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February 28, 2009 2009 年 2 月 28 日 (Torbjörn Granlund)

n=1313: c1200(9000000000......) = 44438633221526432019286175178757 * c1169(2025264808......)

n=1771: c1305(5267055906......) = 71681096707581917661526764511169 * c1273(7347900839......)

n=2611: c2206(3949473173......) = 785196014038266421238835467519 * c2176(5029920049......)

n=2661: c1769(1692468346......) = 65522763278883393189223262364517 * c1737(2583023459......)

February 26, 2009 2009 年 2 月 26 日 (Alfred Reich)

n=15501: c10308(1174591102......) = 5342794743199 * c10295(2198458219......)

n=60220L: c12024(1270995395......) = 3641316992217280732201 * c12002(3490482695......)

n=60260L: c11440(3540999999......) = 31602866242561 * c11427(1120467989......)

n=60940L: c11032(5018955843......) = 11156178789361 * c11019(4498812665......)

n=60980M: c12192(3576409999......) = 54411167716967461 * c12175(6572933737......)

February 25, 2009 2009 年 2 月 25 日 (Alfred Reich)

n=34220L: c6473(2132100722......) = 75127795805328243966661 * c6450(2837965228......)

n=55020L: c6241(2557786117......) = 478348049635681 * c6226(5347123542......)

n=55260L: c7344(9048972901......) = 12439067053593421 * c7328(7274639538......)

n=55500L: c7189(2349304364......) = 81235496686501 * c7175(2891967748......)

n=55540L: c11091(4093874061......) = 3238569866851181 * c11076(1264099349......)

February 24, 2009 2009 年 2 月 24 日 (Alfred Reich)

n=56700L: c6468(3022573961......) = 321661997785044001 * c6450(9396739378......)

February 24, 2009 2009 年 2 月 24 日 (Kurt Beschorner)

n=5195: c4132(1716981932......) = 41844623117862690128411041 * c4106(4103231920......)

n=5195: c4106(4103231920......) = 24923914382489630019813822881 * c4078(1646303168......)

February 23, 2009 2009 年 2 月 23 日 (Torbjörn Granlund)

n=1179: c754(1035097296......) = 3135838744378703586545458839576204733 * c717(3300862643......)

n=1283: c1209(1911389610......) = 44599745740045620598108321464797 * p1177(4285651361......)

n=1461: c924(2064412845......) = 16241574232951132120061577080704111 * c890(1271066964......)

n=1735: c1306(3506966946......) = 844556568976857441218927023235311 * c1273(4152435817......)

n=1741: c1719(1016624885......) = 6001739613161891244633370331153347 * c1685(1693883691......)

n=1871: c1838(1317051232......) = 52061216852311647348650418176627 * p1806(2529812616......)

n=2169: c1426(1318166092......) = 874155566907441403823123359363081 * c1393(1507930788......)

n=2201: c2062(2691724713......) = 272560060413759358287226560354893 * c2029(9875712199......)

n=2419: c2309(5598034715......) = 3316129703123032367359481850059641 * c2276(1688122967......)

n=3351: c2222(2362319610......) = 161084894714746886468097974203 * c2193(1466505978......)

n=3447: c2256(1978057847......) = 4913089593274532137038528907603 * c2225(4026097651......)

February 22, 2009 2009 年 2 月 22 日 (Kurt Beschorner)

n=5169: c3444(9009009009......) = 15784939567494044812664431 * c3419(5707344630......)

n=5183: c5025(1664040221......) = 867279469834769569609 * c5004(1918689740......)

n=5203: c4620(9999999999......) = 106286409758981444653 * c4600(9408540586......)

n=6235: c4689(9279649534......) = 2771570614113887784878921 * c4665(3348155550......)

n=6755: c4609(1111099888......) = 1302592089848122726031 * c4587(8529914295......)

n=8379: c4537(1000000000......) = 8410325526747442476806671 * c4512(1189014618......)

n=8565: c4550(1340142166......) = 508167783600952807927561 * c4526(2637204107......)

February 15, 2009 2009 年 2 月 15 日 (Torbjörn Granlund)

n=1283: c1241(1638573870......) = 85726837758167572600643561430917 * c1209(1911389610......)

n=1857: c1208(9067199676......) = 2846323681930901273525828205850987 * c1175(3185582769......)

n=2385: c1225(2094877334......) = 661058968918694729591873150281 * p1195(3168971956......)

n=3933: c2300(1334469926......) = 6731702951627085963014582960041 * c2269(1982366030......)

n=4305: c1906(6408573581......) = 2214076372726695057889144879667914591 * c1870(2894468167......)

February 16, 2009 2009 年 2 月 16 日 (Yousuke Koide)

n=611: c549(1227328514......) = 76315077954516185354436343718117089011443009 * c505(1608238565......)

n=890: c304(3355975555......) = 14368738499109009207276617717065856029384012938971 * c255(2335609041......)

February 12, 2009 2009 年 2 月 12 日 (Torbjörn Granlund)

n=2231: c2039(3230536919......) = 3621730393042571630784422304709419547 * c2002(8919871357......)

n=2315: c1763(1058768494......) = 464121182584950688730417444081 * c1733(2281232862......)

n=2443: c2055(7667738843......) = 6349174822732294159318327863283 * c2025(1207674864......)

n=2493: c1590(1672618008......) = 2622783507925000328319223872899083 * c1556(6377262945......)

n=2769: c1681(1109999999......) = 1182168823365470923551733943080693 * c1647(9389521852......)

n=3015: c1498(1694738040......) = 6683196382767193429742833074601 * c1467(2535819604......)

n=3213: c1664(4081459614......) = 219238980780238627259779200985933 * c1632(1861648690......)

n=3483: c2203(2377165036......) = 38374845542732805340738766173237 * c2171(6194591803......)

February 12, 2009 2009 年 2 月 12 日 (Kurt Beschorner)

n=5073: c3147(3143827430......) = 545619535047853749517 * c3126(5761940745......)

n=5123: c4962(3241296129......) = 11240333139661300281465479 * c4937(2883629950......)

n=5143: c4943(6926840316......) = 754823082492798706451483 * c4919(9176773309......)

n=5151: c3201(1109999999......) = 399765205746588240964969 * c3177(2776629841......)

n=7221: c4581(5697981077......) = 23624281916710329117271 * c4559(2411917152......)

n=7735: c4587(1868785928......) = 30938282496019250200067311 * c4561(6040367395......)

n=8475: c4450(7314554663......) = 118231189398651442387801 * c4427(6186654046......)

n=11209: c10173(2025545413......) = 7410979487022827 * c10157(2733168290......)

n=11211: c7201(1109999999......) = 5274108873961999 * x7185(2104620944......)

n=11211: x7185(2104620944......) = 98604637104685759 * c7168(2134403620......)

n=11213: c11206(9008295649......) = 4998485570369 * x11194(1802204992......)

n=11213: x11194(1802204992......) = 1526541168747334877 * c11176(1180580667......)

n=11215: c8961(2306047875......) = 12210071895140906921 * c8942(1888643978......)

n=11217: c7468(6017056651......) = 44831409331518374881 * c7449(1342152018......)

n=11219: c10336(2350455709......) = 9372924979405030213 * c10317(2507707801......)

n=11223: c7057(1001000999......) = 106894774458631 * c7042(9364358595......)

n=11229: c7046(4524781814......) = 32086879178161 * x7033(1410165753......)

n=11229: x7033(1410165753......) = 2564952678129637 * x7017(5497823664......)

n=11229: x7017(5497823664......) = 290445913058441797 * c7000(1892890695......)

n=11233: c10948(9000000000......) = 17225267102311 * c10935(5224882695......)

n=11235: c5067(2151387007......) = 143498292237511 * c5053(1499242237......)

n=11239: c11219(1648584379......) = 4439667470570929 * c11203(3713305986......)

n=11243: c11235(2369950175......) = 11723885843347 * x11222(2021471555......)

n=11243: x11222(2021471555......) = 293925643241774896243 * c11201(6877493004......)

n=11245: c8237(3764564839......) = 24892208244671 * c8224(1512346675......)

n=11257: c11250(9311691844......) = 238954696546463119 * c11233(3896844037......)

n=11259: c7452(9999999999......) = 782719196932693 * c7438(1277597386......)

n=11263: c9625(4029754724......) = 5295462957452756999 * c9606(7609825159......)

n=11273: c11263(3233724527......) = 231194903392307 * x11249(1398700611......)

n=11273: x11249(1398700611......) = 70427433993022681 * x11232(1986016715......)

n=11273: x11232(1986016715......) = 1895314848327287281 * c11214(1047855831......)

n=11275: c7994(7780053853......) = 9569232506425022201 * c7975(8130279882......)

n=11281: c10859(1139715147......) = 9920242889639 * c10846(1148878268......)

n=11299: c11276(1229031331......) = 149979867635491681 * c11258(8194642062......)

February 2, 2009 2009 年 2 月 2 日 (Kurt Beschorner)

# ***** CORRECTION *****

n=49081: c49081(1111111111......) is (probable) prime

Primality testing 1111111111...... [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.31% and helper 0.01% (0.95% proof)
1111111111...... is Fermat and Lucas PRP! (2314.7639s+0.0875s)

# R49081 is a well-known repunit PRP which was found by Harvey Dubner in 1999.

# It seems that I made a mistake when I imported repunit-PRPs to the list.

# R86453 had been classified correctly as a PRP.

# Other known (larger) repunit-PRPs are R109297 and R270343.

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