11...11 (Repunit) 11...11 (レピュニット) | 100...001 | Φn(10)
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Appendix: 付録: PRP factors おそらく素数の因数 (72KB) | Repunit note レピュニットノート (703KB)
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Summary 概要
Last updated: 最終更新日:
Wed, 11 Jan 2023 11:27:53 GMT 2023 年 1 月 11 日 (水) 20 時 27 分 53 秒 (日本時間)
Status: 状態:
1213 of 300000 Φn(10) factorizations were finished. 300000 個中 1213 個の Φn(10) の素因数分解が終わりました。
207135 of 300000 Φn(10) factorizations were cracked. 300000 個中 207135 個の Φn(10) の素因数が見つかりました。
124 of 25997 Rprime factorizations were finished. 25997 個中 124 個の Rprime の素因数分解が終わりました。
19977 of 25997 Rprime factorizations were cracked. 25997 個中 19977 個の Rprime の素因数が見つかりました。
363424 (probable) prime factors were discovered. 363424 個の (おそらく) 素数の因数が見つかりました。
286336 composite factors are remaining. 286336 個の合成数の因数が残っています。
19821 factors are unidentified. 19821 個の因数が未確定です。
Editor: 編集者:
Makoto Kamada
Sources: 情報源:
Kurt Beschorner
Richard Brent
Torbjörn Granlund
Wilfrid Keller
Yousuke Koide
Sam Wagstaff
Paul Zimmermann
NFS@Home
yoyo@home
Henri & Renaud Lifchitz
Φn(10) which is hoped to be factored 分解が期待される Φn(10)
First composite factor: 最初の合成数の因数:
n=353 (c328), n=365 (c288), n=377 (c311), n=383 (c230), n=389 (c270),
n=391 (c312), n=401 (c308), n=403 (c333), n=407 (c216), n=409 (c320)
Smallest composite factor: 最小の合成数の因数:
n=942 (c209), n=1420M (c212), n=2100L (c215), n=407 (c216), n=675 (c216),
n=2820M (c219), n=2460L (c220), n=1290 (c220), n=735 (c228), n=990 (c229)
First blank Φn(10): 素因数が見つかっていない最初の Φn(10):
n=365 (c288), n=509 (c509), n=557 (c557), n=589 (c540), n=647 (c647),
n=649 (c580), n=657 (c432), n=671 (c600), n=730 (c289), n=731 (c672)
Smallest blank Φn(10): 素因数が見つかっていない最小の Φn(10):
n=1340L (c265), n=365 (c288), n=730 (c289), n=920 (c353), n=808 (c400),
n=1078 (c421), n=657 (c432), n=1512 (c433), n=1022 (c433), n=1338 (c445)
Smallest blank Rprime: 素因数が見つかっていない最小の Rprime:
n=509 (c509), n=557 (c557), n=647 (c647), n=991 (c991), n=1117 (c1117),
n=1259 (c1259), n=1447 (c1447), n=1607 (c1607), n=1637 (c1637), n=1663 (c1663)
Φn(10) has the biggest parcentage of factored part: 分解された部分の割合が最大の Φn(10):
n=2420L (c246), n=2820M (c219), n=407 (c216), n=675 (c216), n=383 (c230),
n=884 (c249), n=485 (c251), n=1290 (c220), n=621 (c260), n=942 (c209)
Format 表示形式
Φn(10)=value... 値...<length> <桁数>=(probable) prime factor... (おそらく) 素数の因数...<length> <桁数>exponent 指数
[composite factor... 合成数の因数...<length> <桁数>]
(unidentified factor... 未確定の因数...<length> <桁数>)		×... (percentage of factored part) (分解された部分の割合)
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Φ1(10) = 9 = 32 (100.00%)
Φ2(10) = 11 = 11 (100.00%)
Φ3(10) = 111 = 3 × 37 (100.00%)
Φ4(10) = 101 = 101 (100.00%)
Φ5(10) = 11111 = 41 × 271 (100.00%)
Φ6(10) = 91 = 7 × 13 (100.00%)
Φ7(10) = 1111111 = 239 × 4649 (100.00%)
Φ8(10) = 10001 = 73 × 137 (100.00%)
Φ9(10) = 1001001 = 3 × 333667 (100.00%)
Φ10(10) = 9091 = 9091 (100.00%)
Φ11(10) = 11111111111<11> = 21649 × 513239 (100.00%)
Φ12(10) = 9901 = 9901 (100.00%)
Φ13(10) = 1111111111111<13> = 53 × 79 × 265371653 (100.00%)
Φ14(10) = 909091 = 909091 (100.00%)
Φ15(10) = 90090991 = 31 × 2906161 (100.00%)
Φ16(10) = 100000001 = 17 × 5882353 (100.00%)
Φ17(10) = 11111111111111111<17> = 2071723 × 5363222357<10> (100.00%)
Φ18(10) = 999001 = 19 × 52579 (100.00%)
Φ19(10) = 1111111111111111111<19> = 1111111111111111111<19> (100.00%)
Φ20L(10) = 3541 = 3541 (100.00%)
Φ20M(10) = 27961 = 27961 (100.00%)
Φ21(10) = 900900990991<12> = 43 × 1933 × 10838689 (100.00%)
Φ22(10) = 9090909091<10> = 11 × 23 × 4093 × 8779 (100.00%)
Φ23(10) = 11111111111111111111111<23> = 11111111111111111111111<23> (100.00%)
Φ24(10) = 99990001 = 99990001 (100.00%)
Φ25(10) = 100001000010000100001<21> = 21401 × 25601 × 182521213001<12> (100.00%)
Φ26(10) = 909090909091<12> = 859 × 1058313049<10> (100.00%)
Φ27(10) = 1000000001000000001<19> = 3 × 757 × 440334654777631<15> (100.00%)
Φ28(10) = 990099009901<12> = 29 × 281 × 121499449 (100.00%)
Φ29(10) = 11111111111111111111111111111<29> = 3191 × 16763 × 43037 × 62003 × 77843839397<11> (100.00%)
Φ30(10) = 109889011 = 211 × 241 × 2161 (100.00%)
Φ31(10) = 1111111111111111111111111111111<31> = 2791 × 6943319 × 57336415063790604359<20> (100.00%)
Φ32(10) = 10000000000000001<17> = 353 × 449 × 641 × 1409 × 69857 (100.00%)
Φ33(10) = 90090090090990990991<20> = 67 × 1344628210313298373<19> (100.00%)
Φ34(10) = 9090909090909091<16> = 103 × 4013 × 21993833369<11> (100.00%)
Φ35(10) = 900009090090909909099991<24> = 71 × 123551 × 102598800232111471<18> (100.00%)
Φ36(10) = 999999000001<12> = 999999000001<12> (100.00%)
Φ37(10) = 1111111111111111111111111111111111111<37> = 2028119 × 247629013 × 2212394296770203368013<22> (100.00%)
Φ38(10) = 909090909090909091<18> = 909090909090909091<18> (100.00%)
Φ39(10) = 900900900900990990990991<24> = 900900900900990990990991<24> (100.00%)
Φ40(10) = 9999000099990001<16> = 1676321 × 5964848081<10> (100.00%)
Φ41(10) = 1111111111111111111111111111111111111111­1<41> = 83 × 1231 × 538987 × 201763709900322803748657942361<30> (100.00%)
Φ42(10) = 1098900989011<13> = 7 × 127 × 2689 × 459691 (100.00%)
Φ43(10) = 1111111111111111111111111111111111111111­111<43> = 173 × 1527791 × 1963506722254397<16> × 2140992015395526641<19> (100.00%)
Φ44(10) = 99009900990099009901<20> = 89 × 1052788969<10> × 1056689261<10> (100.00%)
Φ45(10) = 999000000999000999999001<24> = 238681 × 4185502830133110721<19> (100.00%)
Φ46(10) = 9090909090909090909091<22> = 47 × 139 × 2531 × 549797184491917<15> (100.00%)
Φ47(10) = 1111111111111111111111111111111111111111­1111111<47> = 35121409 × 316362908763458525001406154038726382279<39> (100.00%)
Φ48(10) = 9999999900000001<16> = 9999999900000001<16> (100.00%)
Φ49(10) = 1000000100000010000001000000100000010000­001<43> = 505885997 × 1976730144598190963568023014679333<34> (100.00%)
Φ50(10) = 99999000009999900001<20> = 251 × 5051 × 78875943472201<14> (100.00%)
Φ51(10) = 90090090090090090990990990990991<32> = 613 × 210631 × 52986961 × 13168164561429877<17> (100.00%)
Φ52(10) = 990099009900990099009901<24> = 521 × 1900381976777332243781<22> (100.00%)
Φ53(10) = 1111111111111111111111111111111111111111­1111111111111<53> = 107 × 1659431 × 1325815267337711173<19> × 47198858799491425660200071<26> (100.00%)
Φ54(10) = 999999999000000001<18> = 70541929 × 14175966169<11> (100.00%)
Φ55(10) = 9000090000990009900099900999009999099991<40> = 1321 × 62921 × 83251631 × 1300635692678058358830121<25> (100.00%)
Φ56(10) = 999900009999000099990001<24> = 7841 × 127522001020150503761<21> (100.00%)
Φ57(10) = 900900900900900900990990990990990991<36> = 21319 × 10749631 × 3931123022305129377976519<25> (100.00%)
Φ58(10) = 9090909090909090909090909091<28> = 59 × 154083204930662557781201849<27> (100.00%)
Φ59(10) = 1111111111111111111111111111111111111111­1111111111111111111<59> = 2559647034361<13> × 4340876285657460212144534289928559826755­746751<46> (100.00%)
Φ60L(10) = 255522961 = 61 × 4188901 (100.00%)
Φ60M(10) = 39526741 = 39526741 (100.00%)
Φ61(10) = 1111111111111111111111111111111111111111­111111111111111111111<61> = 733 × 4637 × 329401 × 974293 × 1360682471<10> × 106007173861643<15> × 7061709990156159479<19> (100.00%)
Φ62(10) = 909090909090909090909090909091<30> = 909090909090909090909090909091<30> (100.00%)
Φ63(10) = 999000000999000000999999000999999001<36> = 10837 × 23311 × 45613 × 45121231 × 1921436048294281<16> (100.00%)
Φ64(10) = 100000000000000000000000000000001<33> = 19841 × 976193 × 6187457 × 834427406578561<15> (100.00%)
Φ65(10) = 9000090000900909009090090990909909099099­99099991<48> = 162503518711<12> × 5538396997364024056286510640780600481<37> (100.00%)
Φ66(10) = 109890109889010989011<21> = 599144041 × 183411838171<12> (100.00%)
Φ67(10) = 1111111111111111111111111111111111111111­111111111111111111111111111<67> = 493121 × 79863595778924342083<20> × 2821338094317666700126315366099917724567­7<41> (100.00%)
Φ68(10) = 99009900990099009900990099009901<32> = 28559389 × 1491383821<10> × 2324557465671829<16> (100.00%)
Φ69(10) = 9009009009009009009009099099099099099099­0991<44> = 277 × 203864078068831<15> × 1595352086329224644348978893<28> (100.00%)
Φ70(10) = 1099988890111109888900011<25> = 4147571 × 265212793249617641<18> (100.00%)
Φ71(10) = 1111111111111111111111111111111111111111­1111111111111111111111111111111<71> = 241573142393627673576957439049<30> × 4599481134788684631022172889522303430183­9<41> (100.00%)
Φ72(10) = 999999999999000000000001<24> = 3169 × 98641 × 3199044596370769<16> (100.00%)
Φ73(10) = 1111111111111111111111111111111111111111­111111111111111111111111111111111<73> = 12171337159<11> × 1855193842151350117<19> × 4920734163464632693400173948250213148744­6637<44> (100.00%)
Φ74(10) = 909090909090909090909090909090909091<36> = 7253 × 422650073734453<15> × 296557347313446299<18> (100.00%)
Φ75(10) = 9999900000000009999900000999999999900001<40> = 151 × 4201 × 15763985553739191709164170940063151<35> (100.00%)
Φ76(10) = 990099009900990099009900990099009901<36> = 722817036322379041<18> × 1369778187490592461<19> (100.00%)
Φ77(10) = 9000000900090090009009900900990099099009­90999099099909999991<60> = 5237 × 42043 × 29920507 × 1366146685760023293714964475559157409101­81043<45> (100.00%)
Φ78(10) = 1098901098900989010989011<25> = 13 × 157 × 6397 × 216451 × 388847808493<12> (100.00%)
Φ79(10) = 1111111111111111111111111111111111111111­111111111111111111111111111111111111111<79> = 317 × 6163 × 10271 × 307627 × 49172195536083790769<20> × 3660574762725521461527140564875080461079­917<43> (100.00%)
Φ80(10) = 99999999000000009999999900000001<32> = 5070721 × 19721061166646717498359681<26> (100.00%)
Φ81(10) = 1000000000000000000000000001000000000000­000000000000001<55> = 3 × 163 × 9397 × 2462401 × 676421558270641<15> × 130654897808007778425046117<27> (100.00%)
Φ82(10) = 9090909090909090909090909090909090909091<40> = 2670502781396266997<19> × 3404193829806058997303<22> (100.00%)
Φ83(10) = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­111<83> = 3367147378267<13> × 9512538508624154373682136329<28> × 3468957163858578045447411373945054253844­77<42> (100.00%)
Φ84(10) = 1009998990000999899000101<25> = 226549 × 4458192223320340849<19> (100.00%)
Φ85(10) = 9000090000900009090090900909009090990909­909099090999909999099991<64> = 262533041 × 8119594779271<13> × 4222100119405530170179331190291488789678­081<43> (100.00%)
Φ86(10) = 9090909090909090909090909090909090909090­91<42> = 57009401 × 2182600451<10> × 7306116556571817748755241<25> (100.00%)
Φ87(10) = 9009009009009009009009009009099099099099­0990990990990991<56> = 4003 × 72559 × 3101702516580297590451577932373394983427­63245483<48> (100.00%)
Φ88(10) = 9999000099990000999900009999000099990001<40> = 617 × 16205834846012967584927082656402106953<38> (100.00%)
Φ89(10) = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­111111111<89> = 497867 × 103733951 × 104984505733<12> × 5078554966026315671444089<25> × 403513310222809053284932818475878953159<39> (100.00%)
Φ90(10) = 1000999998998999000001001<25> = 29611 × 3762091 × 8985695684401<13> (100.00%)
Φ91(10) = 9000000900000990000099000099900009990009­99900099990099999009999909999991<72> = 547 × 14197 × 17837 × 4262077 × 43442141653<11> × 316877365766624209<18> × 110742186470530054291318013<27> (100.00%)
Φ92(10) = 9900990099009900990099009900990099009900­9901<44> = 1289 × 18371524594609<14> × 4181003300071669867932658901<28> (100.00%)
Φ93(10) = 9009009009009009009009009009009909909909­90990990990990990991<60> = 9009009009009009009009009009009909909909­90990990990990990991<60> (100.00%)
Φ94(10) = 9090909090909090909090909090909090909090­909091<46> = 6299 × 4855067598095567<16> × 297262705009139006771611927<27> (100.00%)
Φ95(10) = 9000090000900009000990009900099000990099­90099900999009990999909999099991<72> = 191 × 59281 × 63841 × 1289981231950849543985493631<28> × 965194617121640791456070347951751<33> (100.00%)
Φ96(10) = 99999999999999990000000000000001<32> = 97 × 206209 × 66554101249<11> × 75118313082913<14> (100.00%)
Φ97(10) = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­11111111111111111<97> = 12004721 × 846035731396919233767211537899097169<36> × 1093998468553705375403392668420701191076­62296580348039<54> (100.00%)
Φ98(10) = 9999999000000099999990000000999999900000­01<42> = 197 × 5076141624365532994918781726395939035533<40> (100.00%)
Φ99(10) = 9990000009990000009990000009990009999990­00999999000999999001<60> = 199 × 397 × 34849 × 3628537243429904693247662354742688697863­11886053883<51> (100.00%)
Φ100L(10) = 99004980069800499001<20> = 7019801 × 14103673319201<14> (100.00%)
Φ100M(10) = 101005020070200501001<21> = 60101 × 1680588011350901<16> (100.00%)
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