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 (81KB) | Repunit note レピュニットノート (713KB)
Changes: 更新履歴: Recent changes 最近の更新 (133KB) | Past changes 過去の更新Past changes 過去の更新
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2003 2003 年 December 12 月 November 11 月 October 10 月 September 9 月
Summary 概要
Last updated: 最終更新日:
Tue, 19 Nov 2024 01:55:23 GMT 2024 年 11 月 19 日 (火) 10 時 55 分 23 秒 (日本時間)
Status: 状態:
1283 of 300000 Φn(10) factorizations were finished. 300000 個中 1283 個の Φn(10) の素因数分解が終わりました。
213393 of 300000 Φn(10) factorizations were cracked. 300000 個中 213393 個の Φn(10) の素因数が見つかりました。
130 of 25997 Rprime factorizations were finished. 25997 個中 130 個の Rprime の素因数分解が終わりました。
20081 of 25997 Rprime factorizations were cracked. 25997 個中 20081 個の Rprime の素因数が見つかりました。
388320 (probable) prime factors were discovered. 388320 個の (おそらく) 素数の因数が見つかりました。
293605 composite factors are remaining. 293605 個の合成数の因数が残っています。
12469 factors are unidentified. 12469 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=377 (c311), n=383 (c230), n=389 (c270), n=391 (c312),
n=401 (c308), n=403 (c333), n=407 (c216), n=409 (c320), n=413 (c337)
Smallest composite factor: 最小の合成数の因数:
n=2100L (c215), n=407 (c216), n=675 (c216), n=1104 (c217), n=2820M (c219),
n=2460L (c220), n=1290 (c220), n=735 (c228), n=754 (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=509 (c509), n=557 (c557), n=589 (c540), n=647 (c647), n=657 (c432),
n=671 (c600), n=807 (c536), n=808 (c400), n=835 (c664), n=901 (c832)
Smallest blank Φn(10): 素因数が見つかっていない最小の Φn(10):
n=920 (c353), n=808 (c400), n=1078 (c421), n=657 (c432), n=1512 (c433),
n=1022 (c433), n=1338 (c445), n=2260L (c448), n=1362 (c453), n=922 (c460)
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=503 (c269), n=2420L (c246), n=2820M (c219), n=407 (c216), n=675 (c216),
n=383 (c230), n=1104 (c217), n=884 (c249), n=485 (c251), n=1290 (c220)
Format 表示形式
Rn = 10n-19=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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remove soft hyphens ソフトハイフンを取り除く | plain text version プレーンテキスト版
R1 = 101-19 = 1
R2 = 102-19 = 11 = 11 (100.00%)
R3 = 103-19 = 111 = 3 × 37 (100.00%)
R4 = 104-19 = 1111 = 11 × 101 (100.00%)
R5 = 105-19 = 11111 = 41 × 271 (100.00%)
R6 = 106-19 = 111111 = 3 × 7 × 11 × 13 × 37 (100.00%)
R7 = 107-19 = 1111111 = 239 × 4649 (100.00%)
R8 = 108-19 = 11111111 = 11 × 73 × 101 × 137 (100.00%)
R9 = 109-19 = 111111111 = 32 × 37 × 333667 (100.00%)
R10 = 1010-19 = 1111111111<10> = 11 × 41 × 271 × 9091 (100.00%)
R11 = 1011-19 = 11111111111<11> = 21649 × 513239 (100.00%)
R12 = 1012-19 = 111111111111<12> = 3 × 7 × 11 × 13 × 37 × 101 × 9901 (100.00%)
R13 = 1013-19 = 1111111111111<13> = 53 × 79 × 265371653 (100.00%)
R14 = 1014-19 = 11111111111111<14> = 11 × 239 × 4649 × 909091 (100.00%)
R15 = 1015-19 = 111111111111111<15> = 3 × 31 × 37 × 41 × 271 × 2906161 (100.00%)
R16 = 1016-19 = 1111111111111111<16> = 11 × 17 × 73 × 101 × 137 × 5882353 (100.00%)
R17 = 1017-19 = 11111111111111111<17> = 2071723 × 5363222357<10> (100.00%)
R18 = 1018-19 = 111111111111111111<18> = 32 × 7 × 11 × 13 × 19 × 37 × 52579 × 333667 (100.00%)
R19 = 1019-19 = 1111111111111111111<19> = 1111111111111111111<19> (100.00%)
R20 = 1020-19 = 11111111111111111111<20> = 11 × 41 × 101 × 271 × 3541 × 9091 × 27961 (100.00%)
R21 = 1021-19 = 111111111111111111111<21> = 3 × 37 × 43 × 239 × 1933 × 4649 × 10838689 (100.00%)
R22 = 1022-19 = 1111111111111111111111<22> = 112 × 23 × 4093 × 8779 × 21649 × 513239 (100.00%)
R23 = 1023-19 = 11111111111111111111111<23> = 11111111111111111111111<23> (100.00%)
R24 = 1024-19 = 111111111111111111111111<24> = 3 × 7 × 11 × 13 × 37 × 73 × 101 × 137 × 9901 × 99990001 (100.00%)
R25 = 1025-19 = 1111111111111111111111111<25> = 41 × 271 × 21401 × 25601 × 182521213001<12> (100.00%)
R26 = 1026-19 = 11111111111111111111111111<26> = 11 × 53 × 79 × 859 × 265371653 × 1058313049<10> (100.00%)
R27 = 1027-19 = 111111111111111111111111111<27> = 33 × 37 × 757 × 333667 × 440334654777631<15> (100.00%)
R28 = 1028-19 = 1111111111111111111111111111<28> = 11 × 29 × 101 × 239 × 281 × 4649 × 909091 × 121499449 (100.00%)
R29 = 1029-19 = 11111111111111111111111111111<29> = 3191 × 16763 × 43037 × 62003 × 77843839397<11> (100.00%)
R30 = 1030-19 = 111111111111111111111111111111<30> = 3 × 7 × 11 × 13 × 31 × 37 × 41 × 211 × 241 × 271 × 2161 × 9091 × 2906161 (100.00%)
R31 = 1031-19 = 1111111111111111111111111111111<31> = 2791 × 6943319 × 57336415063790604359<20> (100.00%)
R32 = 1032-19 = 11111111111111111111111111111111<32> = 11 × 17 × 73 × 101 × 137 × 353 × 449 × 641 × 1409 × 69857 × 5882353 (100.00%)
R33 = 1033-19 = 111111111111111111111111111111111<33> = 3 × 37 × 67 × 21649 × 513239 × 1344628210313298373<19> (100.00%)
R34 = 1034-19 = 1111111111111111111111111111111111<34> = 11 × 103 × 4013 × 2071723 × 5363222357<10> × 21993833369<11> (100.00%)
R35 = 1035-19 = 11111111111111111111111111111111111<35> = 41 × 71 × 239 × 271 × 4649 × 123551 × 102598800232111471<18> (100.00%)
R36 = 1036-19 = 111111111111111111111111111111111111<36> = 32 × 7 × 11 × 13 × 19 × 37 × 101 × 9901 × 52579 × 333667 × 999999000001<12> (100.00%)
R37 = 1037-19 = 1111111111111111111111111111111111111<37> = 2028119 × 247629013 × 2212394296770203368013<22> (100.00%)
R38 = 1038-19 = 11111111111111111111111111111111111111<38> = 11 × 909090909090909091<18> × 1111111111111111111<19> (100.00%)
R39 = 1039-19 = 111111111111111111111111111111111111111<39> = 3 × 37 × 53 × 79 × 265371653 × 900900900900990990990991<24> (100.00%)
R40 = 1040-19 = 1111111111111111111111111111111111111111<40> = 11 × 41 × 73 × 101 × 137 × 271 × 3541 × 9091 × 27961 × 1676321 × 5964848081<10> (100.00%)
R41 = 1041-19 = 1111111111111111111111111111111111111111­1<41> = 83 × 1231 × 538987 × 201763709900322803748657942361<30> (100.00%)
R42 = 1042-19 = 1111111111111111111111111111111111111111­11<42> = 3 × 72 × 11 × 13 × 37 × 43 × 127 × 239 × 1933 × 2689 × 4649 × 459691 × 909091 × 10838689 (100.00%)
R43 = 1043-19 = 1111111111111111111111111111111111111111­111<43> = 173 × 1527791 × 1963506722254397<16> × 2140992015395526641<19> (100.00%)
R44 = 1044-19 = 1111111111111111111111111111111111111111­1111<44> = 112 × 23 × 89 × 101 × 4093 × 8779 × 21649 × 513239 × 1052788969<10> × 1056689261<10> (100.00%)
R45 = 1045-19 = 1111111111111111111111111111111111111111­11111<45> = 32 × 31 × 37 × 41 × 271 × 238681 × 333667 × 2906161 × 4185502830133110721<19> (100.00%)
R46 = 1046-19 = 1111111111111111111111111111111111111111­111111<46> = 11 × 47 × 139 × 2531 × 549797184491917<15> × 11111111111111111111111<23> (100.00%)
R47 = 1047-19 = 1111111111111111111111111111111111111111­1111111<47> = 35121409 × 316362908763458525001406154038726382279<39> (100.00%)
R48 = 1048-19 = 1111111111111111111111111111111111111111­11111111<48> = 3 × 7 × 11 × 13 × 17 × 37 × 73 × 101 × 137 × 9901 × 5882353 × 99990001 × 9999999900000001<16> (100.00%)
R49 = 1049-19 = 1111111111111111111111111111111111111111­111111111<49> = 239 × 4649 × 505885997 × 1976730144598190963568023014679333<34> (100.00%)
R50 = 1050-19 = 1111111111111111111111111111111111111111­1111111111<50> = 11 × 41 × 251 × 271 × 5051 × 9091 × 21401 × 25601 × 182521213001<12> × 78875943472201<14> (100.00%)
R51 = 1051-19 = 1111111111111111111111111111111111111111­11111111111<51> = 3 × 37 × 613 × 210631 × 2071723 × 52986961 × 5363222357<10> × 13168164561429877<17> (100.00%)
R52 = 1052-19 = 1111111111111111111111111111111111111111­111111111111<52> = 11 × 53 × 79 × 101 × 521 × 859 × 265371653 × 1058313049<10> × 1900381976777332243781<22> (100.00%)
R53 = 1053-19 = 1111111111111111111111111111111111111111­1111111111111<53> = 107 × 1659431 × 1325815267337711173<19> × 47198858799491425660200071<26> (100.00%)
R54 = 1054-19 = 1111111111111111111111111111111111111111­11111111111111<54> = 33 × 7 × 11 × 13 × 19 × 37 × 757 × 52579 × 333667 × 70541929 × 14175966169<11> × 440334654777631<15> (100.00%)
R55 = 1055-19 = 1111111111111111111111111111111111111111­111111111111111<55> = 41 × 271 × 1321 × 21649 × 62921 × 513239 × 83251631 × 1300635692678058358830121<25> (100.00%)
R56 = 1056-19 = 1111111111111111111111111111111111111111­1111111111111111<56> = 11 × 29 × 73 × 101 × 137 × 239 × 281 × 4649 × 7841 × 909091 × 121499449 × 127522001020150503761<21> (100.00%)
R57 = 1057-19 = 1111111111111111111111111111111111111111­11111111111111111<57> = 3 × 37 × 21319 × 10749631 × 1111111111111111111<19> × 3931123022305129377976519<25> (100.00%)
R58 = 1058-19 = 1111111111111111111111111111111111111111­111111111111111111<58> = 11 × 59 × 3191 × 16763 × 43037 × 62003 × 77843839397<11> × 154083204930662557781201849<27> (100.00%)
R59 = 1059-19 = 1111111111111111111111111111111111111111­1111111111111111111<59> = 2559647034361<13> × 4340876285657460212144534289928559826755­746751<46> (100.00%)
R60 = 1060-19 = 1111111111111111111111111111111111111111­11111111111111111111<60> = 3 × 7 × 11 × 13 × 31 × 37 × 41 × 61 × 101 × 211 × 241 × 271 × 2161 × 3541 × 9091 × 9901 × 27961 × 2906161 × 4188901 × 39526741 (100.00%)
R61 = 1061-19 = 1111111111111111111111111111111111111111­111111111111111111111<61> = 733 × 4637 × 329401 × 974293 × 1360682471<10> × 106007173861643<15> × 7061709990156159479<19> (100.00%)
R62 = 1062-19 = 1111111111111111111111111111111111111111­1111111111111111111111<62> = 11 × 2791 × 6943319 × 57336415063790604359<20> × 909090909090909090909090909091<30> (100.00%)
R63 = 1063-19 = 1111111111111111111111111111111111111111­11111111111111111111111<63> = 32 × 37 × 43 × 239 × 1933 × 4649 × 10837 × 23311 × 45613 × 333667 × 10838689 × 45121231 × 1921436048294281<16> (100.00%)
R64 = 1064-19 = 1111111111111111111111111111111111111111­111111111111111111111111<64> = 11 × 17 × 73 × 101 × 137 × 353 × 449 × 641 × 1409 × 19841 × 69857 × 976193 × 5882353 × 6187457 × 834427406578561<15> (100.00%)
R65 = 1065-19 = 1111111111111111111111111111111111111111­1111111111111111111111111<65> = 41 × 53 × 79 × 271 × 265371653 × 162503518711<12> × 5538396997364024056286510640780600481<37> (100.00%)
R66 = 1066-19 = 1111111111111111111111111111111111111111­11111111111111111111111111<66> = 3 × 7 × 112 × 13 × 23 × 37 × 67 × 4093 × 8779 × 21649 × 513239 × 599144041 × 183411838171<12> × 1344628210313298373<19> (100.00%)
R67 = 1067-19 = 1111111111111111111111111111111111111111­111111111111111111111111111<67> = 493121 × 79863595778924342083<20> × 2821338094317666700126315366099917724567­7<41> (100.00%)
R68 = 1068-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111<68> = 11 × 101 × 103 × 4013 × 2071723 × 28559389 × 1491383821<10> × 5363222357<10> × 21993833369<11> × 2324557465671829<16> (100.00%)
R69 = 1069-19 = 1111111111111111111111111111111111111111­11111111111111111111111111111<69> = 3 × 37 × 277 × 203864078068831<15> × 11111111111111111111111<23> × 1595352086329224644348978893<28> (100.00%)
R70 = 1070-19 = 1111111111111111111111111111111111111111­111111111111111111111111111111<70> = 11 × 41 × 71 × 239 × 271 × 4649 × 9091 × 123551 × 909091 × 4147571 × 102598800232111471<18> × 265212793249617641<18> (100.00%)
R71 = 1071-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111<71> = 241573142393627673576957439049<30> × 4599481134788684631022172889522303430183­9<41> (100.00%)
R72 = 1072-19 = 1111111111111111111111111111111111111111­11111111111111111111111111111111<72> = 32 × 7 × 11 × 13 × 19 × 37 × 73 × 101 × 137 × 3169 × 9901 × 52579 × 98641 × 333667 × 99990001 × 999999000001<12> × 3199044596370769<16> (100.00%)
R73 = 1073-19 = 1111111111111111111111111111111111111111­111111111111111111111111111111111<73> = 12171337159<11> × 1855193842151350117<19> × 4920734163464632693400173948250213148744­6637<44> (100.00%)
R74 = 1074-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111<74> = 11 × 7253 × 2028119 × 247629013 × 422650073734453<15> × 296557347313446299<18> × 2212394296770203368013<22> (100.00%)
R75 = 1075-19 = 1111111111111111111111111111111111111111­11111111111111111111111111111111111<75> = 3 × 31 × 37 × 41 × 151 × 271 × 4201 × 21401 × 25601 × 2906161 × 182521213001<12> × 15763985553739191709164170940063151<35> (100.00%)
R76 = 1076-19 = 1111111111111111111111111111111111111111­111111111111111111111111111111111111<76> = 11 × 101 × 722817036322379041<18> × 909090909090909091<18> × 1111111111111111111<19> × 1369778187490592461<19> (100.00%)
R77 = 1077-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111<77> = 239 × 4649 × 5237 × 21649 × 42043 × 513239 × 29920507 × 1366146685760023293714964475559157409101­81043<45> (100.00%)
R78 = 1078-19 = 1111111111111111111111111111111111111111­11111111111111111111111111111111111111<78> = 3 × 7 × 11 × 132 × 37 × 53 × 79 × 157 × 859 × 6397 × 216451 × 265371653 × 1058313049<10> × 388847808493<12> × 900900900900990990990991<24> (100.00%)
R79 = 1079-19 = 1111111111111111111111111111111111111111­111111111111111111111111111111111111111<79> = 317 × 6163 × 10271 × 307627 × 49172195536083790769<20> × 3660574762725521461527140564875080461079­917<43> (100.00%)
R80 = 1080-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111<80> = 11 × 17 × 41 × 73 × 101 × 137 × 271 × 3541 × 9091 × 27961 × 1676321 × 5070721 × 5882353 × 5964848081<10> × 19721061166646717498359681<26> (100.00%)
R81 = 1081-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­1<81> = 34 × 37 × 163 × 757 × 9397 × 333667 × 2462401 × 440334654777631<15> × 676421558270641<15> × 130654897808007778425046117<27> (100.00%)
R82 = 1082-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­11<82> = 11 × 83 × 1231 × 538987 × 2670502781396266997<19> × 3404193829806058997303<22> × 201763709900322803748657942361<30> (100.00%)
R83 = 1083-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­111<83> = 3367147378267<13> × 9512538508624154373682136329<28> × 3468957163858578045447411373945054253844­77<42> (100.00%)
R84 = 1084-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­1111<84> = 3 × 72 × 11 × 13 × 29 × 37 × 43 × 101 × 127 × 239 × 281 × 1933 × 2689 × 4649 × 9901 × 226549 × 459691 × 909091 × 10838689 × 121499449 × 4458192223320340849<19> (100.00%)
R85 = 1085-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­11111<85> = 41 × 271 × 2071723 × 262533041 × 5363222357<10> × 8119594779271<13> × 4222100119405530170179331190291488789678­081<43> (100.00%)
R86 = 1086-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­111111<86> = 11 × 173 × 1527791 × 57009401 × 2182600451<10> × 1963506722254397<16> × 2140992015395526641<19> × 7306116556571817748755241<25> (100.00%)
R87 = 1087-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­1111111<87> = 3 × 37 × 3191 × 4003 × 16763 × 43037 × 62003 × 72559 × 77843839397<11> × 3101702516580297590451577932373394983427­63245483<48> (100.00%)
R88 = 1088-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­11111111<88> = 112 × 23 × 73 × 89 × 101 × 137 × 617 × 4093 × 8779 × 21649 × 513239 × 1052788969<10> × 1056689261<10> × 16205834846012967584927082656402106953<38> (100.00%)
R89 = 1089-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­111111111<89> = 497867 × 103733951 × 104984505733<12> × 5078554966026315671444089<25> × 403513310222809053284932818475878953159<39> (100.00%)
R90 = 1090-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­1111111111<90> = 32 × 7 × 11 × 13 × 19 × 31 × 37 × 41 × 211 × 241 × 271 × 2161 × 9091 × 29611 × 52579 × 238681 × 333667 × 2906161 × 3762091 × 8985695684401<13> × 4185502830133110721<19> (100.00%)
R91 = 1091-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­11111111111<91> = 53 × 79 × 239 × 547 × 4649 × 14197 × 17837 × 4262077 × 265371653 × 43442141653<11> × 316877365766624209<18> × 110742186470530054291318013<27> (100.00%)
R92 = 1092-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­111111111111<92> = 11 × 47 × 101 × 139 × 1289 × 2531 × 18371524594609<14> × 549797184491917<15> × 11111111111111111111111<23> × 4181003300071669867932658901<28> (100.00%)
R93 = 1093-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­1111111111111<93> = 3 × 37 × 2791 × 6943319 × 57336415063790604359<20> × 9009009009009009009009009009009909909909­90990990990990990991<60> (100.00%)
R94 = 1094-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­11111111111111<94> = 11 × 6299 × 35121409 × 4855067598095567<16> × 297262705009139006771611927<27> × 316362908763458525001406154038726382279<39> (100.00%)
R95 = 1095-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­111111111111111<95> = 41 × 191 × 271 × 59281 × 63841 × 1111111111111111111<19> × 1289981231950849543985493631<28> × 965194617121640791456070347951751<33> (100.00%)
R96 = 1096-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­1111111111111111<96> = 3 × 7 × 11 × 13 × 17 × 37 × 73 × 97 × 101 × 137 × 353 × 449 × 641 × 1409 × 9901 × 69857 × 206209 × 5882353 × 99990001 × 66554101249<11> × 75118313082913<14> × 9999999900000001<16> (100.00%)
R97 = 1097-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­11111111111111111<97> = 12004721 × 846035731396919233767211537899097169<36> × 1093998468553705375403392668420701191076­62296580348039<54> (100.00%)
R98 = 1098-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­111111111111111111<98> = 11 × 197 × 239 × 4649 × 909091 × 505885997 × 1976730144598190963568023014679333<34> × 5076141624365532994918781726395939035533<40> (100.00%)
R99 = 1099-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­1111111111111111111<99> = 32 × 37 × 67 × 199 × 397 × 21649 × 34849 × 333667 × 513239 × 1344628210313298373<19> × 3628537243429904693247662354742688697863­11886053883<51> (100.00%)
R100 = 10100-19 = 1111111111111111111111111111111111111111­1111111111111111111111111111111111111111­11111111111111111111<100> = 11 × 41 × 101 × 251 × 271 × 3541 × 5051 × 9091 × 21401 × 25601 × 27961 × 60101 × 7019801 × 182521213001<12> × 14103673319201<14> × 78875943472201<14> × 1680588011350901<16> (100.00%)
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