Factorizations of Phi

11...11 (Repunit) | 100...001 | Phi_n(10)
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Summary
Last updated: Sat, 26 May 2012 12:53:22 GMT Status: 1047 of 100000 Phi_n(10) factorizations were finished. 74534 of 100000 Phi_n(10) factorizations were cracked. 106 of 9592 R_prime factorizations were finished. 7345 of 9592 R_prime factorizations were cracked. 140328 (probable) prime factors were discovered. 101340 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=495 (c164), n=1050 (c165), n=960 (c172), n=810 (c173), n=483 (c180), n=465 (c181), n=1620L (c185), n=1980M (c187), n=429 (c191), n=405 (c193) 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=383 (c230), n=507 (c200), n=884 (c249), n=621 (c260), n=1650 (c266), n=960 (c172), n=1062 (c235), n=2420L (c298), n=483 (c180)

Format
Φ_n(10)	=	value..._<length>	=	(probable) prime factor..._<length>^exponent [composite factor..._<length>] (unidentified factor..._<length>)	·	...	(factored part)

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%)

Φ_20L(10) = 3541 = 3541 (100.00%)

Φ_20M(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%)

Φ_60L(10) = 255522961 = 61 · 4188901 (100.00%)

Φ_60M(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%)

Φ_100L(10) = 99004980069800499001_<20> = 7019801 · 14103673319201_<14> (100.00%)

Φ_100M(10) = 101005020070200501001_<21> = 60101 · 1680588011350901_<16> (100.00%)

Factorizations of Phi_n(10)