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Factorizations of 100...001

11...11 (Repunit) | 100...001 | Phi_n(10)
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Summary
Last updated:
Wed, 08 Feb 2012 14:18:32 GMT
Status:
1045 of 100000 Phi_n(10) factorizations were finished.
74444 of 100000 Phi_n(10) factorizations were cracked.
106 of 9592 R_prime factorizations were finished.
7269 of 9592 R_prime factorizations were cracked.
140041 (probable) prime factors were discovered.
101342 composite factors are remaining.
0 factors are unidentified.
Sources:
Kurt Beschorner, Richard Brent, Greg Childers,
Torbjörn Granlund, Makoto Kamada, Yousuke Koide,
Giovanni Di Maria, Alfred Reich, Maksym Voznyy,
Sam Wagstaff, Paul Zimmermann, NFS@Home,
yoyo@home, Henri & Renaud Lifchitz
Wanted list of Phi_n(10)
First composite:
n=281 (c210), n=283 (c211), n=323 (c271), n=337 (c268), n=341 (c226),
n=343 (c238), n=353 (c328), n=359 (c275), n=365 (c288), n=371 (c255)
Smallest composite:
n=870 (c164), n=495 (c164), n=1050 (c165), n=876 (c166), n=960 (c172),
n=810 (c173), n=483 (c180), n=465 (c181), n=1620L (c185), n=1980M (c187)
First blank Phi_n(10):
n=365 (c288), n=469 (c396), n=509 (c509), n=557 (c557), n=589 (c540),
n=625 (c501), n=640 (c256), n=647 (c647), n=649 (c580), n=657 (c432)
Smallest blank Phi_n(10):
n=640 (c256), n=1340L (c265), n=365 (c288), n=1110 (c288), n=730 (c289),
n=920 (c353), n=776 (c384), n=469 (c396), n=808 (c400), n=1078 (c421)
Smallest blank R_prime:
n=509 (c509), n=557 (c557), n=647 (c647), n=991 (c991), n=1117 (c1117),
n=1213 (c1213), n=1259 (c1259), n=1291 (c1291), n=1373 (c1373), n=1447 (c1447)
Biggest factored part:
n=1030 (c199), n=876 (c166), n=383 (c230), n=507 (c200), n=884 (c249),
n=621 (c260), n=1650 (c266), n=960 (c172), n=1062 (c235), n=2420L (c298)
Format
10n+1=value...<length>=(probable) prime factor...<length>exponent
[composite factor...<length>]
(unidentified factor...<length>)		·... (factored part)
 
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101+1 = 11 = 11 (100.00%)

102+1 = 101 = 101 (100.00%)

103+1 = 1001 = 7 · 11 · 13 (100.00%)

104+1 = 10001 = 73 · 137 (100.00%)

105+1 = 100001 = 11 · 9091 (100.00%)

106+1 = 1000001 = 101 · 9901 (100.00%)

107+1 = 10000001 = 11 · 909091 (100.00%)

108+1 = 100000001 = 17 · 5882353 (100.00%)

109+1 = 1000000001<10> = 7 · 11 · 13 · 19 · 52579 (100.00%)

1010+1 = 10000000001<11> = 101 · 3541 · 27961 (100.00%)

1011+1 = 100000000001<12> = 112 · 23 · 4093 · 8779 (100.00%)

1012+1 = 1000000000001<13> = 73 · 137 · 99990001 (100.00%)

1013+1 = 10000000000001<14> = 11 · 859 · 1058313049<10> (100.00%)

1014+1 = 100000000000001<15> = 29 · 101 · 281 · 121499449 (100.00%)

1015+1 = 1000000000000001<16> = 7 · 11 · 13 · 211 · 241 · 2161 · 9091 (100.00%)

1016+1 = 10000000000000001<17> = 353 · 449 · 641 · 1409 · 69857 (100.00%)

1017+1 = 100000000000000001<18> = 11 · 103 · 4013 · 21993833369<11> (100.00%)

1018+1 = 1000000000000000001<19> = 101 · 9901 · 999999000001<12> (100.00%)

1019+1 = 10000000000000000001<20> = 11 · 909090909090909091<18> (100.00%)

1020+1 = 100000000000000000001<21> = 73 · 137 · 1676321 · 5964848081<10> (100.00%)

1021+1 = 1000000000000000000001<22> = 72 · 11 · 13 · 127 · 2689 · 459691 · 909091 (100.00%)

1022+1 = 10000000000000000000001<23> = 89 · 101 · 1052788969<10> · 1056689261<10> (100.00%)

1023+1 = 100000000000000000000001<24> = 11 · 47 · 139 · 2531 · 549797184491917<15> (100.00%)

1024+1 = 1000000000000000000000001<25> = 17 · 5882353 · 9999999900000001<16> (100.00%)

1025+1 = 10000000000000000000000001<26> = 11 · 251 · 5051 · 9091 · 78875943472201<14> (100.00%)

1026+1 = 100000000000000000000000001<27> = 101 · 521 · 1900381976777332243781<22> (100.00%)

1027+1 = 1000000000000000000000000001<28> = 7 · 11 · 13 · 19 · 52579 · 70541929 · 14175966169<11> (100.00%)

1028+1 = 10000000000000000000000000001<29> = 73 · 137 · 7841 · 127522001020150503761<21> (100.00%)

1029+1 = 100000000000000000000000000001<30> = 11 · 59 · 154083204930662557781201849<27> (100.00%)

1030+1 = 1000000000000000000000000000001<31> = 61 · 101 · 3541 · 9901 · 27961 · 4188901 · 39526741 (100.00%)

1031+1 = 10000000000000000000000000000001<32> = 11 · 909090909090909090909090909091<30> (100.00%)

1032+1 = 100000000000000000000000000000001<33> = 19841 · 976193 · 6187457 · 834427406578561<15> (100.00%)

1033+1 = 1000000000000000000000000000000001<34> = 7 · 112 · 13 · 23 · 4093 · 8779 · 599144041 · 183411838171<12> (100.00%)

1034+1 = 10000000000000000000000000000000001<35> = 101 · 28559389 · 1491383821<10> · 2324557465671829<16> (100.00%)

1035+1 = 100000000000000000000000000000000001<36> = 11 · 9091 · 909091 · 4147571 · 265212793249617641<18> (100.00%)

1036+1 = 1000000000000000000000000000000000001<37> = 73 · 137 · 3169 · 98641 · 99990001 · 3199044596370769<16> (100.00%)

1037+1 = 10000000000000000000000000000000000001<38> = 11 · 7253 · 422650073734453<15> · 296557347313446299<18> (100.00%)

1038+1 = 100000000000000000000000000000000000001<39> = 101 · 722817036322379041<18> · 1369778187490592461<19> (100.00%)

1039+1 = 1000000000000000000000000000000000000001<40> = 7 · 11 · 132 · 157 · 859 · 6397 · 216451 · 1058313049<10> · 388847808493<12> (100.00%)

1040+1 = 1000000000000000000000000000000000000000­1<41> = 17 · 5070721 · 5882353 · 19721061166646717498359681<26> (100.00%)

1041+1 = 1000000000000000000000000000000000000000­01<42> = 11 · 2670502781396266997<19> · 3404193829806058997303<22> (100.00%)

1042+1 = 1000000000000000000000000000000000000000­001<43> = 29 · 101 · 281 · 9901 · 226549 · 121499449 · 4458192223320340849<19> (100.00%)

1043+1 = 1000000000000000000000000000000000000000­0001<44> = 11 · 57009401 · 2182600451<10> · 7306116556571817748755241<25> (100.00%)

1044+1 = 1000000000000000000000000000000000000000­00001<45> = 73 · 137 · 617 · 16205834846012967584927082656402106953<38> (100.00%)

1045+1 = 1000000000000000000000000000000000000000­000001<46> = 7 · 11 · 13 · 19 · 211 · 241 · 2161 · 9091 · 29611 · 52579 · 3762091 · 8985695684401<13> (100.00%)

1046+1 = 1000000000000000000000000000000000000000­0000001<47> = 101 · 1289 · 18371524594609<14> · 4181003300071669867932658901<28> (100.00%)

1047+1 = 1000000000000000000000000000000000000000­00000001<48> = 11 · 6299 · 4855067598095567<16> · 297262705009139006771611927<27> (100.00%)

1048+1 = 1000000000000000000000000000000000000000­000000001<49> = 97 · 353 · 449 · 641 · 1409 · 69857 · 206209 · 66554101249<11> · 75118313082913<14> (100.00%)

1049+1 = 1000000000000000000000000000000000000000­0000000001<50> = 11 · 197 · 909091 · 5076141624365532994918781726395939035533<40> (100.00%)

1050+1 = 1000000000000000000000000000000000000000­00000000001<51> = 101 · 3541 · 27961 · 60101 · 7019801 · 14103673319201<14> · 1680588011350901<16> (100.00%)

1051+1 = 1000000000000000000000000000000000000000­000000000001<52> = 7 · 11 · 13 · 103 · 4013 · 21993833369<11> · 291078844423<12> · 377526955309799110357<21> (100.00%)

1052+1 = 1000000000000000000000000000000000000000­0000000000001<53> = 73 · 137 · 1580801 · 6325274402021507450906224122454439230492­01<42> (100.00%)

1053+1 = 1000000000000000000000000000000000000000­00000000000001<54> = 11 · 9090909090909090909090909090909090909090­909090909091<52> (100.00%)

1054+1 = 1000000000000000000000000000000000000000­000000000000001<55> = 101 · 109 · 9901 · 153469 · 999999000001<12> · 59779577156334533866654838281<29> (100.00%)

1055+1 = 1000000000000000000000000000000000000000­0000000000000001<56> = 112 · 23 · 331 · 4093 · 5171 · 8779 · 9091 · 20163494891<11> · 318727841165674579776721<24> (100.00%)

1056+1 = 1000000000000000000000000000000000000000­00000000000000001<57> = 17 · 113 · 5882353 · 73765755896403138401<20> · 119968369144846370226083377<27> (100.00%)

1057+1 = 1000000000000000000000000000000000000000­000000000000000001<58> = 7 · 11 · 13 · 1458973 · 909090909090909091<18> · 753201806271328462547977919407<30> (100.00%)

1058+1 = 1000000000000000000000000000000000000000­0000000000000000001<59> = 101 · 349 · 38861 · 618049 · 1181180637520183640867963573625866958318­7541<44> (100.00%)

1059+1 = 1000000000000000000000000000000000000000­00000000000000000001<60> = 11 · 1889 · 1090805842068098677837<22> · 4411922770996074109644535362851087<34> (100.00%)

1060+1 = 1000000000000000000000000000000000000000­000000000000000000001<61> = 73 · 137 · 1676321 · 99990001 · 5964848081<10> · 100009999999899989999000000010001<33> (100.00%)

1061+1 = 1000000000000000000000000000000000000000­0000000000000000000001<62> = 11 · 81131 · 1120522253011683685532152825789043757514­5023592596037161<56> (100.00%)

1062+1 = 1000000000000000000000000000000000000000­00000000000000000000001<63> = 101 · 2049349 · 4831285495545122373055545883590398223973­07149685578249<54> (100.00%)

1063+1 = 1000000000000000000000000000000000000000­000000000000000000000001<64> = 72 · 11 · 13 · 19 · 127 · 2689 · 52579 · 459691 · 909091 · 5274739 · 189772422673235585874485732659<30> (100.00%)

1064+1 = 1000000000000000000000000000000000000000­0000000000000000000000001<65> = 1265011073<10> · 15343168188889137818369<23> · 515217525265213267447869906815873<33> (100.00%)

1065+1 = 1000000000000000000000000000000000000000­00000000000000000000000001<66> = 11 · 131 · 859 · 9091 · 1058313049<10> · 8396862596258693901610602298557167100076­327481<46> (100.00%)

1066+1 = 1000000000000000000000000000000000000000­000000000000000000000000001<67> = 89 · 101 · 9901 · 1052788969<10> · 1056689261<10> · 5419170769<10> · 789390798020221<15> · 2361000305507449<16> (100.00%)

1067+1 = 1000000000000000000000000000000000000000­0000000000000000000000000001<68> = 11 · 9090909090909090909090909090909090909090­90909090909090909090909091<66> (100.00%)

1068+1 = 1000000000000000000000000000000000000000­00000000000000000000000000001<69> = 73 · 137 · 152533657 · 6555274617188258326423007086888436687780­3237222654400793<56> (100.00%)

1069+1 = 1000000000000000000000000000000000000000­000000000000000000000000000001<70> = 7 · 11 · 13 · 47 · 139 · 2531 · 31051 · 143574021480139<15> · 549797184491917<15> · 24649445347649059192745899<26> (100.00%)

1070+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000001<71> = 29 · 101 · 281 · 421 · 3541 · 27961 · 3471301 · 13489841 · 121499449 · 60368344121<11> · 848654483879497562821<21> (100.00%)

1071+1 = 1000000000000000000000000000000000000000­00000000000000000000000000000001<72> = 11 · 290249 · 3132106946418106835541520932340538954170­6979493156189716729115659<65> (100.00%)

1072+1 = 1000000000000000000000000000000000000000­000000000000000000000000000000001<73> = 17 · 8929 · 5882353 · 9999999900000001<16> · 1119946242580356142905139433307201254339­79169<45> (100.00%)

1073+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000001<74> = 11 · 293 · 10826684964539959837294043117<29> · 2865788889761949979999225923309086021030­11<42> (100.00%)

1074+1 = 1000000000000000000000000000000000000000­00000000000000000000000000000000001<75> = 101 · 149 · 3109 · 111149 · 708840373781<12> · 669031686661427842829<21> · 40548140514062774758071840361<29> (100.00%)

1075+1 = 1000000000000000000000000000000000000000­000000000000000000000000000000000001<76> = 7 · 11 · 13 · 211 · 241 · 251 · 2161 · 5051 · 9091 · 78875943472201<14> · 1000009999999998999989999900000000010000­1<41> (100.00%)

1076+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000001<77> = 73 · 137 · 457 · 1403417 · 5240808656722481737<19> · 2974783307863656284148053052903024835550­43017<45> (100.00%)

1077+1 = 1000000000000000000000000000000000000000­00000000000000000000000000000000000001<78> = 112 · 23 · 463 · 4093 · 8779 · 24179 · 590437 · 909091 · 7444361 · 4539402627853030477<19> · 4924630160315726207887<22> (100.00%)

1078+1 = 1000000000000000000000000000000000000000­000000000000000000000000000000000000001<79> = 101 · 521 · 3121 · 9901 · 53397071018461<14> · 1900381976777332243781<22> · 6060517860310398033985611921721<31> (100.00%)

1079+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000001<80> = 11 · 1423 · 9615060929<10> · 6644317454149057909799751015802107695839­2938976011506949065646573<65> (100.00%)

1080+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­1<81> = 353 · 449 · 641 · 1409 · 69857 · 1634881 · 18453761 · 947147262401<12> · 349954396040122577928041596214187605761<39> (100.00%)

1081+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­01<82> = 7 · 11 · 13 · 19 · 1459 · 52579 · 70541929 · 2458921051<10> · 14175966169<11> · 456502382570032651<18> · 610600386089858349939139<24> (100.00%)

1082+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­001<83> = 101 · 68389 · 1447745997018511893740076606031686237538­345362413531560645573104006506749609<76> (100.00%)

1083+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­0001<84> = 11 · 167 · 997 · 3565183 · 2097307081<10> · 7742098247001476863<19> · 9431769031413300684826029009602942998788­41<42> (100.00%)

1084+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­00001<85> = 73 · 137 · 7841 · 99990001 · 11189053009<11> · 603812429055411913<18> · 127522001020150503761<21> · 148029423400750506553<21> (100.00%)

1085+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­000001<86> = 11 · 103 · 4013 · 9091 · 87211 · 787223761 · 21993833369<11> · 1602207948210144520667419183035809176643­86555934641<51> (100.00%)

1086+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­0000001<87> = 101 · 338669 · 2923500556298303355222653948542706598448­925085853709961673200056984872843366529<79> (100.00%)

1087+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­00000001<88> = 7 · 11 · 13 · 59 · 638453709757<12> · 135080726389891<15> · 154083204930662557781201849<27> · 1274194732898148471766404179653<31> (100.00%)

1088+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­000000001<89> = 17 · 5882353 · 10100113 · 9900879227786858424257223656804730798555­422102713108259184822982673560177<73> (100.00%)

1089+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­0000000001<90> = 11 · 179 · 12147237304901893<17> · 4180967272673252032291190917188955510245­874180001164839931077197586653<70> (100.00%)

1090+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­00000000001<91> = 61 · 101 · 181 · 3541 · 9901 · 27961 · 4188901 · 39526741 · 999999000001<12> · 4999437541453012143121<22> · 1105097795002994798105101<25> (100.00%)

1091+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­000000000001<92> = 11 · 859 · 909091 · 21705503 · 1058313049<10> · 5067838741170388910175912578529043989438­9920385627096501794498837<65> (100.00%)

1092+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­0000000000001<93> = 73 · 137 · 2393 · 4178437150016715837818641871709193476807­7726285039694944003301299623485206849143­75257<85> (100.00%)

1093+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­00000000000001<94> = 7 · 11 · 13 · 373 · 44641 · 3590254957<10> · 909090909090909090909090909091<30> · 1838190726228124463315819067778696666309­1011<44> (100.00%)

1094+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­000000000000001<95> = 101 · 45121 · 2144906157509411684424913774078958939881<40> · 1023037643093214557651333120422980213172­396059301<49> (100.00%)

1095+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­0000000000000001<96> = 11 · 9091 · 1812604116731<13> · 121450506296081<15> · 909090909090909091<18> · 4996731930447843676185843959746621491531­100801<46> (100.00%)

1096+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­00000000000000001<97> = 193 · 769 · 19841 · 976193 · 6187457 · 834427406578561<15> · 1253224535459902849<19> · 5376349118996722135857554610727903470969­7<41> (100.00%)

1097+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­000000000000000001<98> = 11 · 102527361354613106010527<24> · 323338434891034089173475790125293<33> · 2742269936605462168329562307947106658888­1<41> (100.00%)

1098+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­0000000000000000001<99> = 29 · 101 · 281 · 121499449 · 9999999999999900000000000000999999999999­9900000000000000999999999999990000000000­0001<84> (100.00%)

1099+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­00000000000000000001<100> = 7 · 112 · 13 · 19 · 23 · 4093 · 8779 · 52579 · 599144041 · 7093127053<10> · 183411838171<12> · 1411225248778861822822335393177961449383­05111168717<51> (100.00%)

10100+1 = 1000000000000000000000000000000000000000­0000000000000000000000000000000000000000­000000000000000000001<101> = 73 · 137 · 401 · 1201 · 1601 · 1676321 · 5964848081<10> · 1296944190290577505513857711845642744990­75700947656757821537291527196801<72> (100.00%)

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