102> = 1242505016132702919907_<22> × 321930289863134774281390210545910706737390060353248796493168385592837665658171613_<81>

4×10¹⁰²-9 = 3(9)₁₀₁1_<103> = 19 × 197 × 159239027032849_<15> × 89342573911788731_<17> × 3355526347347494765062846183242829_<34> × 22385744135541414977650142665848487_<35>

4×10¹⁰³-9 = 3(9)₁₀₂1_<104> = 89 × 7348321 × 545099119 × 92975796938529587_<17> × 246815893242841067_<18> × 455914728317345369_<18> × 10724566125055079702147046804421081_<35>

4×10¹⁰⁴-9 = 3(9)₁₀₃1_<105> = 43 × 409 × 3110999 × 4335631 × 10342885269851_<14> × 140742896567473_<15> × 1062270653575649523714584464177_<31> × 1090467352009655798670870606607_<31>

4×10¹⁰⁵-9 = 3(9)₁₀₄1_<106> = 13 × 4049 × 230177683 × 5089468623085822110371775885182959_<34> × 64868403116863325702101470038639463824085108816719708634719_<59> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 1.24 hours on Pentium 4 2.4GHz, Windows XP / November 18, 2007 2007 年 11 月 18 日)

4×10¹⁰⁶-9 = 3(9)₁₀₅1_<107> = 7² × 31 × 829 × 5641 × 14753 × 527513318280406704433683764738692440130410049_<45> × 723565441067403738662633995275117669829853586533_<48>

4×10¹⁰⁷-9 = 3(9)₁₀₆1_<108> = 190125920843_<12> × 2103868837170852718371967159514240270498075443738141548131610224029698744616010054224608219061637_<97>

4×10¹⁰⁸-9 = 3(9)₁₀₇1_<109> = 211 × 1129 × 5536417031655899_<16> × 656886980652235583190527_<24> × 14429686178846832587868560401_<29> × 319968523864926281807959061371083793_<36>

4×10¹⁰⁹-9 = 3(9)₁₀₈1_<110> = 53 × 7969641884935205730310904257533114365615152149547_<49> × 94698982969196667127271104615127284069462500623071914214001_<59> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 0.96 hours on Cygwin on AMD XP 2700+ / November 18, 2007 2007 年 11 月 18 日)

4×10¹¹⁰-9 = 3(9)₁₀₉1_<111> = 61 × 463 × 947 × 36299 × 64577 × 86111 × 368453 × 60111533 × 630641640613593647_<18> × 158397422352643703820307_<24> × 33488629391928160215301711261193567_<35>

4×10¹¹¹-9 = 3(9)₁₁₀1_<112> = 13 × 79 × 2053 × 1897145318011355363300956967527037877929133085218344826081574402956511263588896198168211338194135828964761_<106>

4×10¹¹²-9 = 3(9)₁₁₁1_<113> = 7 × 23 × 67² × 46757 × 55243 × 169709 × 87796968481_<11> × 9368987878212461_<16> × 34734396543207627172561909369_<29> × 4418997809718205768560805948969128889_<37>

4×10¹¹³-9 = 3(9)₁₁₂1_<114> = 7867 × 50845303165120122028727596288292868946231091902885470954620566925130291089360620312698614465488750476674717173_<110>

4×10¹¹⁴-9 = 3(9)₁₁₃1_<115> = 17² × 47 × 617 × 3469 × 47161 × 381357863 × 1982502477023_<13> × 2551886715660056082059_<22> × 4129570129161813841531043869_<28> × 366166948392750909072952624571_<30>

4×10¹¹⁵-9 = 3(9)₁₁₄1_<116> = 465053419121_<12> × 48540212971357_<14> × 4565203528103689_<16> × 388146190346759943944292211077936423971024540269272004873010728374421498427_<75>

4×10¹¹⁶-9 = 3(9)₁₁₅1_<117> = 29 × 167 × 317 × 6091 × 36217 × 81839 × 133373771 × 830083951270177_<15> × 8577012162065861_<16> × 726279061919048761_<18> × 20926320650104033519325587218683355651331_<41>

4×10¹¹⁷-9 = 3(9)₁₁₆1_<118> = 13 × 9973 × 214363 × 581922332049027043_<18> × 531991308851942132115845825480210110671439_<42> × 464912723832181683082293085018597257414298049209_<48> (Sinkiti Sibata / Msieve v. 1.28 for P42 x P48 / 7.54 hours on Pentium3 750MHz, Windows Me / November 18, 2007 2007 年 11 月 18 日)

4×10¹¹⁸-9 = 3(9)₁₁₇1_<119> = 7 × 24359 × 36382287863_<11> × 1715548838023451276899_<22> × 3204327551100096307916697319_<28> × 1172931096162755918903544011307055767008967058230164269_<55>

4×10¹¹⁹-9 = 3(9)₁₁₈1_<120> = definitely prime number 素数

4×10¹²⁰-9 = 3(9)₁₁₉1_<121> = 19 × 97 × 3347 × 89627 × 13472671 × 195022804897_<12> × 26159207707463133368869943944733_<32> × 105263157894736842105263157894736842105263157894736842105263_<60>

4×10¹²¹-9 = 3(9)₁₂₀1_<122> = 31 × 207550763771542349075740138245104441965655783933_<48> × 6216901143594248208194826668257714111385850652570251799400319368993225117_<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 1.55 hours on Cygwin on AMD 64 3200+ / November 18, 2007 2007 年 11 月 18 日)

4×10¹²²-9 = 3(9)₁₂₁1_<123> = 53 × 197689 × 191000601601_<12> × 493060093873981_<15> × 2608655530952645899_<19> × 78655827078856343401733_<23> × 1975692680562017890358804953016577832115900417449_<49>

4×10¹²³-9 = 3(9)₁₂₂1_<124> = 13 × 15601 × 14877774143167099699747_<23> × 470762130228440485791543763322013994572073144603_<48> × 2815948587112211304623095233966680241651606098227_<49> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 2.60 hours on Pentium 4 2.4GHz, Windows XP / November 18, 2007 2007 年 11 月 18 日)

4×10¹²⁴-9 = 3(9)₁₂₃1_<125> = 7 × 79 × 67187 × 4145861 × 679928401 × 70949947126910415444647891266160232938407859977_<47> × 5382940938022136860142931615845020393406317220316048073_<55>

4×10¹²⁵-9 = 3(9)₁₂₄1_<126> = 43 × 3271 × 9595471 × 296377134243523374156060249291119671964793449628338174285262650903842695326462431018241723161147304591463797875357_<114>

4×10¹²⁶-9 = 3(9)₁₂₅1_<127> = 173 × 709 × 1793399 × 159075667 × 123805374165243868085316016373_<30> × 131703755921620208014649133623_<30> × 7010505260167127084147004476059947918274173937609_<49>

4×10¹²⁷-9 = 3(9)₁₂₆1_<128> = 28597 × 1398748120432213169213553869286988145609679336993390915130957792775465957967618981011994265132706227926006224429135923348603_<124>

4×10¹²⁸-9 = 3(9)₁₂₇1_<129> = 241 × 1746565317767_<13> × 148218399686044608087191_<24> × 77257925744689962320417057501_<29> × 82987551867219917012448132780082987551867219917012448132780083_<62>

4×10¹²⁹-9 = 3(9)₁₂₈1_<130> = 13 × 2063359 × 149122042113033985994532365764904552386517473543046892134472143573807414176443511619794564255513610424704422404289465716973_<123>

4×10¹³⁰-9 = 3(9)₁₂₉1_<131> = 7 × 17 × 59 × 773 × 723564791 × 250214207989_<12> × 50930050051704367752914146546619588270224810241099_<50> × 799315121261189397901309758464692809702923108613928727_<54>

4×10¹³¹-9 = 3(9)₁₃₀1_<132> = 83 × 157 × 43427 × 89517934664444970329_<20> × 2706709430006427754108248781033420387_<37> × 2917230383237813120633073932480522042054906957099018520221291471441_<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 2.06 hours on Core 2 Quad Q6600 / November 17, 2007 2007 年 11 月 17 日)

4×10¹³²-9 = 3(9)₁₃₁1_<133> = 359 × 8423 × 1395047 × 488266873 × 5045396267_<10> × 17702820451_<11> × 120840716754001_<15> × 453907009693924437841_<21> × 269952174593306396039669287_<27> × 1468411861087106185253786003407_<31>

4×10¹³³-9 = 3(9)₁₃₂1_<134> = 283 × 2206451413_<10> × 17745322828110113689579957_<26> × 3609900924935868884393553722022192916008376697080113513902182884643650707317688815148572213895197_<97>

4×10¹³⁴-9 = 3(9)₁₃₃1_<135> = 23 × 163 × 3083 × 6661 × 186283 × 2907419 × 434826671 × 3754592877473_<13> × 474717736202574865914293_<24> × 20832581206768470618341726869_<29> × 594145999077637914442282147060469278819_<39>

4×10¹³⁵-9 = 3(9)₁₃₄1_<136> = 13 × 53 × 71 × 717631 × 5476770683_<10> × 608840507813_<12> × 40266621886486270135726643_<26> × 848609592447617662992638138586825443628335178372470676088764528990820467296627_<78>

4×10¹³⁶-9 = 3(9)₁₃₅1_<137> = 7 × 31 × 179 × 289067 × 12221768408569_<14> × 4929272942288469413_<19> × 6265355337053585617939_<22> × 6475919213812378888572319171_<28> × 1457419800611451039734374629295231356806366627_<46>

4×10¹³⁷-9 = 3(9)₁₃₆1_<138> = 79 × 997 × 5237 × 655387 × 18609511 × 217696138293088164184518991_<27> × 365234386003280635200403386279689112427897130966004676283859706524186487861765417504363403_<90>

4×10¹³⁸-9 = 3(9)₁₃₇1_<139> = 19 × 211 × 22783 × 473774831 × 254128194179_<12> × 58676451232029416603_<20> × 2067397236615734055061_<22> × 4112502436486078502075149_<25> × 729112006146231857757290002160431335436328591_<45>

4×10¹³⁹-9 = 3(9)₁₃₈1_<140> = 827 × 3169 × 100185797 × 974921923 × 18849219647987_<14> × 8290159254208310080147936628003905810782930509779232189523941213775684048461272819925784127168553729081_<103>

4×10¹⁴⁰-9 = 3(9)₁₃₉1_<141> = 193 × 1009 × 165527 × 9015029 × 318197099659911533_<18> × 4205472414155209188944371_<25> × 28730710303722801189996006104739370162441_<41> × 35802897529245969120774911383627717355267_<41>

4×10¹⁴¹-9 = 3(9)₁₄₀1_<142> = 13 × 191 × 20359 × 195319 × 12420177806754397_<17> × 163736308730108767707475962968700893_<36> × 199209262950089812594969876563503547961581096151892699792833892052250192212997_<78> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 5.44 hours on Core 2 Quad Q6600 / November 18, 2007 2007 年 11 月 18 日)

4×10¹⁴²-9 = 3(9)₁₄₁1_<143> = 7 × 107 × 155731 × 110242819 × 292292453 × 108873161835557496912230201617128500051561735049298977361_<57> × 97749457018750228999485760145263043889030650310456600905023807_<62>

4×10¹⁴³-9 = 3(9)₁₄₂1_<144> = 23319815050804253_<17> × 41320276617255065999_<20> × 65592239078997416563125307_<26> × 6328768545120330781276890083775149723778473759165061794733839591210761469954001079_<82>

4×10¹⁴⁴-9 = 3(9)₁₄₃1_<145> = 29 × 149 × 143357 × 4179362655121_<13> × 115107344774745155473488635437584064431083661453869669_<54> × 13422818791946308724832214765100671140939597315436241610738255033557047_<71>

4×10¹⁴⁵-9 = 3(9)₁₄₄1_<146> = 67 × 11529868409241733729_<20> × 51779855951746915613207527045979455969975971369762642935411255512701536677331213503472055536703777671434517482031353309260637_<125>

4×10¹⁴⁶-9 = 3(9)₁₄₅1_<147> = 17 × 43 × 151 × 7759 × 28481543869_<11> × 35256146990949820675155255501335850511972129326274272679_<56> × 465116279069767441860465116279069767441860465116279069767441860465116279_<72>

4×10¹⁴⁷-9 = 3(9)₁₄₆1_<148> = 13 × 89 × 6167403400563579766175239_<25> × 9859117276170965916528849893551257536137453_<43> × 56857301497661450675385390309929156870609092238968154609890852061865551467889_<77> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 16.03 hours on Cygwin on AMD XP 2700+ / November 19, 2007 2007 年 11 月 19 日)

4×10¹⁴⁸-9 = 3(9)₁₄₇1_<149> = 7² × 53² × 673 × 847507 × 26834343679421_<14> × 23909542862637059743_<20> × 4651884471734792048380131661572294455090942337043_<49> × 170711446743697725633505677829515883121491856455923629_<54>

4×10¹⁴⁹-9 = 3(9)₁₄₈1_<150> = 797 × 279587197 × 6930505097787449_<16> × 259011771676803216882760438429105713862269153762654978763387122923529476117102696830468777066082263142406640371598807420951_<123>

4×10¹⁵⁰-9 = 3(9)₁₄₉1_<151> = 79 × 331 × 171077 × 73525909 × 123379312751_<12> × 10206815431870182840270817231_<29> × 7493498919620788902689385842385931447646537_<43> × 1288711252427299289691976770992371416501780989937179_<52>

4×10¹⁵¹-9 = 3(9)₁₅₀1_<152> = 31 × 5519 × 371213 × 1158569 × 54827975693_<11> × 85431185431_<11> × 683451293547552766493247508223331705485919834283_<48> × 169811308556460662649467994337463527761352643619555931552038754243_<66> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 27.46 hours on Pentium 4 2.4GHz, Windows XP / November 21, 2007 2007 年 11 月 21 日)

4×10¹⁵²-9 = 3(9)₁₅₁1_<153> = 103035186006031_<15> × 1934982246763493955490755927821_<31> × 100315363558355014647859823017153_<33> × 19999999999999999999999999999999999999999999999999999999999999999999999999997_<77>

4×10¹⁵³-9 = 3(9)₁₅₂1_<154> = 13 × 7963 × 3046082801_<10> × 2125945121483_<13> × 36758374772653_<14> × 18100935169352815275707_<23> × 42510316950321522868841089_<26> × 210957277462653394690465901462374782796266121499135809783812023957_<66>

4×10¹⁵⁴-9 = 3(9)₁₅₃1_<155> = 7 × 7159 × 23203 × 6478104454016753760887_<22> × 4312505747417765608582777589439413779944095761779091_<52> × 1231367864992827282186416781081264122250201636487892575467458025747902057_<73>

4×10¹⁵⁵-9 = 3(9)₁₅₄1_<156> = 1821613 × 3583357 × 4637483 × 32771932477841795426235506521_<29> × 403208254555383837372946873770549114630370766010235538732585825933608884811798208240341232025096911389953557_<108>

4×10¹⁵⁶-9 = 3(9)₁₅₅1_<157> = 19 × 23 × 307 × 5693 × 8179 × 1237661 × 2486863 × 4822777 × 45908403975780047456872133_<26> × 8232288831717810579373722530878388597_<37> × 114139310551026338652399651844405362963557000608503422372020997_<63>

4×10¹⁵⁷-9 = 3(9)₁₅₆1_<158> = 2306893 × 17339339102420441693654625507121483311102855659105125378593632214411331604890213807055637170861414031773471938230338381537418510524762093430427852527187_<152>

4×10¹⁵⁸-9 = 3(9)₁₅₇1_<159> = 241 × 523 × 1571 × 4561 × 5647 × 1372638681719_<13> × 685978596651857_<15> × 32352462130214742144908089_<26> × 402766851937457023692444225437_<30> × 6392332516138127241768447324856462524373231004706954463263139_<61>

4×10¹⁵⁹-9 = 3(9)₁₅₈1_<160> = 13 × 199 × 2130173 × 64929089 × 24131072597_<11> × 952589489681209_<15> × 74079493501806378527450601403663790436099271_<44> × 6564912794659200412500871081575072082513907943647734630671406825808638043_<73> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 77.01 hours on Pentium 4 2.4GHz, Windows XP / November 24, 2007 2007 年 11 月 24 日)

4×10¹⁶⁰-9 = 3(9)₁₅₉1_<161> = 7 × 47 × 1987 × 6299 × 414473453 × 16487355097_<11> × 19966584998152201_<17> × 501471938213707291_<18> × 259021994710197509542516797106845199244858179099_<48> × 548100043780603304955338234337098221979945589533507_<51>

4×10¹⁶¹-9 = 3(9)₁₆₀1_<162> = 53 × 21806825430466113390135407080568754712841_<41> × 346092091000860392504443010316442896408178789678554842890548184933093473061870388053493738110298874615414662714544919267_<120> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.29 / November 20, 2007 2007 年 11 月 20 日)

4×10¹⁶²-9 = 3(9)₁₆₁1_<163> = 17 × 1277 × 1523 × 2530899979_<10> × 94728548632440270893171_<23> × 133940570111507996479098559_<27> × 313827973953327557599392191_<27> × 3957387137241634817201597568481_<31> × 3033556371527318787524930840338672101713_<40>

4×10¹⁶³-9 = 3(9)₁₆₂1_<164> = 79 × 2711431 × 1507192123_<10> × 3204540690671_<13> × 248748268553561479_<18> × 227089159325096042476973_<24> × 2129679099007734476891559517_<28> × 321387735053205686267572567444278274455091556569548545847621764557_<66>

4×10¹⁶⁴-9 = 3(9)₁₆₃1_<165> = 825611 × 1402504993_<10> × 18909138091_<11> × 8812588523511893_<16> × 2748849941029302910494614920725892417409755520329614893557061_<61> × 754143246424861575508278194050733980225970187173199288191709719_<63>

4×10¹⁶⁵-9 = 3(9)₁₆₄1_<166> = 13² × 2488043 × 178101449 × 53413120622881228787039620154426573307960318677092493375505243684627286403897026319389625184870935049908649420094106231903695336468369821350035121077_<149>

4×10¹⁶⁶-9 = 3(9)₁₆₅1_<167> = 7 × 31 × 113 × 229 × 24979 × 385787823329569_<15> × 5278397362612613211007287739_<28> × 1890937814311875696421686100672206606653923849_<46> × 74059954315926416227569410612850650660129447590211704312173034536059_<68>

4×10¹⁶⁷-9 = 3(9)₁₆₆1_<168> = 43 × 443 × 3803 × 8363 × 42090948879771092306041949813824861415659616231911_<50> × 15685944386992125078642922951658875275870814395996579224833998729276744713659512994944344360612430130357121_<107> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.32 / January 5, 2008 2008 年 1 月 5 日)

4×10¹⁶⁸-9 = 3(9)₁₆₇1_<169> = 211 × 233713 × 10689751 × 30870029 × 174101240977_<12> × 27501614868292675787_<20> × 1901624710396775316537341_<25> × 1265800626727778453024504210132287247243_<40> × 21327495454449983020338735825860051020986349407972619_<53>

4×10¹⁶⁹-9 = 3(9)₁₆₈1_<170> = 173 × 563 × 462212928665557_<15> × 61333882543515533360951_<23> × 67426291872596114148024503677_<29> × 214849165378180616457207496167989576239109216001953503018360303758200797034032319912192428035188231_<99>

4×10¹⁷⁰-9 = 3(9)₁₆₉1_<171> = 61 × 71 × 263 × 1069 × 784009 × 730869849769_<12> × 188791641851297_<15> × 92965737425275667_<17> × 13941520301475528498949_<23> × 123958877689262908298519237788099_<33> × 18900957529184282114771140692935766432229545915707371997947_<59>

4×10¹⁷¹-9 = 3(9)₁₇₀1_<172> = 13 × 1481551 × 2094373 × 35330951 × 23561463756765050201124699355493115971879_<41> × 28941009474935683843948897020903479139997_<41> × 4115993992441463544706180751361765698756507413749483861195184714376893_<70> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs / 96.52 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / November 4, 2008 2008 年 11 月 4 日)

4×10¹⁷²-9 = 3(9)₁₇₁1_<173> = 7 × 29 × 83 × 6271 × 161471 × 3708068388463_<13> × 803341897652669_<15> × 606376773754238324363_<21> × 1047920541237702507248025832637_<31> × 7562273344413334909707814556227561_<34> × 163788380802911156632732710348911066987517958987_<48>

4×10¹⁷³-9 = 3(9)₁₇₂1_<174> = definitely prime number 素数

4×10¹⁷⁴-9 = 3(9)₁₇₃1_<175> = 19 × 53 × 1019 × 2633 × 42719 × 13351343 × 9391183921538689_<16> × 454731869459094847_<18> × 6923141487770868883_<19> × 60685815889202975701_<20> × 199478980651013971577_<21> × 1380394194751915908017_<22> × 5254035963287563578959421946859218396907_<40>

4×10¹⁷⁵-9 = 3(9)₁₇₄1_<176> = 881 × 502411279 × 90370087395723989678725058277633153989461415339847760073141662282120456740059938920059986947649598798444671510431155920820192813041951544163357335628914648815191209_<164>

4×10¹⁷⁶-9 = 3(9)₁₇₅1_<177> = 79 × 1031 × 9712441 × 98836273 × 160330424167_<12> × 259333214069_<12> × 636360516185020985689_<21> × 9967375987265890256911580767_<28> × 19398642095053346265761396702230843840931134820562560620756547041707080504364694471387_<86>

4×10¹⁷⁷-9 = 3(9)₁₇₆1_<178> = 13 × 227 × 385001 × 5083123 × 1162925053_<10> × 332230023790700823439_<21> × 64657499314578118063033769725403663002679_<41> × 27726100791358863600050685537869345949466612785403199549604397338078169719410730274414575719_<92> (matsui / GGNFS-0.77.1-20060722-nocona / April 26, 2009 2009 年 4 月 26 日)

4×10¹⁷⁸-9 = 3(9)₁₇₇1_<179> = 7 × 17 × 23 × 67 × 293 × 52201 × 31220972566629346037_<20> × 55916398361587507836687691938105593431350598515146351210658005213_<65> × 8169177456550289517691354506398079361026545374532074621024709760357587770970084513_<82>

4×10¹⁷⁹-9 = 3(9)₁₇₈1_<180> = 45509197 × 1874814157831_<13> × 56509686961164460509008717533_<29> × 82962091612775212635725896046171705731169425764309250070648134475290867457795804761148442726391599194995848372501717823470479622361_<131>

4×10¹⁸⁰-9 = 3(9)₁₇₉1_<181> = 1153 × 4000853 × 14192805091_<11> × 1612351060219207303_<19> × 1075823634240573613236619945236180905716293882720442899436436921102117_<70> × 35221606618830262913343738393249032649822049079574497991150497364103099939_<74>

4×10¹⁸¹-9 = 3(9)₁₈₀1_<182> = 31 × 587 × 12239 × 13095488550241_<14> × 4460116554200837_<16> × 3075008695410793039634658756642754100336392116486231060385034374663966161150639781687262650938183292256095536759895392902983609896041999450609681_<145>

4×10¹⁸²-9 = 3(9)₁₈₁1_<183> = 1871 × 6709 × 14341 × 177127 × 225859 × 751763 × 1719409 × 7464124611017_<13> × 45186538905301_<14> × 94820315277907_<14> × 7391867565690931020532600599163374944095489619_<46> × 181770388080836974514656491761082559023131975054065757127548899_<63>

4×10¹⁸³-9 = 3(9)₁₈₂1_<184> = 13 × 291521 × 175760151760128614736111330301882810113296736746728352650439858811633452129329386893_<84> × 6005184777904143133368396782495819629853737419435935288123825152255604348922994197853024855519_<94> (Serge Batalov / Msieve-1.38 snfs / 120.00 hours on Opteron-2.6GHz; Linux x86_64 / November 12, 2008 2008 年 11 月 12 日)

4×10¹⁸⁴-9 = 3(9)₁₈₃1_<185> = 7 × 1489 × 8233 × 9241 × 162557 × 90668547845459_<14> × 188080429537884826493_<21> × 6577596128333935936571_<22> × 169566414790523540512576421_<27> × 16314628258551292008434336517105846942520383292613380752344187754615265581346898185381_<86>

4×10¹⁸⁵-9 = 3(9)₁₈₄1_<186> = 35063491934201_<14> × 11407876909425532766767515070105844680213096690807109262204032112482211097777055634465400185816885175799524693160422392762895179447778330591954913521449642117729318052647791_<173>

4×10¹⁸⁶-9 = 3(9)₁₈₅1_<187> = 7321913 × 159129109 × 4211620326587_<13> × 175746623295851659_<18> × 62014234844721324719_<20> × 2319100651175680426597602137387367174469580704823_<49> × 32250659949410643441501571216321459031954131891410903461965466986948633363_<74>

4×10¹⁸⁷-9 = 3(9)₁₈₆1_<188> = 53 × 10684013423190202598370871_<26> × 1626349888286077666713489931346081_<34> × 1156412510086878791154526581085081807094186719_<46> × 37559770618664727055350154373325301900026821932736805523253002218736318566782328163_<83> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1057010532 for P34 / October 26, 2008 2008 年 10 月 26 日) (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 gnfs for P46 x P83 / 246.89 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 11, 2008 2008 年 11 月 11 日)

4×10¹⁸⁸-9 = 3(9)₁₈₇1_<189> = 43² × 59 × 241 × 313 × 94427 × 3614470427_<10> × 19340062151882758570550401967047_<32> × 170653684700895671770239219522913_<33> × 213089577421509928559482959036656417177388199_<45> × 202503753322468777288652868121333740631106564440682715437_<57>

4×10¹⁸⁹-9 = 3(9)₁₈₈1_<190> = 13 × 79 × 5973538769414641_<16> × 20781366525303489622716768590229880681_<38> × 31375001761462013103697668026376674624654776647124316571555426864479743924882565051571614750837097034995171172364843563578914251410373_<134> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=34890979 for P38 / May 2, 2011 2011 年 5 月 2 日)

4×10¹⁹⁰-9 = 3(9)₁₈₉1_<191> = 7² × 1097 × 2777 × 323537 × 3184710803_<10> × 63716737888419215547415929687932010189450906872448170069806562750426211617_<74> × 4081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653_<94>

4×10¹⁹¹-9 = 3(9)₁₉₀1_<192> = 89 × 305254752356293_<15> × 7425626411708544883_<19> × 262214928886895897078887971744126374204083_<42> × 7561658168981530963355391622990846884778957115241506376403767002283987245749089487139172111153299702982917422388747_<115> (KTakahashi / GMP-ECM 6.4.4 B1=3000000, sigma=3764813989 for P42 / December 21, 2013 2013 年 12 月 21 日)

4×10¹⁹²-9 = 3(9)₁₉₁1_<193> = 19² × 643 × 5743731053_<10> × 13387084763939_<14> × 6888003416488249330043_<22> × 21689554339683136588679658930304369012462798870108076460065939_<62> × 1500091411952965086038653440170200318545430389961301405134148425303374129832161763_<82>

4×10¹⁹³-9 = 3(9)₁₉₂1_<194> = 356020398676981933_<18> × 2055639902606412744129429071884327080386461134321599_<52> × 54656028336871819601847490147533195539336289169465581194632272137735082474802472537999286047691863636741453163263918573820173_<125> (Evan Engler / YAFU (ver. 1.35-dev) for P52 x P125 / January 16, 2021 2021 年 1 月 16 日)

4×10¹⁹⁴-9 = 3(9)₁₉₃1_<195> = 17 × 109 × 347 × 14159 × 787429 × 784377317 × 1289241992537_<13> × 38650745043061_<14> × 36454802699034857_<17> × 145923420596482481004347_<24> × 45740554784041081835936926224367892182088323307351_<50> × 5866952744783258583080885755055224630524999042809897791_<55>

4×10¹⁹⁵-9 = 3(9)₁₉₄1_<196> = 13 × 107 × 317 × 683 × 4813 × 34945726168123_<14> × 235346907565680687670001_<24> × 84023102213882289455105713911646201_<35> × 3993335105848129845498334339702023428427294782244533437466867913637243996141634999335678685464308070534367797009_<112> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3729024413 for P35 / September 23, 2008 2008 年 9 月 23 日)

4×10¹⁹⁶-9 = 3(9)₁₉₅1_<197> = 7 × 31 × 1033 × 1801 × 26891720626840241453_<20> × 425574857812513991947_<21> × 136136864578743359737953547522723_<33> × 1855514081798741393807817969446545214189_<40> × 34272964492098008972146833105500148126083732893462398747862634497615158084103_<77>

4×10¹⁹⁷-9 = 3(9)₁₉₆1_<198> = 281910298133_<12> × 190480094567465618641014493_<27> × 7449025353749847708792163940858645078093979533400210025452931994205704095434922560694382108924013878016266620120475224815233471656885159688499655327843956585239_<160>

4×10¹⁹⁸-9 = 3(9)₁₉₇1_<199> = 211 × 1637 × 3844549383673931497619_<22> × 79382035150980920346405340690307261392830949801_<47> × 119405769425714490171006230771951087269574666783273_<51> × 317786813596113683738897417841728349760581713829816055800984665620078724099_<75>

4×10¹⁹⁹-9 = 3(9)₁₉₈1_<200> = 877 × 19306917307_<11> × 2362367512238169842814551460351364624763526014197834021710043197746268915212743618127338511233575062172571178528000029762748237070971655452443973681727811458036330149383339715017027238569_<187>

4×10²⁰⁰-9 = 3(9)₁₉₉1_<201> = 23 × 29 × 53 × 197 × 379 × 3671 × 9187 × 28463 × 170547889 × 2351903621_<10> × 1221402604855740137021_<22> × 60059632438639530286975417_<26> × 107607507117527462741165517473467_<33> × 49861360773942694081325021246938997255965585182246410257045279125241288931457688087_<83>

4×10²⁰¹-9 = 3(9)₂₀₀1_<202> = 13 × 11842799 × 1803406453_<10> × 2220194263669079_<16> × 53348426169923083_<17> × 1166568154373795165761511707_<28> × 104266778771382632137951610299920123165342937251568662918164741420036887490286230927059861854945885129398920094404223797533319_<126>

4×10²⁰²-9 = 3(9)₂₀₁1_<203> = 7 × 79 × 383 × 617 × 2393 × 397963 × 774799 × 1690313 × 21610019 × 216954797 × 217194433913_<12> × 4359913632001_<13> × 18484717176979_<14> × 176407766384435368999_<21> × 11562800031772242924518824714175876232173_<41> × 1466104189413658796569889069140426117523998627396976056080427_<61>

4×10²⁰³-9 = 3(9)₂₀₂1_<204> = 985938912916866838801_<21> × 49069470515507153084854289_<26> × 28141154233422218672123348749929565734361618659554108881_<56> × 293803324384143347756636750650792144890216672206188160964497667930853870976495802895748389478539012199_<102> (ebina / Msieve 1.53 snfs for P56 x P102 / August 7, 2022 2022 年 8 月 7 日)

4×10²⁰⁴-9 = 3(9)₂₀₃1_<205> = 439 × 701 × 2317751 × 5551873 × 21897763 × 9012245475577_<13> × 322353810266010223_<18> × 3631408672796406702085696216743007169009354928263686873187008923205595863_<73> × 4372506411149619576025256338954642702426504653677338907773680184342622318497_<76>

4×10²⁰⁵-9 = 3(9)₂₀₄1_<206> = 71 × 64845766618293547_<17> × 27491258710228943998999495345482419182530645671394074347663502124142853_<71> × 316027873488720198982239687920664036287262908382499345785358864287746603382709640756848625267473400263983431382958231_<117> (Bob Backstrom / Msieve 1.54 snfs for P71 x P117 / October 17, 2021 2021 年 10 月 17 日)

4×10²⁰⁶-9 = 3(9)₂₀₅1_<207> = 47 × 787 × 2068430377411_<13> × 1303454060208099067_<19> × 71811408358293195292411_<23> × 77125858976287579050890129854699_<32> × 37144778449564313154341134715055031_<35> × 19531312895566268888765389214062836488273_<41> × 998224205171980635252280650332109241844941_<42>

4×10²⁰⁷-9 = 3(9)₂₀₆1_<208> = 13 × 7039 × 12973 × 493250413 × 80921269180941493_<17> × 8441059203269124378725948752519102700083022924740230578115922132863599_<70> × 10000878847323814188909570363002935421008017619937838531890564634342048485762372389426002724052434048991_<104> (Bob Backstrom / YAFU, GMP-ECM B1=11000, sigma=2906899029 for P70 x P104 / July 28, 2024 2024 年 7 月 28 日)

4×10²⁰⁸-9 = 3(9)₂₀₇1_<209> = 7 × 1499 × 397633 × 72924583 × 32500127761170009153191422527529_<32> × 81143272388834334896650363044075567399043782163_<47> × 6198620635061424030493749864953890386771151005333743_<52> × 8042133907689848374500596451675451989411649913723669050575553_<61>

4×10²⁰⁹-9 = 3(9)₂₀₈1_<210> = 43 × 157 × 1344799 × 43219643 × 456637813 × 52186574700410202710543580507939239_<35> × [42778215758823271283365202134828897965312572658602223157505026013428737320090590105223875557676570260944693618416666386090018930911972785693795598359_<149>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1610337776 for P35 / November 4, 2008 2008 年 11 月 4 日) Free to factor

4×10²¹⁰-9 = 3(9)₂₀₉1_<211> = 17 × 19 × 467 × 2333 × 3961175617793_<13> × 3347237247165798725331239871160802804281762325288903139153487422487976442557810503419931_<88> × 857265323617659665666523789112730390055722246035147878268324046292327475353621945992284612087441063009_<102>

4×10²¹¹-9 = 3(9)₂₁₀1_<212> = 31 × 67 × 1907 × 3169 × 395448671 × [8058615637588173282347575467486607487799336802402892318644677892935480193398494054573528576268437708581307652915930605834372668524365878972744353022629470411564500027782037497755941023184376431_<193>] Free to factor

4×10²¹²-9 = 3(9)₂₁₁1_<213> = 173 × 53299 × 42876259 × 5594493493318388089_<19> × 20909268680821569816065383_<26> × 5159197730271147217349752990276548876845323_<43> × 1696335989904637732334935062814384104990952215712079_<52> × 988289716009437275446318931091762783722563293522184539500353_<60>

4×10²¹³-9 = 3(9)₂₁₂1_<214> = 13 × 53 × 83 × 46511 × 20879639623952929785933043_<26> × [72025121798108409233842522065435116582765026496376434367204039232590046757519564170865747537195002680126761039194558857562633016243332063395673539376739329935540307771477767135041_<179>] Free to factor

4×10²¹⁴-9 = 3(9)₂₁₃1_<215> = 7 × 5237 × 34159 × 135257 × 144512707 × 255054928321_<12> × 8581253024316133683871_<22> × 70366470719053751070081322438416837323_<38> × 71688355828884849285727325871272978657_<38> × 148016327942507378622392718611581342547343863899729003040292494919737429668418883589_<84>

4×10²¹⁵-9 = 3(9)₂₁₄1_<216> = 79 × 163 × 180953387521507871_<18> × 171663743072338266564887148567062526733640502410291091642136206963746944559806932138235194935994380010451085187744180789748032714180965121610975677058994212875151283546675512614546605870601924173_<195>

4×10²¹⁶-9 = 3(9)₂₁₅1_<217> = 97 × 131 × 907 × 971 × 1663 × 211153 × 2334911 × 62038633 × 785013631 × 10956056139051043916590023409_<29> × 9795426399848232136433658361416964220351_<40> × 16021201316639818235833142024355288672757596038111_<50> × 5206172069618515898494220381496970287426897628124942838563_<58>

4×10²¹⁷-9 = 3(9)₂₁₆1_<218> = 153138923096637815337324392839746144304740150626975813_<54> × 261200739767238216403031051949070797540409290687764527939818984072695012732362463527871657040814436595996243277659214477992470411020857002428756477130421386528676107_<165> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 201.57 hours, 62.91 hours / June 27, 2009 2009 年 6 月 27 日)

4×10²¹⁸-9 = 3(9)₂₁₇1_<219> = 241 × 911 × 2719 × 8543 × 430741 × 11511113 × 34640887 × 1991149621_<10> × 56507163833737820197672277_<26> × 17549207512483876748254230582091_<32> × 57204838642635824463463028377398262905391805414776179409_<56> × 4042823160116869432898157597719278823120018001928691757871030681_<64>

4×10²¹⁹-9 = 3(9)₂₁₈1_<220> = 13 × 839 × 82467488022247679727947415497469791627336296247529111727738703553530989716089_<77> × 4447048973020707963671116712924416171932599147193348095813779150964307930192515153073852957342284283845468243469970491789991587228466841917_<139> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 250.14 hours, 69.87 hours / May 1, 2009 2009 年 5 月 1 日)

4×10²²⁰-9 = 3(9)₂₁₉1_<221> = 7 × 1304659 × 3513431 × 22141753 × 12373930450664908843_<20> × 26184862097599361168293556342151923_<35> × 159250894289275575513806398823291602495061691198560909053340523515792467_<72> × 1091142984253028074855253881145711454222019861072878061773867745555021996423_<76>

4×10²²¹-9 = 3(9)₂₂₀1_<222> = 151 × 1481 × 43987 × 122861081880593685057526556505729911_<36> × 4520901491708664102216490947309660917_<37> × 73208964310774170192698424594773491343809456883679266073045536368506914914466981873365542119647546265130785085360591902960495469798780506369_<140> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3686803269 for P37 / November 4, 2008 2008 年 11 月 4 日) (KTakahashi / GMP-ECM 6.4.4 B1=3000000, sigma=3578397712 for P36 / December 22, 2013 2013 年 12 月 22 日)

4×10²²²-9 = 3(9)₂₂₁1_<223> = 23 × 1012147 × 1975997557667018723564857673835915138808888432213897783622339442788448713477390141945784555010290007281551_<106> × 86956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478261_<110>

4×10²²³-9 = 3(9)₂₂₂1_<224> = 178643 × 43436879 × 162340517 × 16794970462970350799_<20> × 109702385123835820767567110173_<30> × 17234279655112338870804656441415583958437362921504443164270233279512818351598712300614757732961924029188836166061510146445768957731218168949630287526465917_<155> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=766755851 for P30 / November 2, 2008 2008 年 11 月 2 日)

4×10²²⁴-9 = 3(9)₂₂₃1_<225> = 677 × 12697 × 831043 × 54670303 × 1130429630033873669_<19> × 13815806123380392068501_<23> × 137192114622451866628779759037281403166279150792129455795886714703171863952755707_<81> × 478020270900772726633696605954219944463744295928749633602720299644323342149372542277_<84>

4×10²²⁵-9 = 3(9)₂₂₄1_<226> = 13 × 3819696010750597_<16> × [80554134890918714843219524447740449092908749517089885811728036093553440552453642999186640832559817408954172518033321888039314154346974487636600248247435391010058951132692487160606983723560130154373003279605431_<209>] Free to factor

4×10²²⁶-9 = 3(9)₂₂₅1_<227> = 7 × 17 × 31 × 53 × 1372831668613383547870044381977_<31> × 23098824314409211398591501573261950597735785754115833490357410540732332572989623_<80> × 6451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451613_<112>

4×10²²⁷-9 = 3(9)₂₂₆1_<228> = 687707 × 371639483 × 1515901607401889_<16> × 1032437298303243697422891016343669463744635607971675243782255307384911511456734794313424356241113953389772942272639396030992371562774622041321632359649141989935854372089845229976535638443750909120399_<199>

4×10²²⁸-9 = 3(9)₂₂₇1_<229> = 19 × 29 × 79 × 211 × 269 × 46091 × 141642068744903728734080380860557_<33> × 66720394280058370841709380872145894939733576500903_<50> × 7477136952660057610131641830487159799848955980602003638351811_<61> × 497100539534504959831516767690043182490203130774494939527873200330969211_<72>

4×10²²⁹-9 = 3(9)₂₂₈1_<230> = 15889 × 2517464912832777393165082761659009377556800302095789539933287179809931399081125306816036251494744791994461577191767889735036817924350179369375039335389263012146768204418150922021524325004720246711561457612184530178110642582919_<226>

4×10²³⁰-9 = 3(9)₂₂₉1_<231> = 43 × 61 × 181 × 96497 × 829756981 × 526124351571380221566747059280628606635611899137939746959670084844353770479041712935130444030667_<96> × 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<116>

4×10²³¹-9 = 3(9)₂₃₀1_<232> = 13 × 2314547 × 132938457370840899885676250122511097120815566800893519253526632940401595779948433837078137669138845610958728557982321245715767408349153286715582923004936902256766575788829387481737163986001447500393082401138405185849458962081_<225>

4×10²³²-9 = 3(9)₂₃₁1_<233> = 7² × 503 × 15031 × 3834191 × 5583119 × 6544399742820969529407841_<25> × 41493132409708849993961614871982844651028070979055904408757610584660729478322747116357_<86> × 18574254102686318016620255264499950584015414667812075794431937770191719340776172937008476822441053131_<101>

4×10²³³-9 = 3(9)₂₃₂1_<234> = 31973 × 4142689 × 239003509289_<12> × 11355474299929_<14> × 1112716981600764213152482188294069031739505203433494550274585709542453327227562242953305068656198974213787159493188989224792626290716028485740596542143218171612651035142995380661306955934162447457163_<199>

4×10²³⁴-9 = 3(9)₂₃₃1_<235> = 252481430303_<12> × 14233541343533_<14> × 79171895467787_<14> × 9471209741101499_<16> × 506583805706942727181861_<24> × 50068989168351494592204398161861_<32> × 8325386712283388629555879931366734094616947743_<46> × 7029372274658901576417661765722869204475035431907927006123940343512211180833331_<79>

4×10²³⁵-9 = 3(9)₂₃₄1_<236> = 89 × 8969 × 7320037 × 23673778073821711017054533587495901836159_<41> × [289164591678319746378916772508496118707626003746531882117293165495036166800315509758986753690343097246399020999705233630255469573450589961153794548376578863255431698161486983087263797_<183>] (KTakahashi / GMP-ECM 6.4.4 B1=3000000, sigma=3435681213 for P41 / January 19, 2014 2014 年 1 月 19 日) Free to factor

4×10²³⁶-9 = 3(9)₂₃₅1_<237> = 191 × 8248949 × 714997972759321_<15> × 22950984299621533137884728246439_<32> × 991811671612623385550841555017839892819_<39> × 28203043059484251487882072762043305121719614244673667495654922297_<65> × 553091130404568883549143340580413178416536717655739844547962308344784263446097_<78>

4×10²³⁷-9 = 3(9)₂₃₆1_<238> = 13 × 165953750818291137381672377369_<30> × 86247580418114063168182947448042170563_<38> × 21497237085371017790885303619639658026600981428021037498959428854828701397853173045117752456175430759456678502375755247820994396190489950630319288966802551146795736115481_<170> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=2541232610 for P30 / November 3, 2008 2008 年 11 月 3 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1384465417 for P38 / May 3, 2011 2011 年 5 月 3 日)

4×10²³⁸-9 = 3(9)₂₃₇1_<239> = 7 × 223 × 5228659514109126391498531522208323958331928046131_<49> × 38250721711810786837816564744277352704880578237524903785562032046531313_<71> × 128122998078155028827674567584881486226777706598334401024983984625240230621396540679051889814221652786675208199871877_<117>

4×10²³⁹-9 = 3(9)₂₃₈1_<240> = 53 × 631 × 1187 × 698329 × 933649 × 1329976841_<10> × 479027965831_<12> × 59130044921610281_<17> × [410248662169011989705848636961221308898383625361767931648016616227557884046203953870267331768654827457937774615779686111326495440635952851591496964480847618998172071516834583209375281_<183>] Free to factor

4×10²⁴⁰-9 = 3(9)₂₃₉1_<241> = 71 × 15565393 × 1809720710842767815340166917761946664738252406802091186211056001325106460010448078677115659855981539067984224299_<112> × 2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<121>

4×10²⁴¹-9 = 3(9)₂₄₀1_<242> = 31 × 79 × 73907 × 1255369899787_<13> × 1799396021268199_<16> × 162791655526760799733_<21> × 179194028594672986043_<21> × 333403450873810189809523_<24> × 10059152711789417434542216086430824415874405255946405117791328448907306623634891193153641412019597412820975257872969429973094920761338111235277_<143>

4×10²⁴²-9 = 3(9)₂₄₁1_<243> = 17 × 17417 × 14488801 × 65881399 × 2194247719_<10> × 45230755231_<11> × 39243438138434903_<17> × 82493772245610301788337353942271_<32> × 3835995654100008613560231526090607813_<37> × 1148303381753459263937532296032611816041798243095825917207326175575587070103921456048688063386346672790951369351782741_<118>

4×10²⁴³-9 = 3(9)₂₄₂1_<244> = 13² × 1620523 × 18917917748103512524609_<23> × [772048803921848523968852685498834223050085320557341912320400746405229064342749644216420133766650676394900786195206701835499585828212522135978713138512042602470850389422223271355291768401998126112123579358309582877_<213>] Free to factor

4×10²⁴⁴-9 = 3(9)₂₄₃1_<245> = 7 × 23 × 67 × 6389 × 1255591 × 1846821995548619239_<19> × 873192647167017533911_<21> × 2445409000264004985346080302093575163_<37> × 5770283446250729246099452389095675049097_<40> × 171991496996710309484092016279706178541733683213_<48> × 118110223750443992209744996157769492200408400398154132891719193722281_<69>

4×10²⁴⁵-9 = 3(9)₂₄₄1_<246> = 17573 × 11223067 × 95091449 × 504808921 × [42250712810402420322967365346732922952127222558971055343165327692752399042566749780487338910584435190462188668674797809565360337178848708454880332778225293301790980276068136455489626282787637003305399876101859141727969_<218>] Free to factor

4×10²⁴⁶-9 = 3(9)₂₄₅1_<247> = 19 × 59 × 1559 × 13003 × 252444851578307_<15> × 1132294115524073_<16> × 1476825069370893260540808898912662128916853503986650844219312049234362445397625242702793784200603323_<100> × 416974864952176659286921762537731373167739280498222726745880301034569498329218744986251818415970890775078491_<108>

4×10²⁴⁷-9 = 3(9)₂₄₆1_<248> = 1453 × 276239 × 2105963 × 3990001 × 10954619018073076933_<20> × [1082650708444936370588129006278800375365298729450186163329662492739819969833160015348395383059316894261095415990648775201719065324307177693102648608028023898984116103322656136559772379401228227294332778180187_<208>] Free to factor

4×10²⁴⁸-9 = 3(9)₂₄₇1_<249> = 107 × 241 × 31536909893_<11> × 807932595751_<12> × 15473661967469980997_<20> × 9336975976397637344374611852234644275771_<40> × 67921085334223439767801410472062272050391919676586092874931678368742117499_<74> × 62038450235564933442218840576529640620666357432793040061287595166043436265300664996855027_<89>

4×10²⁴⁹-9 = 3(9)₂₄₈1_<250> = 13 × 11118150952998709252666041406775345134314224536305734253569_<59> × 27674773349728543971461886494944024780027250034184418990444098974867816369781962915408831471917946812709403792160496417138904191102019340891652850104232170737868384357842228591924447445616403_<191> (matsui / Msieve 1.40 snfs / June 8, 2010 2010 年 6 月 8 日)

4×10²⁵⁰-9 = 3(9)₂₄₉1_<251> = 7 × 233 × 144593 × 10817778017_<11> × 41765060149_<11> × 323601526579_<12> × 9993023712544651881405293_<25> × 397869046237867494121907980309_<30> × 70950032524214449038440162186879_<32> × 3721939007586273114581978136315755902636906895389_<49> × 1104938488904480115616998648501886905041655534575552950019302930656654642413_<76>

4×10²⁵¹-9 = 3(9)₂₅₀1_<252> = 43 × 9302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837_<250>

4×10²⁵²-9 = 3(9)₂₅₁1_<253> = 47 × 53 × 887 × 10243 × 7010931025589_<13> × 9496596035573_<13> × 72990180616825855013_<20> × 16510776897831556985977_<23> × 1363935016086710284190348118562849_<34> × 2115455595883918282267614450587132366299796154935856176143403_<61> × 763417782830847162690688109374854069023847014203787937595485836154119973418775879_<81>

4×10²⁵³-9 = 3(9)₂₅₂1_<254> = 311 × 1929654049227643_<16> × [66653068406500849673327401525636300925737122531429319857364465363165095327623581155500179421905576790645660456313537985295042020727270442705445379056796879170307289353682592243266834117241996139466444232572574608983995435704684056503667_<236>] Free to factor

4×10²⁵⁴-9 = 3(9)₂₅₃1_<255> = 79 × 83 × 6299 × 32843 × 3835231 × 9504490972515427489_<19> × 1195589420583881466001_<22> × 16764844081995121858257311_<26> × 8927757006598681262632931194240133629_<37> × 2268642375519091333458799446695979155571481664083795247_<55> × 19926453316790260570873229151431163816821436679406746821262860054342284432777657_<80>

4×10²⁵⁵-9 = 3(9)₂₅₄1_<256> = 13 × 173 × 431 × 1049 × 92347 × 3190239826003_<13> × 8303917648031_<13> × 77382894533230357_<17> × 55569830976755946311_<20> × 373942281817067109811885764113374377819380443170163816043240608081417312630711013069968572517560396161039141988595162505151237538356935278446207919650638583015605941995987826994333_<180>

4×10²⁵⁶-9 = 3(9)₂₅₅1_<257> = 7 × 29 × 31 × 2477 × 2963 × 193441 × 3909575333_<10> × 9956140027_<10> × 71529536223356588000887317708692914881364823122198486570716063082947853469443365847902713213788499628499_<104> × 1608014948402127570106586247594522610290635832095644274448651737684348026668594835032873733512861038079830762256699673_<118>

4×10²⁵⁷-9 = 3(9)₂₅₆1_<258> = 1213 × 218849 × 450113838620959_<15> × 3347589974555544085889675642670025829685268667557385507618268933721506720056746740588897582894459914038343411652472381588347696354852067117281879781570525171496422784854784567902896462961218069755444646294059841911336505263049038026877_<235>

4×10²⁵⁸-9 = 3(9)₂₅₇1_<259> = 17 × 199 × 211 × 727 × 43003 × 98411 × 91312817 × 108307883 × 32253271614371_<14> × 10480156240669628026286652343_<29> × 1238884993026977280505283074694462147755684809988667268631988063351_<67> × 439778908259318879132175124451656910736124888008620424152716208102430896908420952389976088353089547098694511271471669_<117>

4×10²⁵⁹-9 = 3(9)₂₅₈1_<260> = 1237 × 74231 × 158161 × [2754264080349269851023268480901108709140394262078817996697780148298011142719787659984130299080982811434984248572487715608905386531911518063353199718986422376251253829785589462226449862140096155349190057305731869162768166647926245280370015120910573_<247>] Free to factor

4×10²⁶⁰-9 = 3(9)₂₅₉1_<261> = 331 × 12197 × 103423915189057_<15> × 7741441883141489944158832660919_<31> × 7805130056799676072052136059222932498058574784538345051201955549937727648892976307464232959867873_<97> × 15854625846360807465839312919222637107991076910585397853870551265862533057270279414491351892335733031540359985607_<113>

4×10²⁶¹-9 = 3(9)₂₆₀1_<262> = 13 × 373 × 200401 × 24018523143427_<14> × 31235506555973_<14> × 2597867335026662437_<19> × 25199615893274979283_<20> × 83811223230197321240674937626880777800877763313526012186515883388341749330979895619356468548421994218725772824338672376722692063382766935802047803212915496285457336409186226552356270490599_<188>

4×10²⁶²-9 = 3(9)₂₆₁1_<263> = 7 × 8093 × 92767 × 1361827 × 22377233 × 386273829607_<12> × 4567358173159_<13> × 62212943607129307_<17> × 540506822274149821_<18> × 20250623254125963298303817_<26> × 43957292806838607565682258237_<29> × 9567602985986402661630952546491957560608990072545800111_<55> × 494328683079133106401078242337242213766572794591865006865231436633400917_<72>

4×10²⁶³-9 = 3(9)₂₆₂1_<264> = 692401 × 9895009 × 35535649770710729757443_<23> × 1642940556338967218438931696187049214688945341253978565098714364058102541933995363289608773491617127914078605567759217559187347446597451869315657230105092490253417721995379517398336312294656505739435742430392250208738917213576493_<229>

4×10²⁶⁴-9 = 3(9)₂₆₃1_<265> = 19 × 463 × 883 × 312007369 × 2035213286473_<13> × 275297805609606581_<18> × 81483035220514238963_<20> × 224921079033736342221790746096952105532091294451_<48> × 834662212681919642405556463667806222934803506974724243740903_<60> × 192565755118774612646331983883006930030794800546537948994802291846665356618143697402920173027_<93>

4×10²⁶⁵-9 = 3(9)₂₆₄1_<266> = 53 × 4164438573637_<13> × [181228986281563915251141583721036344000470040275182289215724972821475775463200879766445812253849209485627728270364010444606720455247543584819379753555045754240772861960690315272697738677501523512851739812046332520468803993091949892406585062989266810431_<252>] Free to factor

4×10²⁶⁶-9 = 3(9)₂₆₅1_<267> = 23 × 557 × 71162352319717499_<17> × 2739490804091120297_<19> × 202774642894094696157617_<24> × 5387015255111323942626049346281287077863_<40> × 93664776152606764401059753977917406656658975593547100495177002729005709733_<74> × 1565375987184300132253742064897937509211101557738800048039377218390189814067798915031396989_<91>

4×10²⁶⁷-9 = 3(9)₂₆₆1_<268> = 13 × 79 × 32573 × 3115019387_<10> × [38385838742536574783372481538719220878065279206907354262004875718207513250614139950212940331134579598569854171296260522513038413984132442610646146837948176638329725419880068728816730404963711907552090330612013635508792595813523538707071381248146756083_<251>] Free to factor

4×10²⁶⁸-9 = 3(9)₂₆₇1_<269> = 7 × 7229 × 66905292289873_<14> × 120160125308467_<15> × 157756740409116882389_<21> × 2221939400887640132398081007_<28> × 245627325886145161242134796623575019_<36> × 1548812039046919635536662930007713724729614506751564661212755368239186562789_<76> × 737339247296593171731659164098751163305183427019906464474193591876106604044019_<78>

4×10²⁶⁹-9 = 3(9)₂₆₈1_<270> = 220738723 × 32898098813_<11> × 900088061495140402991_<21> × 61196370238116068348597908776304184764872155602615474107940058897013367651822621567530698504801785845765841094610556996137932962666483571222204061773091777147856462420760628921324608668875879586662809321743609181632151237247057199_<230>

4×10²⁷⁰-9 = 3(9)₂₆₉1_<271> = 257 × 1039 × 30169 × 99257 × 7020006299581572894488170104402102406297674139_<46> × 10749361742827382298904906120880763303050229911440763032084434365062835850279407_<80> × 66293214889456064171832012993470118333388577679074546720143193344161225098611157148065895455600119327786801020915509297623388246213_<131>

4×10²⁷¹-9 = 3(9)₂₇₀1_<272> = 31 × 30202177735606346764907_<23> × [42722832503695827914321127770301452455246372564329943356686659384169839329541774435734593642755496300432927925871631930845604006614931847264993896026811651957046732318766511595785813401107256782754754246157689633422423934389651482772892607147348923_<248>] Free to factor

4×10²⁷²-9 = 3(9)₂₇₁1_<273> = 43 × 23719 × 7835404340941139_<16> × 26265181432486679_<17> × 930663416767988537114497_<24> × 19027796247545542861547220531447668624061661591338963907296386541991857083085115088901913792033_<95> × 107614850749561407878824124427790571175221117550451406518629318663620901554531941180527256812039819026153650029950983_<117>

4×10²⁷³-9 = 3(9)₂₇₂1_<274> = 13 × 769 × 692209815359_<12> × 578032884152747004261208739111100206260126240181680661942162475576036683730359748569977921055172005223372261795906603883208923650353218479594748401646920227959361806752583269954399632881597514180908469811074696058905018012645449264727753613483209668219907117_<258>

4×10²⁷⁴-9 = 3(9)₂₇₃1_<275> = 7² × 17 × 283 × 317 × 653 × 17264088293_<11> × 1328613771450100770246781828785320550322299965818189662049_<58> × 7000751848412477959806057766604418499857831431396426422451_<58> × 576483264949148720398224057113036271804100390023761971950737_<60> × 8854872751704570530521108482218419399537655969341394293738394189902236177869491_<79>

4×10²⁷⁵-9 = 3(9)₂₇₄1_<276> = 71 × 401 × 84474682647521_<14> × 818953304680362191_<18> × 6718572700095321910194940175935384879_<37> × 30226964810738355816644210088518044047158063430029864753580832080349747055498133633088448033525649794573852209720340727234565183662557560147731245778372056078296302820707693240744095857406884453469709409_<203> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=1764086939 for P37 / February 27, 2014 2014 年 2 月 27 日)

4×10²⁷⁶-9 = 3(9)₂₇₅1_<277> = 22082396421516652591_<20> × 2792516776165070836944026656509845283656971_<43> × 716199815546524866079650590503056034131183398218468977769146136824078266907549975600350599517207_<96> × 90569880271293352518303498238803858248630888025984330258335249566554794436493185827628586008360528546509702442784359533_<119>

4×10²⁷⁷-9 = 3(9)₂₇₆1_<278> = 67 × 929 × 17987 × 36599 × 12973319 × 80809574813441_<14> × 565436964030157_<15> × 1515401837949872107_<19> × 1765110289183705733593895669591_<31> × 615663986020623026981504914545261373583048698272679697412062651112455416702096848424307335241517875265006799695704312568778114219634588991497632984593608755838109576255627474513559_<180> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=4171225888 for P31 / February 27, 2014 2014 年 2 月 27 日)

4×10²⁷⁸-9 = 3(9)₂₇₇1_<279> = 53 × 113 × 241 × 20663 × 41803841074986331004467759752042705661_<38> × 331468644256359068076837242793801952073119679096103445167011822018914725489819506339762119501373_<96> × 967913662101340560422010356676184484343996515510816435173982480762715965735856361612544161060833373663069254222523350917098194841020181_<135>

4×10²⁷⁹-9 = 3(9)₂₇₈1_<280> = 13 × 89 × 1031 × 8191 × 11885072201_<11> × 1175935190363_<13> × 649382801709079_<15> × 243280349283105805921_<21> × [185412075980039968962242842836101051717026383534786282416221441289061420525616572475724184424684540954018706920028563565753055842564938100362152006153149743892318485511051461757476577655979301351433392354185413559_<213>] Free to factor

4×10²⁸⁰-9 = 3(9)₂₇₉1_<281> = 7 × 79 × 7873 × 438869 × 754242675153051504745993_<24> × 7036463668833882894493692791_<28> × 64765040431139423250597025178825030172814291640805945008454962342549492619879321196452169216447274551849343_<107> × 60905079120205992651499182035774058280731042907790381089516679191263999393874607733267630012429589633047391859_<110>

4×10²⁸¹-9 = 3(9)₂₈₀1_<282> = 352237 × 66116564428341103933_<20> × 327688085009441514698183304096854321_<36> × [52414818807970628835039384773766750411044054155348614012225165019257480137097191366360897279190370636000287082433411071789091681449994362696054866180780348080852281534547621052697640545310284487807248972161988654220773151_<221>] (Serge Batalov / GMP-ECM B1=3000000, sigma=2672261608 for P36 / February 28, 2014 2014 年 2 月 28 日) Free to factor

4×10²⁸²-9 = 3(9)₂₈₁1_<283> = 19 × 167 × 511171 × 31993217 × 416824282517_<12> × 40464415611439_<14> × 1023170883475949245909_<22> × 214884373867410502156141386709_<30> × 40059260051938443901187811141767299_<35> × 57043556884754993123007599776067037686087494765852279033731828829_<65> × 9096555792178228083391163737686299219008089428520929845394614809182168672125704646024235237_<91>

4×10²⁸³-9 = 3(9)₂₈₂1_<284> = 3169 × 3719 × 4250591 × [798476714240762304289927317927791738703273513215974404954580973493719053901007970687185281370572533405841786624835084802044373214279686219659739152616127094593700535792317828880418459640137315574828176597521673354697993089417977990056136224533802179883646662641961882991_<270>] Free to factor

4×10²⁸⁴-9 = 3(9)₂₈₃1_<285> = 29 × 18121 × 477623 × 10062555889_<11> × 5499130730309_<13> × 11753001510582599_<17> × 142203315288161311512583_<24> × 1628892178337141932454034590460430447783_<40> × 2969240859409506695099012352547967144102089819518203_<52> × 3562837145624505123345782996745374516782957870662099008996375345266376225912969224718234215768341650186195378035432153661_<121>

4×10²⁸⁵-9 = 3(9)₂₈₄1_<286> = 13 × 55812131887890896923_<20> × 79937829311186296877639_<23> × 68966101383640516446167371855786022310853016696718283063648159268421464915465728285961096528403280675638895904473279671087246024797801377438233086352611255046832833125984319855825990465309197229740336085477419596728250567726896174291039098831_<242>

4×10²⁸⁶-9 = 3(9)₂₈₅1_<287> = 7 × 31 × 367 × 79869969541_<11> × 213191226127907995641964733297_<30> × 228969479001528543632608227557_<30> × 300364480242690431385063688008727003_<36> × 1654770841768982551074895703714451566312262310294250115213002864298336917_<73> × 259189448587394079995709224242217573207735348894143323496982198581906017312796640460823662146191460771471_<105>

4×10²⁸⁷-9 = 3(9)₂₈₆1_<288> = 157 × 50934683 × [50020350585806977048610190992840947242126788720749730735044346193952167937960908636080068210941357173768388620557768023258911798136788734716663127366299360350348517936922129762920791492700738261146186564062115736046512046245780916763584211777672925591294231391776597665625943961_<278>] Free to factor

4×10²⁸⁸-9 = 3(9)₂₈₇1_<289> = 23 × 211 × 1201 × 342511487 × 95528206800101_<14> × 129614923656859_<15> × 3137467624232877973853_<22> × 1168960033824751568738318599288806794044795142960334049_<55> × 30972672201765739736938580712102556265014782254894828718827693754781089763714082501_<83> × 1424581581949223240674405227318668880791852510435284297667922774714016704281163739428947_<88>

4×10²⁸⁹-9 = 3(9)₂₈₈1_<290> = [39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<290>] Free to factor

4×10²⁹⁰-9 = 3(9)₂₈₉1_<291> = 17 × 61 × 227 × 617 × 5231 × 262908713 × 7911360529_<10> × 185405024863733_<15> × 1698566896904071_<16> × 42148020350828467_<17> × 19181467147855111285267_<23> × 511073459929064433496515670727_<30> × 1134320138268801249042282616951572493682856422065040483699499756236497921_<73> × 1714933198151159483494274806473776743828925126376508366289766922631413467958045570827771419_<91>

4×10²⁹¹-9 = 3(9)₂₉₀1_<292> = 13 × 53 × 5237 × 10601 × 59735477155129_<14> × 44616186287502712079_<20> × 454027205499851838839_<21> × 41594031977050983708088540381120781759_<38> × 2077656184064841971084288262193150304189081625784995837984244214934695103479814232637980914377895067517523482338022901652944507321424967075229299547366468046715394518695954016878961657020957_<190> (Serge Batalov / GMP-ECM B1=3000000, sigma=1545062547 for P38 / February 28, 2014 2014 年 2 月 28 日)

4×10²⁹²-9 = 3(9)₂₉₁1_<293> = 7 × 149 × 14243 × 106441 × 1088196679_<10> × 11297303071_<11> × 1570076584418759_<16> × 2011840031262686851_<19> × 4448748130740857754356733813222510745804262837_<46> × 95519408968726075748994090904376099816839216393188114257850974641_<65> × 1532990132749980953389945553120218010491917071949279249377201842143209739521102656071536651055954979955117249500808887_<118>

4×10²⁹³-9 = 3(9)₂₉₂1_<294> = 43 × 79² × 1151 × 403189284072959_<15> × [3211833685071499366692493292881187812638884393310717978560527311696699590583927526848566449252753885735603806821030642633231027720963771938680833158710315158924609316667108797610331249587025472759181589769639309219213773559474536361602373761542425825111205522854726483973_<271>] Free to factor

4×10²⁹⁴-9 = 3(9)₂₉₃1_<295> = 6328193 × 2807442959_<10> × 1689189684351792543788723_<25> × 9315019792951667720337833_<25> × 37217298101001103011342694765763_<32> × 19847917526656775016866295121378364453_<38> × 608892479187265731705994468981721335175199066679255978067665568322719_<69> × 31813154456124267948681707302764451170058560372489661494512147777300060017072412206709935547_<92>

4×10²⁹⁵-9 = 3(9)₂₉₄1_<296> = 83 × 1494676633763_<13> × 3903314172297168405628645213336843_<34> × 82604012786733003405553219786216246542205184291162227355222354497931210907400429948277304129818833225027162793486091921937879986950269831230248412317913642657772771239382693959315868083557282075452028574422770692128404990604179755006856987584939853_<248> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=554131394 for P34 / December 3, 2013 2013 年 12 月 3 日)

4×10²⁹⁶-9 = 3(9)₂₉₅1_<297> = 151 × 163 × 54917 × 108959 × 752584291 × 79496880961_<11> × 360248308916767_<15> × 3382153529722873153_<19> × 22142194087798266515774322687941954125664442651683_<50> × 3803413556430766247732445539023188610808389140958333384583058412229_<67> × 442415990509240840865930832306408338652347903847608419715878443771841429161619240227976036213865734077353497221067_<114>

4×10²⁹⁷-9 = 3(9)₂₉₆1_<298> = 13 × 182070532509348742770764491843683391_<36> × 668503735825351157067606241570007290027_<39> × 2527977114573086766546526287646398331473046089181770092871541877372974784720397275772930035752552194671829810614008725909018969756523608599150065487278697127477585511240720657451001952598006610288488497384636079535110319751_<223> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=986245908 for P36 / February 27, 2014 2014 年 2 月 27 日) (KTakahashi / GMP-ECM 6.4.4 B1=11000000, sigma=4163654588 for P39 / October 2, 2014 2014 年 10 月 2 日)

4×10²⁹⁸-9 = 3(9)₂₉₇1_<299> = 7 × 47 × 173 × 197 × 1340484529_<10> × 783752398071339239_<18> × 36080667658326733243_<20> × 3634354939784511165317_<22> × 153014654938477682173751_<24> × 228523786955320896343849_<24> × 4925878260251331708626032851043074292536566448573065337112672161101403488977937_<79> × 150335330555761799982346599520277823222294967921805913894675204804052376237077781705390405123139713_<99>

4×10²⁹⁹-9 = 3(9)₂₉₈1_<300> = 643 × 115035841 × 336199363 × 103968628968644175121_<21> × [154709379155695336098250291193930148487138808276254346130499600845282996030714668018661286166007042356549084205033194396583348223233336680499368315056713138941105352219435313834066870522399685752214680028293390662827890898867687737380046063667024596050349039759_<261>] Free to factor

4×10³⁰⁰-9 = 3(9)₂₉₉1_<301> = 19 × 487 × 250250505961_<12> × 1824453361909318934020125483109157972584403451163125882265065433_<64> × 2250962543871412830161298255938234659251521136933600855735504876723568950774217694093_<85> × 420631149137981990420608602170580936167680773461758324158080753438724281697849613462731528024601426730766721198010524787747092795030330583_<138>

4×10³⁰¹-9 = 3(9)₃₀₀1_<302> = 31 × 107² × 1464391 × 36570187 × 38715517 × 18022392049342564660122961_<26> × 8095454631303223375438498052951_<31> × [372569904695611793473055093784523796435602455019890141858638849487303543901342414201197629681176844801740956134964250021267087945050057633694101438890935665993995484344998883809123310681633669677553112305018621665485791_<219>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:671956220 for P31 / July 15, 2021 2021 年 7 月 15 日) Free to factor

4×10³⁰²-9 = 3(9)₃₀₁1_<303> = 109 × 206127409853_<12> × 5351699092147_<13> × 41659474526382217853629_<23> × 232357967917576122963811199234684498812206335392391_<51> × 3541933914244940727356281485918685455317930382157304642870395201_<64> × 97027367754065425165181173621119251060810058720182234045762222524054645187828405948586729316796098149047845834331461971247418816223279407551_<140>

4×10³⁰³-9 = 3(9)₃₀₂1_<304> = 13 × 997 × [308618162178844224982640228377440012344726487153768999305609135097600493789059486150759972224365403904019751562379446030398888974616156160790062495177841215955558984646246431602499807113648638222359385849857264099992284545945528894375433994290563999691381837821155775017359771622559987655273512846231_<300>] Free to factor

4×10³⁰⁴-9 = 3(9)₃₀₃1_<305> = 7 × 53 × 59 × 9437 × 1077079 × 3473719 × 764892666772199274490037661811796227973_<39> × 17930947920257063532703516829435538148362253000748922501535367754063948223945638948206096726431_<95> × 3773584905660377358490566037735849056603773584905660377358490566037735849056603773584905660377358490566037735849056603773584905660377358490566037735849_<151>

4×10³⁰⁵-9 = 3(9)₃₀₄1_<306> = 10213653845927837_<17> × 39163261848694743640598935448329520465594776843522832258061150875647021299162924069006234273899602930003921051843122445571879746769303577411067985596651764483992008326816984169103795377303707888536598391427457678667111901695601560155131548344572197470886303178331893537745606934226262619043_<290>

4×10³⁰⁶-9 = 3(9)₃₀₅1_<307> = 17 × 79 × 3677 × 8990693 × 294240857 × 921385311825262730764919_<24> × 18536972846671778888746448349596139528250921_<44> × 13024370107576147632519746158741250510023486439810098022457117528012765562134071_<80> × 1376440289607705711643874895620590896694660344209270221136185143972927196557968203597288965288158512426106493567881141417634298421288841289_<139>

4×10³⁰⁷-9 = 3(9)₃₀₆1_<308> = 576380555236408568077_<21> × 841019479988943260455841_<24> × [82517225111060335705669437035075780261014530098213501172513494196853142090930449328776622754199679993442517664312652449394134024411323591137678313544251557342654954796448556480448113262394112926253051884969207088582893971457427014462475159148369809249922571270963_<263>] Free to factor

4×10³⁰⁸-9 = 3(9)₃₀₇1_<309> = 241 × 409 × 941 × 141906841 × 782375039 × 3782508951828121_<16> × 299550549437767373_<18> × 28301991263223655079_<20> × 22278480958586947780123247_<26> × 32826981394635607932036482961957538515492937504121287_<53> × 92971411597094466836812021838084115808539485027367635029013923_<62> × 17814706504328977485410892424619338104938573843248529336228689546358190125162267028033028349_<92>

4×10³⁰⁹-9 = 3(9)₃₀₈1_<310> = 13 × 307 × 2671 × 3359 × 3795405871_<10> × [29433109532729617232178966374336922312891483151009656651496168834646391006656770894423561681972341564824366381782221059001095387125050926785677701836329033543983330755391476731838283220137000307362896789837044345628300158372259555644221129019669106489842236316272610035688757511198027333279_<290>] Free to factor

4×10³¹⁰-9 = 3(9)₃₀₉1_<311> = 7 × 23 × 67 × 71 × 343866401642039_<15> × 141423577541870006652967_<24> × 1176075110392218874344361392155876226533549449_<46> × 105015204394259862679542119957655122688478278199700532417643933576919_<69> × 1111621257288759311574554337362336029819886569891919818320899807496833211589_<76> × 7822495402005635711932598925376137473625943127630073484216479297850123896513649_<79>

4×10³¹¹-9 = 3(9)₃₁₀1_<312> = 359 × 138955740997_<12> × 55781124969235747307_<20> × 680159359867116424363_<21> × 2487591984573976571869603_<25> × 106529797518554560102421230854064043_<36> × 797518654635992259779707740334222276693149117235152743378033579378791682903402193210016554553541705922407230362256877080766281248550363324748106792024170799336196351430970069551615710866774998840453_<198> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3900212173 for P36 x P198 / July 15, 2021 2021 年 7 月 15 日)

4×10³¹²-9 = 3(9)₃₁₁1_<313> = 29 × 97 × 125353 × 21225989 × 845647631 × 1256265547_<10> × 97436968800347339_<17> × 141325597716279667_<18> × 43135946585687043827750397163601212657_<38> × 39134557867852232577558454632800142255822036800416522850859882961102818904957125240913476934321_<95> × 21640751895235374752390739537526410686353388293787540565070651038085291064841286534914579421812560407779824260723_<113>

4×10³¹³-9 = 3(9)₃₁₂1_<314> = 109989767642046514039_<21> × 16229318571941924208601898118526223879479_<41> × [22408223188657757196748648213944994600926347978343370656522829777532080546540787179119640270756972791114161659524334036831397356176972598466615753063661605965827723375556687309047375805685216904870076924199254028546646169160850623652256784833146112437511_<254>] (Dmitry Domanov / GMP-ECM 7.0.5 B1=11000000 for P41 / February 28, 2024 2024 年 2 月 28 日) Free to factor

4×10³¹⁴-9 = 3(9)₃₁₃1_<315> = 43 × 179 × 8678368395079_<13> × 2733863182530927049217_<22> × 496078180985187011253921599029146472448633_<42> × 59573402681404398007654718102866364909302643_<44> × 1915938687245105985797755896058272648806048756431283226141003881366035015771171783110925141_<91> × 38684724398115424654512004896712075071304442379362845270019006771965113736013768988351468162809875399_<101>

4×10³¹⁵-9 = 3(9)₃₁₄1_<316> = 13 × 17902267 × 1446730973_<10> × 462976954920062306207483563_<27> × [25660283808032508300042533950210310980805171992889702846924561841927187617967779681485071810499200520235537547157214741437125360172976219634345812942469235382255446291430111951981319685549176965329042801638343037661030273333117336859584688973919265205050849448553604293079_<272>] Free to factor

4×10³¹⁶-9 = 3(9)₃₁₅1_<317> = 7³ × 31 × 571 × 8308493 × 627908707 × 19547338624799_<14> × 176891153250092117_<18> × 25560955073898763070557830367_<29> × 765613002593259893435771444351052001550447832917_<48> × 4486195411014709158764439342476979691484480174887014872203008588690204116766979_<79> × 4159977593448370364304706171478541066565887961579230858181342138794851799577442531362916884055114039300431969_<109>

4×10³¹⁷-9 = 3(9)₃₁₆1_<318> = 53 × 9831762551728153977893_<22> × 48032289022050459163109812883233482086711_<41> × [15981570560735633936363093903429208495662150106126269872354522802987774297244836700022845421021775350982814108468205316651533699256758714746851551149729752486447750802855109328515588791973746532585307225092913554562572551189273926386976207342809030972889_<254>] (Dmitry Domanov / GMP-ECM 7.0.5 B1=11000000 for P41 / February 28, 2024 2024 年 2 月 28 日) Free to factor

4×10³¹⁸-9 = 3(9)₃₁₇1_<319> = 19 × 211 × 1895315654240578217_<19> × 27027959896545436523_<20> × 52589677955822857981_<20> × 3896040234710280092225221728653869867_<37> × 5874207548035032880370430336726048734418437859121_<49> × 1661715856862486631625209578684315662965911900561608691_<55> × 9738658207678451324435719062537714360497552822646565456174754048863655310132922791044018520009793860700775434306628537_<118>

4×10³¹⁹-9 = 3(9)₃₁₈1_<320> = 79 × 517747 × 74596649 × [13109797704417644018256358287284251578262959335330333965154764425731387476512931906530435653798594876259779382842707162597960323834335463083661220573336706068587202865950967222632767892443315275753132410329257688721413753140422469204608346494048258454864444502950372521013529498692650674907741726681981643_<305>] Free to factor

4×10³²⁰-9 = 3(9)₃₁₉1_<321> = 15073 × 269741 × 1023361 × 2269267633_<10> × 51894756337_<11> × 1244702530203678363132386159041482385491409469399_<49> × 300244161062830630302818080353294695395582491459143920704439_<60> × 8845587159376599603050287573778844195307606321990000300773593282138846596884883531_<82> × 246949676822489123478546797860086337445136656832298441810501694114885422418729064737492466489097_<96>

4×10³²¹-9 = 3(9)₃₂₀1_<322> = 13² × 41064293 × 14589665840811306060241995889868781320641_<41> × [39506048420542741919319675390679187283868070471158953439116208175259205052604638274739773094069648295959527343682253801493557749299679465873073675333797207022510143727929401653641995276061704595609562064943037199438829469137464433503497754123719647019927918521850840556403_<272>] (Dmitry Domanov / GMP-ECM 7.0.5 B1=3000000 for P41 / September 19, 2023 2023 年 9 月 19 日) Free to factor

4×10³²²-9 = 3(9)₃₂₁1_<323> = 7 × 17 × 6011 × 1645747984609139286241_<22> × 13899436859622480875900698576457_<32> × 23143371269685496536153160328427093498540901_<44> × 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383_<97> × 20115883014377928383893387007175234704920014913458230162438995215793488735504372470773121940594252835379458979121030084588169_<125>

4×10³²³-9 = 3(9)₃₂₂1_<324> = 89 × 773 × 99787 × 115192841437_<12> × 29455222694952143337197_<23> × [17172310121806940771558844731183430187604346413241773787787027614747090645981486935259912667769802097808745489974549514554450288657270708169327923338126153549240641642188729166521881882558129262225916551480980905065361820659987496793980829682452599548572280710200222456032965690321_<281>] Free to factor

4×10³²⁴-9 = 3(9)₃₂₃1_<325> = 293 × 836131 × 1237373 × 922383270197_<12> × 994957995931_<12> × 179397930216237714296595927956723_<33> × 7189045804898519263081151795037204467531679369449028078511722416595386581264805003152843804006862295551307784080752976388969_<124> × 11148400639791637102996387547716707811007020632209029670143600424942142750952687051685685837339502521886454403702834010533758301361_<131>

4×10³²⁵-9 = 3(9)₃₂₄1_<326> = 6753161 × 444095929 × 13337551076083765487843831140519603825247699569567730900176617734684369475104681208006746905359970704513431958948962091059826683131999176053044663954056522663978783709831680199635953576609997183939641641535127592787130114901875361696131563745631457149914066554119142185965886086010748985309211693736129332245239_<311>

4×10³²⁶-9 = 3(9)₃₂₅1_<327> = 17091071 × 60901619 × 195831422029_<12> × 356890571400141061_<18> × 166140237444137244767_<21> × 190635692847477990579123632346869310511_<39> × 631467424737264651495425260061946168071504561817690296672097889180937084893277408137330615731353547645619_<105> × 274925122460187569485340308736925473178651132530416258339342177005623400903082611229363119849296902241572092263825625137_<120>

4×10³²⁷-9 = 3(9)₃₂₆1_<328> = 13 × 2195723 × 5959879 × [23512653581752087168971864005896820674627992432680030811442558388996460572296134985027024292969700457485870891231453414295762765301208339021922258719698019731827889636107207227564367573840940249784698512678061506533795207647681825043961941277345476233764420872389502148374439233042695836450108063067046881682115871_<314>] Free to factor

4×10³²⁸-9 = 3(9)₃₂₇1_<329> = 7 × 479 × 1847 × 6359 × 6529 × 7297 × 10370741 × 53292601 × 97689419 × 205274357 × 139874026753_<12> × 3925375099814913149_<19> × 25826391871341962471_<20> × 69298219423145010197_<20> × 2153254071713608720591373_<25> × 6582418788086270165044449804136959083935788871362889026363451583633652174166909560151_<85> × 138113436171072982352946240535290905803608686060864069536374354358642139888493009820335510911672656033_<102>

4×10³²⁹-9 = 3(9)₃₂₈1_<330> = 1998329 × 22998146337119_<14> × 1609178735466889770313213717_<28> × [5408737224100048555041813288042877286680465375120901120314075358327514394344982640521369787090937782107045732819102615473735956537159279528297249351950429803304408568696845263989598350852063785128506124084704588047873496922799248021929877942412414226995772113801028326632181464190573_<283>] Free to factor

4×10³³⁰-9 = 3(9)₃₂₉1_<331> = 53 × 71881 × 238245737904007_<15> × 94136405394950299_<17> × 838305023383274289860418539450587157_<36> × 1403781958927021896724841424949479359_<37> × 2551589809127749396488652666886417210600862321179209_<52> × 615183048749711493044799857844699363803138896771654939937_<57> × 25343717347214324824522098723663613215893017202640604427624247481323908812513490062007103784101162836271292998421_<113>

4×10³³¹-9 = 3(9)₃₃₀1_<332> = 31 × 191 × 45343748044418267_<17> × 1160354382673727953814450082900947_<34> × 128397588743463323125734483751100466519795933473451930511085466139639195559419275254257412393933557207057526895777976656454576980575562109698455200797886991873706314945968988340625328054470163401562124981978039337616574327336558236319306957814376169807365964579814454948097411479_<279> (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3773366191 for P34 x P279 / July 15, 2021 2021 年 7 月 15 日)

4×10³³²-9 = 3(9)₃₃₁1_<333> = 23 × 79 × 193 × 729941 × 1137496712761_<13> × 849138863352599004001_<21> × 3151934443985899535720514258097_<31> × 29139773847805639821445881025078673003_<38> × 245334893549794309989767836564265608087_<39> × 13531387192579406360450949532177073435621_<41> × 5305986400511685990731500472797459622030647462365611131005646934719617025247082571798665631818734627082725026872229312742765194453979020894123_<142>

4×10³³³-9 = 3(9)₃₃₂1_<334> = 13 × 41355691204232227_<17> × 407934912180081648561847489_<27> × [18238557224598333953952152620025443561515920572326678566469235198836249253788135425580581494832933387600323073275467181122588614070799852961538203872522860869889898457603040045220378238611609849674631377772471215336305664731546613777013122273372875505869425070603015086043539087802644986769_<290>] Free to factor

4×10³³⁴-9 = 3(9)₃₃₃1_<335> = 7 × 77550151291532631003351523_<26> × 1416288347210403639057173330195587867_<37> × 337473788641314954387395638036113417304047480856561_<51> × 4690700023174550771994364525354487199388452766958125990189_<58> × 126343321023855007144178242728859599541361819987460022346207_<60> × 260134302671767920102022631505867541342722247157905131978577734973578865145671722044817281277952599937931_<105>

4×10³³⁵-9 = 3(9)₃₃₄1_<336> = 43 × 7255582357_<10> × [1282092204827735626681317032920476206626457193465715545367468455751183968181004941656029544477458592623512729334674602653516156525700860622916479315941741102256686690546968361781824007050852541556449098045685267838291258113459360076739643792233691936743500508732685225150592181793848170270150681621203129208081682478971594641_<325>] Free to factor

4×10³³⁶-9 = 3(9)₃₃₅1_<337> = 19 × 83 × 5113 × 107171503 × 1835111041_<10> × 2124971131_<10> × 296146061250647_<15> × 57092174517726937_<17> × 17170380743133123257952990693559_<32> × 44858038464611919885751480065824250801088011690093127023208432690399488635724167714133938508092027766196393_<107> × 91149659654726308272585876863370948930460841622720609441608189978732758903332080233873633785536467083928748067377658532027062552593899_<134>

4×10³³⁷-9 = 3(9)₃₃₆1_<338> = 569 × 897594289 × 65907322904551_<14> × 3610872820753374738772323889_<28> × [329095376255041568055120637544252735673924484367063324976327762267358504203809009059281393094667429272720943625159263482311618981095143480896123639440770704310282803184100572809746483127652624757455292368856969587832010783926468677034599097383952264180956316931881872194983232037322009_<285>] Free to factor

4×10³³⁸-9 = 3(9)₃₃₇1_<339> = 17 × 241 × 14153 × 93889 × 4568033 × 43680967143031_<14> × 5896028798213843137237197474833906963102993131581871751699684425911935230535986344105005014558253978688551536750366043892471178185550208899868740133_<148> × 62452486324637325769890221176637781858386879943374557476881667807207732700425836737424325616490243072104147833422224539009061776816394288678935699086007041701_<158>

4×10³³⁹-9 = 3(9)₃₃₈1_<340> = 13 × 4283 × 15046951 × 1286412649_<10> × 11933505319_<11> × 43760039801_<11> × 7107126030196500985539562943544421600840624999693106846650355418072398508110676352156145782650786327560823376000393524690627947167100166829968699860714201707544151341030023438757569213683773594797816530480416847709522781720711559145154300598016473553571749879652521125885829784269066708345623641209_<298>

4×10³⁴⁰-9 = 3(9)₃₃₉1_<341> = 7 × 29 × 1013 × 5784407203_<10> × 1834192081578759239_<19> × 76541953053300386459_<20> × 262632027912846093091_<21> × 71775898228022209393560983425277906302357674967666842984378404894862822000808900815660770387246947459592034389179117862851_<122> × 12706471680112835654690980720290430949855819667071375215198272273064756284147694488613045888308212030764851003333958296721086670252760342053743103_<146>

4×10³⁴¹-9 = 3(9)₃₄₀1_<342> = 173 × 11479725486836804044463167196274927307_<38> × [201410628762413090443046255746503357381917179160293231907649152313385688829303268837806101473656706049370438829867870318200946044783372090361726255679217720454095524936617737618895202482035653202922118003563900020070916269201030011528117926990531396615216892985067653417450044009345830411888818616177081_<303>] (Marlon Trifunovic / GMP-ECM 7.0.5-dev B1=3000000, sigma=1:214031054 for P38 / February 16, 2022 2022 年 2 月 16 日) Free to factor

4×10³⁴²-9 = 3(9)₃₄₁1_<343> = 4691 × 8627 × 2769503838393179_<16> × 56976208855415157152685472638791_<32> × 1494197448543319671819667216019537347_<37> × 41713247973026961742658321646485423054431_<41> × 1808260737095189373997972911343245292873628525108905125242459880129553110340203951049_<85> × 5557713951456074967962531890753686473889384220379793822875068616831334165905093911472798378503095080109303609626110094430409519_<127>

4×10³⁴³-9 = 3(9)₃₄₂1_<344> = 53 × 67 × [11264432554210081667136018023092086736130667417628836947338777809067868206139115742044494508589129822585187271191213742607716136299633905941988172345818079414249507181075753308927062799211489721205294283300478738383553928470853280765981413686285553365249225570261898056885384398760912419036891016615038017459870459025626584060827935792734441_<341>] Free to factor

4×10³⁴⁴-9 = 3(9)₃₄₃1_<345> = 47 × 2213 × 40853 × 220028549159_<12> × 1531324534463359_<16> × 2439195933333443_<16> × 5375143005441934662479_<22> × 2488278116031430102776096707299610662488043_<43> × 144598623750304627603800978611367204972835492142676576929116325082869033718437561821680337101937_<96> × 59225767811436665677404655299131091454174324294278314763315069306690006550853237485054095184846979975166325383100663147992888076712071_<134>

4×10³⁴⁵-9 = 3(9)₃₄₄1_<346> = 13 × 71 × 79 × 52639 × 69653 × 1435997 × 1030499926292167165478150893_<28> × [10110723751011403958365512257224520317547781629019467293487210276028391494047284239943813172942433506595673235379281985843527463066435159734075847051814707705697133045030465636015311056553502943570365866815040448987008097564106887566576722828904447541206258160262549210878235886708647977617905926489_<299>] Free to factor

4×10³⁴⁶-9 = 3(9)₃₄₅1_<347> = 7 × 31 × 131 × 10631 × 14367479993_<11> × 3164590541963_<13> × 1028215179829719535882320343_<28> × 3226925443320811301909314322467_<31> × 1377280097548571230432695973091803101076339_<43> × 10704249832674713026912742559336870309487534796404441_<53> × 138284106376553420246923079942434034576006381033927871198757392949_<66> × 430361089471713503060658776757056607930496673647784651890647453877752335021838104625034871626829467_<99>

4×10³⁴⁷-9 = 3(9)₃₄₆1_<348> = 140249 × 1503317 × 1897184856214737844987473199603874937334606961595650593809414623258173381875610717254477543872091471854461716409172682929549803612814038244280158702770499042455816608192139600538400919782124168535744662044619512875351774178734377500757395525614473749502948197835636162816269717139556296880091229031571235051666807082669517401320313860627_<337>

4×10³⁴⁸-9 = 3(9)₃₄₇1_<349> = 211 × 797 × 6299 × 774051051841_<12> × 4200221359757_<13> × 2915451063446069399376601224037079185354693746657059794713463255831700287525577363096092505850841359833761517933310832779031230601002765860131859371_<148> × 398382328716015746459924829238394574988800476783971007327645363238035632510627346596410615056501569725970723281044988718808406584224099621078648041761622754642498669901_<168>

4×10³⁴⁹-9 = 3(9)₃₄₈1_<350> = 4744476984283062239215921_<25> × [8430855525805527473154155016317287965032570727912267955715621178940392687243193117749926150586649733983114619832491359453333813246323074160699657389411836733017600803281797412758818537321557102250821694843640227972636060528787163004709905630346839836973556205908185346173051810919979917602431837326153450783172888971156277671_<325>] Free to factor

4×10³⁵⁰-9 = 3(9)₃₄₉1_<351> = 61 × 1607 × 952681 × 9041761 × 65731411 × 1081691158291_<13> × 13680046283699_<14> × 76852616085817677774513791387885482895603_<41> × 251898861882089203262483987189502786622824705946228241740108420753071099837412827838656218659332309040463_<105> × 25157361478776660853308287916031703454789032599368643203698111891201776847435320364875878065064817921353442354089767932359910670007542286114601132482129283_<155>

4×10³⁵¹-9 = 3(9)₃₅₀1_<352> = 13 × 383839 × [801618146390303466577633611207583628312110826915211045015468224157283893266948662570264335587817568543862641127379728720394989325452358130121463185586424757014509488854201090320921812771260065568356283994872048717541228724302877789105087529687427040223394945036049770065854934771329405538019045244731014024910684708151875375633253285081265041613_<345>] Free to factor

4×10³⁵²-9 = 3(9)₃₅₁1_<353> = 7 × 1307 × 17785019238356023897_<20> × 25892411261964964027_<20> × 3214888775730183633684484492940316319_<37> × 382327974808924344375250235945475131233497457127498460037175594820337444676213458154174274593752449576287105681456329_<117> × 7724270944737886318386430126568103804958048509602408131783640761948598469607350643640066420390696866601585926287587705869592946568962890281971168022378259111_<157>

4×10³⁵³-9 = 3(9)₃₅₂1_<354> = 317 × 11369 × 430147 × 11208304489_<11> × 4266302449640526606803_<22> × 105360166747406963213055481171070306921_<39> × 51214572730659138043014649024576208352232528744320050804489550690096161596219188108481243309480887267957345333154722089621837266225461478307329722286927629721227084458972860031377663975081067015530421207118426427284279194748092387607774127703281789912032961053966682190323_<272> (Dmitry Domanov / GMP-ECM 7.0.5 B1=11000000 for P39 x P272 / March 3, 2024 2024 年 3 月 3 日)

4×10³⁵⁴-9 = 3(9)₃₅₃1_<355> = 17 × 19 × 23 × 107 × 66090659226826860491_<20> × 221303620588838744540899263379_<30> × 314129679887073807583524645188651_<33> × 129436443535881527128893364288064480493161761142268211249_<57> × 207379590086116170683595680783934802558717377003150627710449_<60> × 43779968748061432046513482796553162771143586000974553425324771322949_<68> × 931987848923914489652952527655347978675348054328016114007617991049256542266907254327_<84>

4×10³⁵⁵-9 = 3(9)₃₅₄1_<356> = 3169 × 493721 × 1309921 × 2184893 × 103506630718573_<15> × 3814650654088208990161_<22> × 2631153741019649830037041_<25> × [8598282419681752075176837339959670284938188616843205903468814396632681512238977507665735243092944317984254982487792184738870129102546524617256510262056148240461563028833653382111337275027849997290087880466502510985342826463840931212917416983044849939296909377943715677461511_<274>] Free to factor

4×10³⁵⁶-9 = 3(9)₃₅₅1_<357> = 43 × 53 × 337 × 1297 × 1447 × 1787 × 216787 × 29365373 × 1127811197_<10> × 76190529753337_<14> × 113629080538653227_<18> × 11599818465140965879994476653062655563497677557_<47> × 198710711995103149990233169293141838129420782191_<48> × 204381963777669164792577925160889405410315156951866223_<54> × 5303249027172655921940588313560365248852477668638803073380969651997775203643395415597588922210937546209863336469209756209034438146229468862433_<142>

4×10³⁵⁷-9 = 3(9)₃₅₆1_<358> = 13 × 199 × 691399 × 2878769 × 9432027861349523_<16> × 7724627207256381502081_<22> × [10662164871075000841143884172748727009042909667921135162351637014705685076668906767451041720131887254391071897528190280317226891711133791570514438227288434532228536306667313385962461524998964819554527437778310903538986210985059921119674697049202448852432784552955055023098652037678196547024323657368654881_<305>] Free to factor

4×10³⁵⁸-9 = 3(9)₃₅₇1_<359> = 7² × 79 × 811 × 7219 × 1989079332932927_<16> × 8969703468441893_<16> × 86895751811064544336849740319641090775480253420015628669829_<59> × 5888327336151621339092064391533621133226986428026063636851455387805005773_<73> × 77279425539607484572840555647164294919712911147901487533613444201950695923489405913069677_<89> × 2501810197186437126229627022814289861260018713367709797946573918927451225309193178017466201869031_<97>

4×10³⁵⁹-9 = 3(9)₃₅₈1_<360> = 13455875108412711641_<20> × [29726791960926946417682240579163919739467937715963816669987390709773102966203704150577799916938447634862714243068555715895479571434860469989964327991175835508007420739501723141767942330684218244121202171585033713354853260958268615891772271272221441572921020837187020086816441274899950123381890523545791778639408811640808879754791334725654351_<341>] Free to factor

4×10³⁶⁰-9 = 3(9)₃₅₉1_<361> = 1979 × 2593 × 2380977433_<10> × 51067720369_<11> × 2039081640448510323571_<22> × 112032125257256292325042410655727_<33> × 905172686450661562749851540460137766673_<39> × 360880371169402630105325305389368378564231281_<45> × 73041953120006531682243304867114152425466458123310047541535943923877620801_<74> × 1176157985424367085220614176274745306343457486221056269990067414713580079192985994419522536405812661021796259633723616006609_<124>

4×10³⁶¹-9 = 3(9)₃₆₀1_<362> = 31 × 223747 × 1847804769251578753157878751_<28> × 295583832325278891290372057955519911935249_<42> × [10558550883398270480540640243749464549065378298182528414080005492805796281862335714790541429260656859080015674008289502003001622780723675138369994038673287730944779360945451478780113885735603336476592729461471042297962439206414654871111199210919427730378127323945792754309906250041902637_<287>] (Dmitry Domanov / GMP-ECM 7.0.5 B1=11000000 for P42 / March 3, 2024 2024 年 3 月 3 日) Free to factor

4×10³⁶²-9 = 3(9)₃₆₁1_<363> = 59 × 1164613849752444074993_<22> × 65053696559439275202720977_<26> × 29646802258927195774388196337379_<32> × 5511837461824511266624821670808689_<34> × 1147137242371709631910079611455202628254248681165795782894651629_<64> × 3163138541455391797066485435516955368132165099527456308975977784797173528030758604063_<85> × 150919791744741283064128923837226378867962889040741916589329187017248321610532109055108292989991354157_<102>

4×10³⁶³-9 = 3(9)₃₆₂1_<364> = 13 × 599 × 575123 × 1264049 × 7847081079401_<13> × 90044466910849506694742791424666669725292343475923581318875951910752941146796683291458062436362815247131253152987729328933510952105344300090883170299255080915359887005314975298306301797296004734924983762681057162959277982107968935996458803505708890437656297554180373927028753663007630856501206568351524026379124327611030633302961804159_<335>

4×10³⁶⁴-9 = 3(9)₃₆₃1_<365> = 7 × 4567 × 5531 × 645503 × 6976873 × 18550824102112777026647_<23> × 2381336767002444014015255401_<28> × 325612568869149323675616094472872656162481_<42> × 497892182486974750287792449089666784458187470962260411347366511635973641176575824646685926038156271581256219799204240731569729_<126> × 7013708399743531402140830818139282059258463638362124055738476138251407779540967821286042235365980761678081831747998387238404717_<127>

4×10³⁶⁵-9 = 3(9)₃₆₄1_<366> = 157 × 61151 × 1878684683_<10> × [22177004312249987746043231390135983627961345572080344348996917380821170277299346861161403702937904599922761879707434058249109706125502205235664013068057914691633715198337229828427722279270066784911197617280842793459185400023041173402878698656161658719604807810814050338667646929160074902328990926655185651463594927500271611249369619562956024920276311_<350>] Free to factor

4×10³⁶⁶-9 = 3(9)₃₆₅1_<367> = 37441 × 84061 × 16815977 × 107770823 × 2316040002909679_<16> × 147912404254559543507_<21> × 200270244249717633911873_<24> × 8754945331971863643578588567_<28> × 949144353624325440376001410577375375978814883_<45> × 7443284907919028465924707807548173511764945050016169910818198185461325048000226757691114048862859652339_<103> × 165263621461343967146615234240753093905509956335838533801711393326282423692813497174787331122094424554733471_<108>

4×10³⁶⁷-9 = 3(9)₃₆₆1_<368> = 89 × 347 × 907 × 10667 × 378361 × [353821780086180881169104481959058512483108587603106967880138474612833998268682502272358068393245465522778629658879828989152868433321859457773284613605094328030707792800904246153823226801843769879003884220221782854647694668043320115262958803012141273357487615800274657310910658320685071910901172079849743020096320751348404754772362148091768476473851853_<351>] Free to factor

4×10³⁶⁸-9 = 3(9)₃₆₇1_<369> = 29² × 241 × 2713 × 4253 × 5237 × 66857737 × 41715550696982867_<17> × 45046753479013599736939609_<26> × 89177151216694919128342839012937_<32> × 16450357456538149478222257267964459_<35> × 56831071349735800699564104034197250430260949_<44> × 11106952378085416134328784349105056515147150726616078638907_<59> × 280734873559781758253348251445739908956056985830730029555749391702366572037148720479831472201011105110825184173089405824194320945511353_<135>

4×10³⁶⁹-9 = 3(9)₃₆₈1_<370> = 13 × 53 × 10169 × 21481 × 21521 × 409650757 × 15871638564872005940118811532237_<32> × [189937209305368488699756555639288629754328933042439610757146002144712465664722880673604277276266408194890219181050489845842041953296680315735450264930192012047088689971250618837529878219674282350735790738917109109023378282111073445928965951522598594884079230203089816571727313389805069321906612833997171670842974039_<315>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:1412554015 for P32 / July 15, 2021 2021 年 7 月 15 日) Free to factor

4×10³⁷⁰-9 = 3(9)₃₆₉1_<371> = 7 × 17 × 331 × 10139 × 1493783 × 1629098585915315381840811732409037_<34> × 139703661574531915433064323942224155484964759896391_<51> × 12381739908242089010679916203955564903195102834643116757540557250087725658757062968789736160958867_<98> × 23793896485348836084155362360835910425178928920797710161916857648743628889915290695980051085831247984394491270349579323987469196155415850466965348776399545418511815476929867983_<176>

4×10³⁷¹-9 = 3(9)₃₇₀1_<372> = 79 × 151 × 88643 × 740236199 × 28064062864288267_<17> × 135774003867094068492497052683015873150192347_<45> × 134113969884250587364950867226103869796622809232841615482637445473214078180293900598080691009582475041855810519041365162075862386571702235115509024689595293999695294312948909349977881941847516614420835663378699985859167263431367953981954176318795757973871361203662466104447240539477016573241403_<294> (Dmitry Domanov / GMP-ECM 7.0.5 B1=11000000 for P45 x P294 / March 3, 2024 2024 年 3 月 3 日)

4×10³⁷²-9 = 3(9)₃₇₁1_<373> = 19 × 673 × 156033287693_<12> × 309740823289_<12> × 1457961196343189999407_<22> × 20134967641613105163416519618269991614702019_<44> × 536702269647034089326974744111747439562722018687_<48> × 2094605899089145833509298930888551259266468064190461646178542207742096721296987095217288855538371_<97> × 196129518818625224605331844109132005572907239230106882174824783188659356706656419547350123734666037979415918599396117880712943463613520849_<138>

4×10³⁷³-9 = 3(9)₃₇₂1_<374> = [39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<374>] Free to factor

4×10³⁷⁴-9 = 3(9)₃₇₃1_<375> = 10596105529_<11> × 2650288267127376709_<19> × 21691476478039441219_<20> × 4899431565604784118723228083483_<31> × 389595763391679786994327160166767_<33> × 30188495243559431954129076808724172422794849359392479901419669_<62> × 182258522814260407226204545556975019230375927589496525253684233311399812906067616297913_<87> × 62523352205841974641767247686152369037786705686420794585068971430543609011985992247691266480187863785691927767719697_<116>

4×10³⁷⁵-9 = 3(9)₃₇₄1_<376> = 13 × 22147 × 1036490569_<10> × 353984092591_<12> × 867586238720454441888981187_<27> × 43645550710348098146862313041218986554606382887717459835085814345038289794949520266906833230636511991123966819133874328407782796271495263829009903629016345591075639418964119345164491770552353078163655504251514607403855436253526153330164135168291107211232956188530218320328738846472752538457627599287565970483298305047867597_<323>

4×10³⁷⁶-9 = 3(9)₃₇₅1_<377> = 7 × 23 × 31 × 67 × 4403881 × 201496271 × 38749227373442623_<17> × 23785222277923103118099188628420429739593966260699743933477349927854486154481670084027000572733631292076243413718690001102212460927078692317655609049585990575921572073733_<170> × 146259730403886186279957041137190761363460033867303913880003445269962997670445012943335442114705790082617920870515179332209167952282006353839688894523254296294118406917567_<171>

4×10³⁷⁷-9 = 3(9)₃₇₆1_<378> = 43 × 83 × 163 × 15452747 × 26500757 × 8340254803410329_<16> × 328454134361976685952438347_<27> × [612925673760548420262611912263139722938644074908461118732949435181164057750780563527857483899544824759984086315013954702971482402194726108017584618005898580762490546466539230665796420892327358651683961933556839210171519505643590485885098306881985133465256666746948942503086910115190715412093373337346775330832693289_<315>] Free to factor

4×10³⁷⁸-9 = 3(9)₃₇₇1_<379> = 211 × 617 × 186762743 × 3025939986458771807_<19> × 299721566142829669823_<21> × 6007634365195440036739_<22> × 31618164809434211754592287712179187_<35> × 26515433818872756128486451063540368813_<38> × 419817276608201618522516989479656415256109781516871114787_<57> × 484578537409999154675042390540664390207331844965054363441_<57> × 35960856659366982010140181518614170249139085672467809368871_<59> × 4923006679232260879844150105623901082760825132994000095977307_<61>

4×10³⁷⁹-9 = 3(9)₃₇₈1_<380> = [39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<380>] Free to factor

4×10³⁸⁰-9 = 3(9)₃₇₉1_<381> = 71 × 433 × 461 × 76949 × 1032007 × 3896947 × 209094547936744449194474908906729_<33> × 34966959780535052264850174530936020777783_<41> × 34446395954434388140001513015465553314448279869307180102939860821079122131241949069764159546294081893118303_<107> × 362124848020381435553269669228501465689771701143726180072031580407100567034965962565918393207796527030962525986428762374804385655016892692252848716727565796737003612950351342637_<177>

4×10³⁸¹-9 = 3(9)₃₈₀1_<382> = 13 × 251263157 × [1224581874103841226143999725723050165718057533171517431454116083132345950376211772632896164349683418537592012774448693615306649624291346830079398818077843749721302386136570322196868312421576762675525515634222857064923002986497110309301366026805483096323221363917242780215118017910171795271631058538726820551361982241162032730121640188148665553492557238275517219214483990951_<373>] Free to factor

4×10³⁸²-9 = 3(9)₃₈₁1_<383> = 7 × 53 × 829 × 1031 × 2221 × 283112539 × 12110972033_<11> × 1278085313563_<13> × 5806007837521_<13> × 18580007275894843_<17> × 117121349237684572025004166361887_<33> × 2980061483271130133454822323000539259581_<40> × 49371617551587041843675930397116659530937545163_<47> × 182806214988875869300773608643861228898368769920609146878022777_<63> × 100560756952935629434227230943212354457451323996998349267619421881_<66> × 379266725313477244975216442892897216971059794842475211319820147649_<66>

4×10³⁸³-9 = 3(9)₃₈₂1_<384> = 1695185065237_<13> × 1878257758037_<13> × 26739432240885847734761_<23> × 4698243275213016619095460927384615719109080205510944589705524457607444253517795453193198464898965872274069421833899023156985661241648735768789826019748634409803621635101082643350799881715445933178034095306277157044653531480994741353761555211346039384032286382332190725549133694628520703386928298143276323252734906308472386022142447707799_<337>

4×10³⁸⁴-9 = 3(9)₃₈₃1_<385> = 79 × 173 × 276519843869_<12> × 35108586452041_<14> × 137881619042308173307367_<24> × 10356144553255211560838847446569517_<35> × 34876652767087367824771974117100355091162711256918297_<53> × 41733446592368214066530327214400601607954236617362271592609176269988064074729_<77> × 14505196659942842895206338205973180372318448741832572534853326241618359742526002027358440505744124609747208577150542918462980365995792429450917677922476006106784912608891_<170>

4×10³⁸⁵-9 = 3(9)₃₈₄1_<386> = 2267 × 573197 × [30782547796664147471694021684222483391447564231978175967801898273377573708331645712215535176306684658275768423413150753382194538146498560720806109289746663702625400175141461333073216700111815065311189290898762119011149222564553482648611586003523051821436482845683765688851673746281986719702421047153338526723667628767758935687068725490988351800031299540686909121828481122778409_<377>] Free to factor

4×10³⁸⁶-9 = 3(9)₃₈₅1_<387> = 17² × 1999 × 2393 × 7561 × 498479939 × 3728792911_<10> × 57498745506438625549628335013_<29> × 20109277369861359866129287899115275654274037323316659944356086841136043_<71> × 15879996261445769537267415871328221599257192124173107438617771634920532105397393_<80> × 13204518309653988285253533541223281210472029154719159416351911592177934839932596309784809_<89> × 84914855627628876822887170020630119458401404969220347791519669735345970257922349845596771_<89>

4×10³⁸⁷-9 = 3(9)₃₈₆1_<388> = 13 × 2113634564979856340911_<22> × [145574979133273260536047891963398752631006540636826938848442694022257424700390154451165232313585218091303327869391290544399241115913731862942433691262603357840372026517871986868647934304354462011120305625431376814741145319710333488416414387284990624470380649615078979689289951760588907489335201426379226010191511969370773016772726826211123009567083853559553571612637_<366>] Free to factor

4×10³⁸⁸-9 = 3(9)₃₈₇1_<389> = 7 × 443 × 27107 × 2634001 × 46325179 × 125056452794705324377_<21> × 383403235824016344915248750822050157_<36> × 95581846303913650684936313179348791612051241183194251_<53> × 24649019531831500007969147622486775132580007261905157612095323460036978593433099142373379147_<92> × 34522861323878792390385877356200006655021210098971303161875903570112776063389543009387926531293432732559380227080738279210193247596555080851604262310465262862599586559_<167>

4×10³⁸⁹-9 = 3(9)₃₈₈1_<390> = 2543732882382395724300358688115991_<34> × [157249215422874960647187401971149140000545021452808087198375233267288346701908201188271378570831003180497757483339540637331182600804685957189892804663179848801009471341905472005357492470722157062505900701877209302764289360890006656330140764505635321055449304982648751175523998410496935010443411079909685002718895902439605288880424784345983666352832119124001_<357>] (Eric Jeancolas / GMP-ECM 7.0.4 B1=1000000, sigma=1:3701015842 for P34 / July 15, 2021 2021 年 7 月 15 日) Free to factor

4×10³⁹⁰-9 = 3(9)₃₈₉1_<391> = 19 × 47 × 113 × 11071 × 244507 × 13390259 × 21318959 × 126588259468129963800476691109_<30> × 743736208082687143669590291734775986453_<39> × 104315733950970586524012852330913828153019542073_<48> × 369330338075803596253764802097004029292538219506122378093453932829357363544017147256606239_<90> × 14142292454874449256385710545341601030413458600321097720419472709733367544401014551310864221172502405148901436989368784462014075518851628332348975139832488253_<158>

4×10³⁹¹-9 = 3(9)₃₉₀1_<392> = 31 × 1290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161_<391>

4×10³⁹²-9 = 3(9)₃₉₁1_<393> = 601 × 863 × 1009 × 4513 × 457661 × 100531969 × 1456329317141_<13> × 4588440736723_<13> × 31938754629629412334116767753621039_<35> × 34739974096182333336498956398761394712665299128822051_<53> × 863767795454334095995331720940616645856427889828345455035329342862116841141043748872939590809968883391913076573287926075614753_<126> × 574779056018038826079818762673364437285959587892423580463959074733449809079414441607465440021641387381279266470818308397711345799_<129>

4×10³⁹³-9 = 3(9)₃₉₂1_<394> = 13 × 16737557 × 112401551 × 103424254587335872773226506573357875483_<39> × [1581356785813483512645917353073162799094964248315013676741065224742812770419779330959493591766361244462104056891431394205976422940312342196101567586191561359119920977660479700633221024160168249148873122248622979856534043956681955091552864124749417325333387611432167185596117035757015115637576515374165215590540121617925058398225993552277547_<340>] (Dmitry Domanov / GMP-ECM 7.0.5 B1=3000000 for P39 / September 19, 2023 2023 年 9 月 19 日) Free to factor

4×10³⁹⁴-9 = 3(9)₃₉₃1_<395> = 7 × 229 × 29836370592137497650499_<23> × 16729518439454517288281783_<26> × 45003138917615480291651707486311828111477830485732830843961796036510537_<71> × 2772385807556537886278044630282889688258769602192237958344592362510261040148261536809278151720138041797820440202530552797127_<124> × 400682673532747702599827593186249104211952228306848094072962577538564657735619425416018392875826151577920421751986920916957351046332971959489884265159_<150>

4×10³⁹⁵-9 = 3(9)₃₉₄1_<396> = 53 × [7547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547_<394>] Free to factor

4×10³⁹⁶-9 = 3(9)₃₉₅1_<397> = 29 × 197 × 11903 × 4205947 × 52157717415774943068631_<23> × 1202575461497852123709722181169806824814923_<43> × 22388361185594023898713964704438991440520568602692290206129907529_<65> × 49111000098728410999628085323532736039706325695068709498811336069491_<68> × 202788601485676509531082557252180775897090576494738829512582300906640638515328879905860195846578508304986895285186285822618395045725527941023479420310437994781872266708839494968756465861_<186>

4×10³⁹⁷-9 = 3(9)₃₉₆1_<398> = 79 × 1156031 × 27456841 × 56344559 × 4466752391561_<13> × 21556232617860071_<17> × 3789896259271963756298483892922520305523_<40> × [775833993779275535515209567693366018226165426999436392443135115125504275518685139819551344310919347332328502831560814939547414769177871520261834097490002456414974753393053974147403841463322965375183169920428651507092180557562149600805729587405098585662547482135419838910040389190479060861426367968441020197_<306>] (Dmitry Domanov / GMP-ECM 7.0.5 B1=3000000 for P40 / September 20, 2023 2023 年 9 月 20 日) Free to factor

4×10³⁹⁸-9 = 3(9)₃₉₇1_<399> = 23 × 43 × 241 × 6317 × 39503 × 20536689829_<11> × 241585002691_<12> × 2791892855273_<13> × 7002385537531_<13> × 15953688693543275865802877_<26> × 21762838802020382865799787471876924157001_<41> × 1650822877321040398455081458354580460326700853503002329227022520485062724197783051668669873368413008923_<103> × 120971588687236521670810291211217797704710202102135926263422880462220595108007984055675529721463612199695520132939911182253886288797795503983566971990109205724983490250547_<171>

4×10³⁹⁹-9 = 3(9)₃₉₈1_<400> = 13² × 23668639053254437869822485207100591715976331360946745562130177514792899408284023668639053254437869822485207100591715976331360946745562130177514792899408284023668639053254437869822485207100591715976331360946745562130177514792899408284023668639053254437869822485207100591715976331360946745562130177514792899408284023668639053254437869822485207100591715976331360946745562130177514792899408284023668639_<398>

4×10⁴⁰⁰-9 = 3(9)₃₉₉1_<401> = 7² × 3917 × 18873739043_<11> × 1737408773621_<13> × 9318870262441_<13> × 1353143889460780219324261867805948229627354629623799_<52> × 107421636386525513520653234479254640339061189356540018700131_<60> × 288930187492555799536718659699424506652533163856455735889878594247989358356453147_<81> × 46229348644433214755924438644202543849471369171438338376543760504475737398042864287_<83> × 351269691736020689086731151005390507435230742784114223916529804772069637453814458555389_<87>

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4. Related links 関連リンク

A101396 - OEIS (The OEIS Foundation Inc.)