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November 30, 2010 2010 年 11 月 30 日 (Makoto Kamada)

n=84524: c35819(2355862082......) = 5693959006429 * c35806(4137476367......)

n=84526: c39001(1099999999......) = 8180436423121 * c38988(1344671534......)

n=84534: c27620(3734176754......) = 9840711143521 * c27607(3794620835......)

n=84536: c42258(6571160694......) = 6286675017169 * c42246(1045252168......)

n=84642: c28213(1098901098......) = 6190174932979 * c28200(1775234320......)

n=42363: c28181(6485028371......) = 7364677749769 * c28168(8805583342......)

n=42377: c40980(9000000000......) = 8707323303467 * c40968(1033612705......)

n=42403: c42388(5889873462......) = 9758352751039 * c42375(6035725098......)

n=84823: c84221(3569623378......) = 7628166319201 * c84208(4679530085......)

n=84884: c42440(9900990099......) = 5814638884001 * c42428(1702769560......)

n=84886: c42433(2380852465......) = 9149250845687 * c42420(2602237610......)

n=84953: c77220(9000000000......) = 7124587082933 * c77208(1263231103......)

n=84979: c84972(1167421819......) = 7682710899431 * c84959(1519544122......)

n=85005: c45295(1212551775......) = 9145426644631 * c45282(1325855886......)

n=42521: c42000(9000000000......) = 9458077079723 * c41987(9515676309......)

n=42537: c25742(5355421076......) = 7097176964329 * c25729(7545846895......)

n=42539: c35471(3482864625......) = 7941591191507 * c35458(4385600494......)

November 29, 2010 2010 年 11 月 29 日 (Kurt Beschorner)

n=7939: c7407(2053404132......) = 1749359628849238816568437 * c7383(1173803315......)

n=9155: c7296(2641588905......) = 760806092204973706467962081 * c7269(3472092208......)

n=9715: c7363(7232714890......) = 3127103548041813888481 * c7342(2312911862......)

n=10955: c7446(7438221826......) = 33823730232656206635074591 * c7421(2199113396......)

November 29, 2010 2010 年 11 月 29 日 (Makoto Kamada)

n=83021: c81595(5420282697......) = 6465448832671 * c81582(8383459274......)

n=83031: c51062(7488685003......) = 5457867423529 * c51050(1372089943......)

n=83082: c27102(3554635885......) = 7633492573477 * c27089(4656631091......)

n=20827: c20404(3210804722......) = 8061551876321 * c20391(3982861825......)

n=41673: c26738(1104740830......) = 6244275402283 * c26725(1769205807......)

n=83416: c41691(9211450944......) = 8188259537009 * c41679(1124958350......)

n=83423: c83411(1579155914......) = 8360323539151 * c83398(1888869380......)

n=83435: c57590(5627111637......) = 7686249297871 * c57577(7321011092......)

n=83528: c40769(1000099999......) = 7835854312553 * c40756(1276312652......)

n=41765: c33386(8662030773......) = 5507140584761 * c33374(1572872644......)

n=83571: c54913(1109999999......) = 6812759901163 * c54900(1629295639......)

n=83573: c71610(3984795164......) = 7760621707763 * c71597(5134633943......)

n=41811: c21588(1821211725......) = 8870930241559 * c21575(2053010986......)

n=83629: c66078(2719639692......) = 5099979253279 * c66065(5332648541......)

n=83734: c35881(1099999890......) = 5722627737961 * x35868(1922193685......)

n=83734: x35868(1922193685......) = 9680180352487 * c35855(1985700281......)

n=41895: c18144(9999999999......) = 9535967041231 * c18132(1048661342......)

n=83798: c35025(3866409250......) = 6233349425161 * c35012(6202779575......)

n=41899: c35026(8873348448......) = 7900125248159 * c35014(1123190857......)

n=20951: c17268(8610515347......) = 7497576734677 * c17256(1148439776......)

n=83869: c83853(8410676621......) = 5769751081201 * c83841(1457719146......)

n=83923: c68035(3309902202......) = 5779901216041 * c68022(5726572269......)

n=16825: c13429(4854192327......) = 7976088943751 * c13416(6085930537......)

n=42073: c42067(6602241989......) = 7334799904987 * c42054(9001257123......)

n=84149: c77658(3565103342......) = 5358685063889 * c77645(6652944332......)

n=42097: c36961(1111111111......) = 8996153737231 * c36948(1235095734......)

n=84210: c19201(1098890000......) = 8036942779321 * c19188(1367298524......)

n=42147: c23939(6685743704......) = 7868894802049 * c23926(8496420237......)

n=84328: c41329(1000099999......) = 7795338506321 * c41316(1282946210......)

n=84334: c41737(1099999999......) = 7208245658063 * c41724(1526030121......)

n=84415: c67521(2412153530......) = 9755438383961 * c67508(2472624433......)

November 28, 2010 2010 年 11 月 28 日 (Makoto Kamada)

n=82015: c64033(1111099999......) = 9537963458311 * c64020(1164923733......)

n=41011: c40980(2547639721......) = 8074271927041 * c40967(3155256281......)

n=41041: c28793(7614336999......) = 8634930610307 * c28780(8818063912......)

n=82173: c42336(9999999000......) = 9999229393609 * c42324(1000076966......)

n=41103: c27391(6076161866......) = 9012961109557 * c27378(6741582253......)

n=82258: c37381(1099999999......) = 6271241750731 * c37368(1754038583......)

n=82267: c82250(1816410838......) = 6123463852409 * c82237(2966312665......)

n=82321: c81690(1221199371......) = 8436595901089 * c81677(1447502506......)

n=82329: c50630(1557117760......) = 6191258859787 * c50617(2515026096......)

n=82371: c54897(3254376099......) = 6372336538369 * c54884(5107037394......)

n=82417: c81210(1882771531......) = 5025922999711 * c81197(3746120925......)

n=82428: c27456(7894769811......) = 9149338280749 * c27443(8628787754......)

n=82431: c52912(1012465226......) = 5645412330121 * c52899(1793430076......)

n=20617: c20160(3313242814......) = 6534986983601 * c20147(5070006754......)

n=82473: c53425(1109999999......) = 5124496473013 * c53412(2166066472......)

n=82494: c27493(1000999998......) = 5503528556767 * c27480(1818833115......)

n=82526: c41245(8002309562......) = 6270036886579 * c41233(1276277908......)

n=41289: c27518(9917894807......) = 6904622060209 * x27506(1436413857......)

n=41289: x27506(1436413857......) = 7559736786361 * c27493(1900084484......)

n=82625: c65995(2017141669......) = 7966841971001 * c65982(2531921277......)

n=20667: c13607(1423124926......) = 7693511969569 * c13594(1849772810......)

n=82678: c40621(1907169548......) = 8185815585743 * c40608(2329846706......)

n=82689: c53744(1156529992......) = 5567245301281 * c53731(2077382852......)

n=41355: c22020(2477830118......) = 6154140193111 * c22007(4026281561......)

n=41367: c27576(9009009009......) = 9348045163441 * c27563(9637318660......)

n=82742: c37583(2495100527......) = 6366763567561 * c37570(3918946417......)

n=82747: c70920(9000000900......) = 6289734678599 * c70908(1430903107......)

n=82769: c80468(2570851974......) = 6597314040413 * c80455(3896816126......)

n=41409: c26706(1184975987......) = 7202323437787 * c26693(1645269054......)

n=41415: c20000(9009099100......) = 5764239096001 * c19988(1562929460......)

n=82872: c27601(1000000000......) = 8756562146401 * c27588(1142000688......)

n=41437: c37626(1862945616......) = 5715543726707 * c37613(3259437257......)

n=82912: c41436(1206083485......) = 9382349529697 * c41423(1285481297......)

n=82916: c39241(1009999999......) = 5684252484601 * c39228(1776838736......)

n=82920: c22080(9999000100......) = 8753450297521 * c22068(1142292440......)

n=82944: c27648(9999999999......) = 7079164148737 * c27636(1412596146......)

n=82976: c41466(1115895948......) = 8060515828289 * c41453(1384397689......)

n=27659: c26001(3667661315......) = 9308488308397 * c25988(3940125607......)

n=82978: c35514(1353165592......) = 6819927384131 * c35501(1984134898......)

n=82992: c20730(1628290853......) = 9649714209409 * c20717(1687398007......)

November 27, 2010 2010 年 11 月 27 日 (Alfred Reich)

n=12081: c8052(9009009009......) = 1724480816333576801839 * c8031(5224186273......)

n=12367: c12124(3169511612......) = 1487192139534351057115573561 * c12097(2131205194......)

n=12373: c12373(1111111111......) = 27325360511416597951 * c12353(4066226722......)

# The number of blank factorization of repunits up to 100000-digit is now 2559.

n=12395: c9488(8060510445......) = 184617062247694121 * c9471(4366070149......)

n=12509: c10688(6229246177......) = 77681242464095187660961667 * c10662(8018983708......)

n=12517: c12489(3443601812......) = 5908703072659511 * c12473(5828016352......)

n=25609: c25595(8671030662......) = 26719140674671 * c25582(3245250574......)

n=12663: c7099(1334055754......) = 38254844402833106909449 * c7076(3487285794......)

n=12709: c12433(2501735613......) = 31220830091797747 * c12416(8013033625......)

n=12745: c10166(1402762086......) = 5832361282182431 * c10150(2405135791......)

n=12769: c12657(1000000000......) = 22592695963417744550923 * c12634(4426209256......)

n=12911: c12900(2471108241......) = 9198174861727024769 * c12881(2686520182......)

n=12965: c10368(9000090000......) = 8808001357546909788241 * c10347(1021808425......)

n=24321: c14508(1156767178......) = 9667131861564871 * c14492(1196598116......)

n=24379: c24353(1447897287......) = 1029747750513791 * c24338(1406069871......)

n=24439: c24418(1336511506......) = 23574215504823631 * c24401(5669378503......)

n=24659: c24634(3032716616......) = 94176197153701346164519 * c24611(3220258099......)

n=24773: c21202(7449815282......) = 59453029091324443 * c21186(1253058993......)

n=25419: c16404(2357160448......) = 95241707878522142932120761779041 * c16372(2474924589......)

n=31019: c31008(4124163489......) = 1583551991386241 * c30993(2604375171......)

n=31069: c31046(2920508738......) = 16748753384707 * c31033(1743717082......)

n=31105: c24880(9000090000......) = 1395792461824726111 * c24862(6448014477......)

n=31205: c24643(1001441073......) = 1169980565914801 * c24627(8559467591......)

n=31237: c31230(3355692649......) = 1863835345564121 * c31215(1800423335......)

n=31253: c31248(1777578688......) = 14066410160112934921001 * c31226(1263704576......)

n=31321: c31314(4031243589......) = 265282013748282733 * c31297(1519606825......)

n=31327: c31307(5009085440......) = 12092597064428095717 * c31288(4142274330......)

n=31339: c23761(1000000000......) = 430056441105523 * c23746(2325276183......)

n=31351: c30947(4784510943......) = 52585924486759 * c30933(9098463115......)

n=31435: c25138(3976497368......) = 46588201324591 * c25124(8535417242......)

n=31505: c25200(9000090000......) = 431967144411601 * c25186(2083512627......)

n=31709: c30797(2967200232......) = 24790303069517 * c30784(1196919708......)

n=31729: c31722(1023941062......) = 210043540293733 * c31707(4874899087......)

n=31771: c31755(5404426408......) = 49443711902573 * c31742(1093046254......)

n=31805: c25440(9000090000......) = 80656785887681 * c25427(1115850315......)

n=31837: c28074(1104430082......) = 92936422630707787 * c28057(1188371631......)

n=31919: c31308(1802773092......) = 138776692786241 * c31294(1299046011......)

n=31945: c25533(3167098147......) = 326298816330001 * c25518(9706128215......)

n=31979: c31584(9000000000......) = 52279299068387 * c31571(1721522698......)

n=99543: c66360(9009009009......) = 50557787767969 * c66347(1781923103......)

n=99615: c51072(9009099100......) = 111610911769420962511 * c51052(8071880210......)

n=99627: c60349(2297190564......) = 733724036710068559 * c60331(3130864533......)

n=99693: c56160(9990000009......) = 12405701812879 * c56147(8052748776......)

n=99797: c95421(5927712446......) = 135782225399281 * c95407(4365602662......)

November 27, 2010 2010 年 11 月 27 日 (Makoto Kamada)

n=81006: c25768(5694310852......) = 6109124437219 * c25755(9320993393......)

n=81013: c81007(3428794398......) = 5262694404431 * c80994(6515283112......)

n=81033: c54020(9009009009......) = 6186596792923 * c54008(1456214023......)

n=81040: c32385(1000000009......) = 9560428999201 * c32372(1045978177......)

n=40521: c24896(3466964750......) = 7414312226803 * c24883(4676043635......)

n=40537: c34740(9000000900......) = 7966046832409 * c34728(1129795127......)

n=81095: c55432(7340010486......) = 6397262765041 * c55420(1147367359......)

n=40571: c39144(9000000000......) = 5352204054037 * c39132(1681550237......)

n=81158: c28801(1099999889......) = 9448939533419 * c28788(1164151687......)

n=81195: c43297(1109988900......) = 5541335463751 * c43284(2003107206......)

n=81207: c46369(1001000999......) = 7936849300969 * c46356(1261207013......)

n=81289: c73008(9999999999......) = 7087128464573 * c72996(1411008711......)

n=81298: c34824(2935246021......) = 5779745135851 * c34811(5078504245......)

n=81335: c65037(9601804882......) = 7833971336911 * c65025(1225662498......)

n=40673: c40121(6664969814......) = 5435949703841 * c40109(1226091148......)

n=40693: c40666(1671448598......) = 5789031756161 * c40653(2887267973......)

n=81448: c40720(9999000099......) = 9348382100537 * c40708(1069596855......)

n=81458: c37435(2455246985......) = 8819353801051 * c37422(2783930706......)

n=81459: c46441(1000000001......) = 5641380158653 * x46428(1772615872......)

n=81459: x46428(1772615872......) = 6138126915733 * c46415(2887877517......)

n=81531: c54348(9990000009......) = 7945037127613 * c54336(1257388713......)

n=20387: c18131(2806434769......) = 8794412523077 * c18118(3191156615......)

n=40791: c27180(3155216914......) = 7513461614683 * c27167(4199418425......)

n=81602: c40795(2228103921......) = 5695493600011 * c40782(3912047098......)

n=81635: c62945(1111099999......) = 9723075938561 * c62932(1142745368......)

n=20409: c13591(1301296692......) = 9117989985529 * c13578(1427174952......)

n=81670: c32665(1099989000......) = 9122660524961 * c32652(1205776535......)

n=81680: c32628(1665427129......) = 5414109955361 * c32615(3076086639......)

n=81708: c24715(2019585965......) = 8808135881821 * c24702(2292864225......)

n=81739: c70046(6336558187......) = 7109251813693 * c70033(8913115406......)

n=40929: c23377(1109999889......) = 9895667176039 * c23364(1121702932......)

n=40933: c40919(3981410637......) = 8580969397831 * c40906(4639814515......)

n=27303: c17200(1814625648......) = 5604612513013 * c17187(3237736139......)

n=81926: c35899(5548210341......) = 8861915511983 * c35886(6260734864......)

n=81931: c81918(1814954030......) = 5304721731511 * c81905(3421393471......)

n=81941: c80647(5491722753......) = 6263184261773 * c80634(8768259920......)

n=81942: c23396(1110528161......) = 8639101139089 * c23383(1285467253......)

n=81972: c23748(3501699589......) = 8121032847181 * c23735(4311889454......)

n=41000: c15973(1026231589......) = 6411849534001 * c15960(1600523505......)

November 26, 2010 2010 年 11 月 26 日 (Kurt Beschorner)

n=7867: c7844(5011401349......) = 138746755718686158802919 * c7821(3611905246......)

n=7883: c7871(3758556848......) = 2700590809281547603725600773 * c7844(1391753550......)

n=9635: c7334(1571726810......) = 24039524526243756000761 * c7311(6538094414......)

# The ratio of factored part of (17*10^9636-167)/3-1 was raised from 5.52% to 5.75%.

n=10357: c10357(1111111111......) = 7698302422383926647602852413 * c10329(1443319643......)

# The number of blank factorization of repunits up to 100000-digit is now 2560.

November 26, 2010 2010 年 11 月 26 日 (Makoto Kamada)

n=33068: c14161(1009999999......) = 9284397699781 * c14148(1087846549......)

n=49615: c39682(3779135267......) = 6819355902521 * c39669(5541777436......)

n=99319: c90280(9000000000......) = 9091498774117 * c90267(9899357876......)

n=99349: c99342(1553321785......) = 6021609652529 * c99329(2579579008......)

n=99357: c66236(9009009009......) = 6301692885751 * c66224(1429617274......)

n=49687: c45146(1553125826......) = 5122595048231 * c45133(3031912169......)

n=16573: c16547(2519140759......) = 6804675785797 * c16534(3702073160......)

n=99553: c98555(2260096983......) = 6589970965013 * c98542(3429600821......)

n=49791: c28441(1109999889......) = 8052707491963 * c28428(1378418240......)

n=99591: c65453(1629661126......) = 5106318387991 * c65440(3191460075......)

n=16607: c16594(3996779719......) = 7426236453919 * c16581(5381972072......)

n=99767: c99756(1942928501......) = 5463404537881 * c99743(3556259632......)

n=99791: c98352(9000000000......) = 9233713720067 * c98339(9746890874......)

n=20007: c11648(5852379676......) = 5203505069569 * c11636(1124699524......)

n=40049: c38640(9000000000......) = 5717450908111 * c38628(1574128076......)

n=80124: c24240(9901000000......) = 9231615018649 * c24228(1072510062......)

n=80143: c68035(9850541874......) = 7011155358439 * c68023(1404981257......)

n=80184: c24576(9999000100......) = 7494907450057 * c24564(1334105880......)

n=80210: c29552(2219984729......) = 8038627992331 * c29539(2761646305......)

n=80270: c30612(2612820281......) = 6568314536011 * c30599(3977915897......)

n=80301: c47035(5609489865......) = 8107347313573 * c47022(6919020055......)

n=80322: c24320(9100000000......) = 8843757905533 * c24308(1028974345......)

n=80341: c80331(7666263173......) = 9320316507907 * c80318(8225324930......)

n=40181: c38402(3483969060......) = 7462365415199 * x38389(4668719455......)

n=40181: x38389(4668719455......) = 8989070395813 * c38376(5193773382......)

n=80394: c26797(1098901098......) = 5228325950503 * c26784(2101822092......)

n=80446: c36284(1130049484......) = 6323411332213 * c36271(1787088369......)

n=80454: c22873(4878124900......) = 7648812707383 * c22860(6377623674......)

n=20117: c20101(7116364428......) = 7864696087921 * c20088(9048492591......)

n=26827: c26474(2520446901......) = 9859120966147 * c26461(2556462092......)

n=80511: c52427(5419071708......) = 5860725946123 * c52414(9246417180......)

n=80516: c40245(6711422027......) = 5271309894569 * c40233(1273198154......)

n=40259: c39816(9000000000......) = 6105607393283 * c39804(1474054818......)

n=80528: c34465(1000000009......) = 6957319635841 * c34452(1437335155......)

n=80619: c41760(9009009910......) = 7632592054627 * c41748(1180334262......)

n=80712: c25046(2489792711......) = 8477602192369 * c25033(2936906751......)

n=80713: c80681(5739377461......) = 8718554981009 * c80668(6582945768......)

n=80721: c53808(9990000009......) = 5302914595003 * c53796(1883869677......)

n=40363: c39955(5574377682......) = 7799023218671 * c39942(7147533128......)

n=40385: c31353(1521719578......) = 7798892332151 * c31340(1951199623......)

n=80818: c38012(1361066085......) = 7084803855967 * c37999(1921106234......)

n=40411: c32980(6394502696......) = 5183351749283 * c32968(1233661732......)

n=80850: c16795(2473710640......) = 5523672970201 * c16782(4478379972......)

n=80857: c69292(3046185766......) = 7316546170361 * c69279(4163420411......)

n=80864: c32827(6183182978......) = 5486957904737 * c32815(1126887263......)

n=80901: c52787(1333174936......) = 8761513417399 * c52774(1521626313......)

n=80938: c33840(9090909091......) = 5437513665299 * c33828(1671887125......)

n=80946: c26944(2212571421......) = 7665045480721 * c26931(2886573115......)

November 25, 2010 2010 年 11 月 25 日 (Bo Chen)

n=51537: c33441(1109999999......) = 10004716808413 * c33428(1109476681......)

November 25, 2010 2010 年 11 月 25 日 (Kurt Beschorner)

n=10839: c7215(4575091744......) = 17858029224736115580700471 * c7190(2561924211......)

# The ratio of the factored part of (10^10841-97)/3-1 was raised from 0.18% to 0.42%.

# See http://stdkmd.com/nrr/prime/primesize.txt

n=11289: c7281(1109999999......) = 14507587923737949287683 * c7258(7651168518......)

November 25, 2010 2010 年 11 月 25 日 (Makoto Kamada)

n=49029: c32001(1746124097......) = 5354627710921 * c31988(3260962650......)

n=98092: c48417(1009999999......) = 5079476946221 * c48404(1988393708......)

n=98096: c49016(1105178304......) = 5150609054897 * c49003(2145723531......)

n=49104: c14394(1542798225......) = 5887695797281 * c14381(2620376933......)

n=98267: c90696(9000000000......) = 5256288858757 * c90684(1712234666......)

n=98272: c47221(6954271989......) = 6294196106657 * c47209(1104870562......)

n=98281: c94864(9000000000......) = 6244600782631 * c94852(1441245055......)

n=98301: c53994(2411767374......) = 6332614512253 * c53981(3808486005......)

n=32769: c19801(1001000999......) = 6050430147961 * c19788(1654429479......)

n=98325: c47511(3798309462......) = 9867431136151 * c47498(3849339721......)

n=98352: c32721(5196923495......) = 6602734055809 * c32708(7870865995......)

n=98383: c95688(9000000000......) = 8264518308161 * c95676(1088992687......)

n=49200: c12800(9999999999......) = 6551973938401 * c12788(1526257597......)

n=98405: c78715(1524325450......) = 6797422795951 * c78702(2242504985......)

n=98419: c98413(2822392751......) = 5954007198719 * x98400(4740324720......)

n=98419: x98400(4740324720......) = 8928898627919 * c98387(5308969133......)

n=98441: c82320(9999999999......) = 5422921745641 * c82308(1844024396......)

n=49235: c38305(1111099999......) = 8939450457241 * c38292(1242917565......)

n=98506: c49233(7111447985......) = 9799303099007 * c49220(7257095645......)

n=98514: c30240(9990010000......) = 8814113781409 * c30228(1133410601......)

n=32842: c16420(9090909090......) = 5739118119859 * c16408(1584025437......)

n=98595: c44928(9990000009......) = 7933155030991 * c44916(1259272000......)

n=98619: c64681(1109999999......) = 7530444079003 * c64668(1474016656......)

n=49362: c15545(2539288301......) = 5266572165529 * c15532(4821519996......)

n=98762: c44344(5032731149......) = 5067599598499 * x44331(9931193362......)

n=98762: x44331(9931193362......) = 6843768096721 * c44319(1451129439......)

n=32934: c9960(9100000000......) = 5124569854933 * c9948(1775758796......)

n=98832: c31348(1023774585......) = 5813302588609 * c31335(1761089449......)

n=98903: c83145(4553926131......) = 7585212483157 * c83132(6003689602......)

n=98920: c39553(1000099999......) = 5648539929841 * c39540(1770546039......)

n=33017: c32640(9000000000......) = 9452473776973 * c32627(9521317077......)

n=33037: c33017(4241806894......) = 8344709715157 * c33004(5083228823......)

November 24, 2010 2010 年 11 月 24 日 (Kurt Beschorner)

n=7817: c7805(2501483294......) = 225516702199833629952889 * c7782(1109223073......)

n=7837: c7360(9000000000......) = 5132407524475594308359 * c7339(1753563012......)

n=10917: c7263(1565786879......) = 2418414073889416533001 * x7241(6474436684......)

n=10917: x7241(6474436684......) = 572237508770557725160522837 * c7215(1131424729......)

November 24, 2010 2010 年 11 月 24 日 ([XTBA>TSA] IvanleFou)

n=1034: c456(1803071778......) = 16771138093862687229221870527968178411115969 * p413(1075104008......)

# http://www.rechenkraft.net/yoyo/y_factors_ecm.php

# Phi_1034(10) is the 1008th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

November 24, 2010 2010 年 11 月 24 日 (Makoto Kamada)

n=97031: c88195(1159421783......) = 9955077475157 * c88182(1164653701......)

n=48517: c39985(1111110999......) = 6368781954361 * c39972(1744620883......)

n=97047: c62881(1001000999......) = 9024186444319 * c62868(1109242374......)

n=97048: c41563(1030519917......) = 9103141801489 * c41550(1132048626......)

n=97062: c27708(9295768354......) = 6537044556169 * c27696(1422013919......)

n=97088: c46074(3961511538......) = 5087593337089 * c46061(7786612010......)

n=97099: c95920(9000000000......) = 7005536714809 * c95908(1284698141......)

n=97118: c41581(1000000099......) = 7840413348811 * c41568(1275443086......)

n=32377: c32366(7862173201......) = 5570164852093 * c32354(1411479446......)

n=97139: c83256(9000000900......) = 6763563596077 * c83244(1330659610......)

n=97141: c88279(5356872116......) = 5377715268773 * c88266(9961241622......)

n=48594: c12661(5945349945......) = 7127865691129 * c12648(8340996033......)

n=48599: c46457(1488657496......) = 9082169553439 * c46444(1639098992......)

n=97208: c46810(1837186784......) = 8656027019977 * c46797(2122436517......)

n=19447: c19438(2264759307......) = 6763170507031 * c19425(3348665104......)

n=97298: c48648(9090909090......) = 5203584705499 * c48636(1747047392......)

n=97323: c64866(1165331289......) = 7032809126881 * c64853(1656992630......)

n=97411: c94012(2028870632......) = 8884519099009 * c93999(2283602083......)

n=32476: c15477(1934579452......) = 5381930611669 * c15464(3594582673......)

n=97449: c59035(2847636077......) = 9137795848369 * c59022(3116327092......)

n=97475: c66714(3205981275......) = 5940504118151 * c66701(5396816855......)

n=97501: c97490(2848703001......) = 7485058169041 * c97477(3805852857......)

n=48783: c26400(9009009909......) = 5543675826067 * c26388(1625096811......)

n=97601: c82068(7476907918......) = 6780073262453 * c82056(1102776862......)

n=97605: c51832(5641727266......) = 5082410256841 * c51820(1110049559......)

n=48813: c31825(1109999999......) = 8133960698317 * c31812(1364648836......)

n=97724: c44392(6439395492......) = 8516833936909 * c44379(7560785545......)

n=97728: c32513(1000000000......) = 6094622014081 * c32500(1640790844......)

n=97751: c97104(9000000000......) = 9613620040049 * c97091(9361718023......)

n=97752: c32577(1000099999......) = 5472630177433 * c32564(1827457671......)

n=48899: c48336(9000000000......) = 5429883246373 * c48324(1657494202......)

n=97804: c41833(1000000000......) = 5160299634169 * c41820(1937871966......)

n=97833: c65209(3184067375......) = 8819187287227 * c65196(3610386390......)

n=97910: c39161(1099989000......) = 6077333914651 * c39148(1809986114......)

n=48956: c24476(9900990099......) = 5706624090929 * c24464(1734999527......)

November 23, 2010 2010 年 11 月 23 日 (Kurt Beschorner)

n=7751: c7368(6308238900......) = 14228989976261686187 * x7349(4433370823......)

n=7751: x7349(4433370823......) = 27091290789814138013901197 * c7324(1636456105......)

# The ratio of the factored part of (10^7752-19)/9+1 was raised from 1.51% to 2.08%.

# See http://stdkmd.com/nrr/prime/primesize.txt

n=7783: c7528(2314119817......) = 1111468269971395997 * c7510(2082038579......)

n=7789: c7773(1575350493......) = 57493774540076563342963 * c7750(2740036648......)

n=8897: c7201(1111110999......) = 114773685652983524991826283 * c7174(9680886290......)

n=10827: c7179(7108665017......) = 15506674626574343881 * c7160(4584261415......)

November 23, 2010 2010 年 11 月 23 日 (Makoto Kamada)

n=95889: c63918(5219578997......) = 9936861236089 * c63905(5252744175......)

n=13699: c10997(5558926453......) = 7946920451471 * c10984(6995069961......)

n=47953: c47268(9000000000......) = 6322144139791 * c47256(1423567669......)

n=47956: c22669(1487951264......) = 5795445194321 * c22656(2567449460......)

n=95930: c37433(1974312824......) = 7493782708211 * c37420(2634601110......)

n=95943: c63950(1140477238......) = 7800187199347 * c63937(1462115214......)

n=47976: c15963(9175712880......) = 5617078439809 * c15951(1633538320......)

n=96004: c47995(1473298042......) = 7807227207581 * c47982(1887095127......)

n=96062: c46863(4023520004......) = 9048145486409 * c46850(4446789687......)

n=32021: c27995(4337414406......) = 5386291795831 * c27982(8052691110......)

n=96093: c64021(9074089633......) = 6800562532963 * c64009(1334314564......)

n=96174: c29376(9999999990......) = 6112898975899 * c29364(1635885040......)

n=48097: c41214(5197826904......) = 7962946342163 * c41201(6527517178......)

n=96200: c34560(9999999999......) = 5396439048001 * c34548(1853073834......)

n=96213: c59179(1922813752......) = 5166942710359 * c59166(3721376179......)

n=96262: c48119(4087724446......) = 6081505772939 * c48106(6721566334......)

n=48131: c48124(2885642368......) = 7276204406311 * c48111(3965862154......)

n=96275: c76978(4732696343......) = 5262304467401 * c76965(8993581372......)

n=48171: c32112(9009009009......) = 6939623222803 * c32100(1298198579......)

n=96344: c48154(8549418700......) = 5075081961577 * c48142(1684587316......)

n=96373: c90683(2334672743......) = 6676287376009 * c90670(3496962626......)

n=96421: c88986(7778381802......) = 5740816282787 * c88974(1354926097......)

n=16071: c9695(4922636726......) = 7616480302729 * c9682(6463138523......)

n=96433: c95040(9000000000......) = 7185481270441 * c95028(1252525705......)

n=96467: c82680(9000000900......) = 7802365176929 * c82668(1153496497......)

n=32173: c32166(8222735485......) = 9926260276489 * c32153(8283820146......)

n=96523: c82716(7767392702......) = 5137037262827 * c82704(1512037445......)

n=96535: c75251(2019468482......) = 8736275400481 * c75238(2311589767......)

n=96551: c76321(1111110999......) = 5692399403237 * c76308(1951920308......)

n=48286: c20665(1609960098......) = 8818612499117 * c20652(1825638782......)

n=96594: c30264(1797876905......) = 5713429329571 * c30251(3146756180......)

n=96616: c44545(1000099999......) = 5186923387673 * c44532(1928117932......)

n=48323: c41786(3407920767......) = 8947955219809 * c41773(3808602841......)

n=96704: c48315(3446932746......) = 8282860933057 * c48302(4161524351......)

n=96776: c48374(1692212372......) = 5143356781729 * c48361(3290093306......)

n=96807: c60721(1000000000......) = 6533891658001 * c60708(1530481453......)

n=48450: c11521(1000009999......) = 9833744754601 * c11508(1016916774......)

n=96935: c77523(2936479218......) = 7137583835801 * c77510(4114108199......)

November 22, 2010 2010 年 11 月 22 日 (Alfred Reich)

n=31061: c30597(7798226170......) = 282355206417733 * c30583(2761849611......)

n=31093: c27841(1111111111......) = 47621332646130769 * c27824(2333221372......)

n=31145: c24902(9050343006......) = 7642285102841 * c24890(1184245665......)

n=31199: c26717(1072718418......) = 67491785852401 * c26703(1589405887......)

n=31211: c29333(6152665962......) = 8395238587787 * c29320(7328756530......)

n=31251: c18906(2026110237......) = 499092473998113601 * c18888(4059588839......)

n=31483: c29808(9000000000......) = 6375979536119 * c29796(1411547817......)

n=31641: c20569(2792147620......) = 26441225322991 * c20556(1055982688......)

n=31677: c21107(1935973263......) = 5574449910973 * c21094(3472940459......)

n=31853: c31200(9000000000......) = 390987284638992919 * c31183(2301865138......)

n=99197: c82513(1111110999......) = 26073703407258646441 * c82493(4261423790......)

November 22, 2010 2010 年 11 月 22 日 (Serge Batalov)

n=99957: c55667(1453378373......) = 168127852323289 * c55652(8644483074......)

# ECM B1=1000, sigma=3366025544

n=99991: c99991(1111111111......) = 5520306265517599 * c99975(2012770773......)

# ECM B1=5000, sigma=4274774773

# R_99991 was the largest blank R_prime (n<=100000).

November 22, 2010 2010 年 11 月 22 日 (Makoto Kamada)

n=95202: c30234(5835541593......) = 5656422165103 * c30222(1031666559......)

n=95268: c29824(9901000000......) = 6862673726941 * c29812(1442732146......)

n=95290: c35136(9091000000......) = 5040057716201 * c35124(1803749185......)

n=47655: c25340(1049196840......) = 5408186862511 * c25327(1940015882......)

n=95311: c95289(4759427083......) = 5129865050803 * c95276(9277879702......)

n=47666: c23832(9090909090......) = 8851970969813 * c23820(1026992646......)

n=95365: c76269(4610099038......) = 8539277159311 * c76256(5398699389......)

n=47701: c47692(7220472878......) = 5856955836761 * c47680(1232803025......)

n=47760: c12672(9999999900......) = 7886053828801 * c12660(1268061329......)

n=47782: c20473(1099999890......) = 6901990349437 * c20460(1593743013......)

n=95577: c63716(9009009009......) = 8242175686999 * c63704(1093037730......)

n=47793: c31306(6654747697......) = 7353609056719 * c31293(9049634874......)

n=47805: c25482(3745014273......) = 5103780643231 * c25469(7337725766......)

n=95671: c92329(2545854707......) = 9331373926997 * c92316(2728274236......)

n=95687: c94656(9000000000......) = 5547134613169 * c94644(1622459274......)

n=47845: c32773(3332086704......) = 5268563558161 * c32760(6324469028......)

n=47851: c47299(3134719808......) = 5109629118677 * c47286(6134926303......)

n=95716: c47856(9900990099......) = 5894681824501 * c47844(1679647925......)

n=95795: c59126(2670561321......) = 8705999998151 * c59113(3067495200......)

n=47901: c27356(1158627484......) = 8046238973431 * c27343(1439961562......)

n=23955: c12764(2316772557......) = 8467981732081 * c12751(2735920589......)

November 21, 2010 2010 年 11 月 21 日 (Serge Batalov)

n=99940L: c18852(5793365960......) = 1130327396022112368701 * c18831(5125387547......)

# ECM B1=20000, sigma=1229003349

n=30446: c14041(1099999999......) = 2440105683444703 * c14025(4508001466......)

# ECM B1=5000, sigma=484664937

n=99980M: c19992(3576409999......) = 1848253916056919784641 * c19971(1935020923......)

# ECM B1=20000, sigma=200144992

# 1848253916056919784641 is the largest known factor that appears after n=99940M.

Largest known factors that appear after the previous one
  1  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
  2  n=1060M: 22534789481525070481066146802824209631029690388674663333618185041786620876200193924826168812981 (Raman / Sep 22, 2010)
  3  n=1220M: 27186363592392725942593454290345801336551729326489701011779461 (Shaopu Lin / Sep 7, 2007)
  4  n=1500L: 36605832263463437733314604426708004731796978480010361966001 (Polybius / Nov 3, 2010)
  5  n=1860L: 1891014345342089253412148254805092014919223493735583702021 (Yousuke Koide / Aug 14, 2010)
  6  n=5100L: 185898550709887865845976723509058449254706894935901 (Frank Boerner / Jun 28, 2010)
  7  n=13020M: 38362725655723071852811291205867646748081 (Kurt Beschorner / Sep 2, 2010)
  8  n=44666: 41824405819036936327873267050242047 (Alfred Reich / Aug 9, 2010)
  9  n=70140M: 461904211182554850127110960541 (Alfred Reich / Apr 26, 2010)
  10  n=99380M: 6592290434322258947071767721 (Alfred Reich / Apr 26, 2010)
  11  n=99874: 20466106492496275108462693 (Alfred Reich / Mar 29, 2010)
  12  n=99940M: 17594820928226575015141 (Alfred Reich / Dec 2008)
  13  n=99980M: 1848253916056919784641 (Serge Batalov / Nov 21, 2010)
  14  n=99992: 371044131599480009569 (Alfred Reich / Jun 17, 2010)
  15  n=99999: 1756539274631599 (Alfred Reich / Nov 16, 2010)
  16  n=100000: 66489400001 (Kurt Beschorner / Mar 13, 2008)

November 21, 2010 2010 年 11 月 21 日 (Makoto Kamada)

n=47341: c40549(1449358857......) = 5181472260637 * c40536(2797195053......)

n=94684: c47340(9900990099......) = 5705835845921 * c47328(1735239212......)

n=94704: c31534(5801835843......) = 5207172536641 * c31522(1114200807......)

n=47395: c37907(1898949469......) = 6315743667631 * c37894(3006691800......)

n=94804: c46785(1009999999......) = 5192335918661 * c46772(1945174610......)

n=94880: c37889(1000000000......) = 7190075472641 * c37876(1390805985......)

n=47466: c15757(7158766066......) = 9930189463489 * c15744(7209093132......)

n=95007: c57561(1109999999......) = 7643617742443 * c57548(1452191929......)

n=95067: c54211(1753146461......) = 8941678602067 * c54198(1960645801......)

n=47562: c15844(6107481433......) = 6568229442121 * c15831(9298520228......)

November 20, 2010 2010 年 11 月 20 日 (Kurt Beschorner)

n=7717: c7697(2392328944......) = 45480900389371853508000271 * c7671(5260073841......)

n=8053: c8048(3449263064......) = 9340552102231578320413 * c8026(3692782853......)

n=8063: c7315(4293094319......) = 489261952486215292258997 * c7291(8774633501......)

n=9595: c7178(1999954792......) = 37820106992790985480136161 * c7152(5288072805......)

n=10675: c7201(1000010000......) = 2103848037247402838351 * x7179(4753242546......)

n=10675: x7179(4753242546......) = 30244445738294936313315151 * c7154(1571608416......)

November 20, 2010 2010 年 11 月 20 日 (Makoto Kamada)

n=93397: c91742(4741520587......) = 8093771878391 * c91729(5858233539......)

n=93399: c61544(1972687538......) = 6353780795641 * c61531(3104745980......)

n=46737: c31095(1518805482......) = 9097519040443 * c31082(1669472166......)

n=93496: c40316(1069446089......) = 9180399447337 * c40303(1164923264......)

n=93517: c88000(9000000000......) = 6456426585347 * c87988(1393959937......)

n=93532: c45937(1009999999......) = 6733312093141 * x45924(1500004731......)

n=93532: x45924(1500004731......) = 8528768733241 * c45911(1758758829......)

n=46768: c22453(1860423715......) = 7692804528449 * c22440(2418394629......)

n=93561: c57535(1633872596......) = 6012027393997 * c57522(2717673239......)

n=93584: c46775(3371698589......) = 6693417696817 * c46762(5037334799......)

n=46797: c29521(1109999999......) = 5048703142837 * c29508(2198584405......)

n=93688: c39985(1000000000......) = 5516886928057 * c39972(1812616450......)

n=93712: c46843(2667740850......) = 5352801326401 * c46830(4983821904......)

n=93733: c92253(7758260245......) = 7136421006791 * c92241(1087136008......)

n=93770: c37488(9439327612......) = 7271908509601 * c37476(1298053681......)

n=93794: c44837(1099999999......) = 7150259624659 * c44824(1538405677......)

n=93801: c62525(6402922761......) = 6406585787761 * c62512(9994282404......)

n=93803: c88834(5485001069......) = 6880428850523 * c88821(7971888364......)

n=93834: c28800(9990010000......) = 5049597138769 * c28788(1978377626......)

n=46933: c46916(8589386972......) = 5583201775631 * c46904(1538433916......)

n=93866: c46921(9368281999......) = 6999916620331 * c46909(1338341941......)

n=46979: c46427(1229017105......) = 9623095770919 * c46414(1277153563......)

n=93981: c62647(4792969365......) = 9971865282721 * c62634(4806492295......)

n=46992: c14073(8411152532......) = 5634750100321 * c14061(1492728582......)

n=94103: c93282(6831415097......) = 6574248817399 * c93270(1039117211......)

n=94182: c28511(1109889553......) = 8330413534213 * c28498(1332334282......)

n=94183: c89200(1633481133......) = 5115504813893 * c89187(3193196356......)

n=94215: c45600(9009099100......) = 5028988861711 * c45588(1791433496......)

n=31423: c26532(9999999999......) = 9827007802081 * c26520(1017603750......)

n=94320: c24960(9999999999......) = 6505858952641 * c24948(1537076052......)

n=94328: c43489(1000099999......) = 7431977569433 * c43476(1345671445......)

n=47188: c22996(2140329314......) = 9533895890969 * c22983(2244968204......)

n=94384: c44264(4797500521......) = 7670742375377 * c44251(6254284509......)

n=94444: c40465(1009999999......) = 6189560372521 * c40452(1631779866......)

n=94468: c40320(9900990099......) = 9791286536461 * c40308(1011204203......)

n=47254: c23626(9090909090......) = 6358030992449 * c23614(1429830886......)

n=23651: c23222(1698014737......) = 8696413099481 * c23209(1952546087......)

n=18925: c15097(2935584409......) = 7738721674001 * c15084(3793371222......)

n=94667: c93830(2408374147......) = 5948897946751 * c93817(4048437489......)

n=94673: c89067(4903870385......) = 9727386044293 * c89054(5041303350......)

November 19, 2010 2010 年 11 月 19 日 (Makoto Kamada)

n=92332: c44961(1009999999......) = 7427089962389 * c44948(1359886584......)

n=46185: c24605(1966036185......) = 6352384659601 * c24592(3094957705......)

n=92376: c30764(1082520540......) = 8235364463353 * c30751(1314477999......)

n=92396: c46187(9772750686......) = 8193432245809 * c46175(1192754195......)

n=92398: c46198(9090909090......) = 8343476199769 * c46186(1089582911......)

n=92431: c92413(5925826763......) = 6667444743853 * c92400(8887702847......)

n=92437: c88396(9000000000......) = 5641341000733 * c88384(1595365357......)

n=92469: c56858(3807585195......) = 6356419296397 * c56845(5990141646......)

n=92484: c26352(9999990000......) = 6410877309649 * c26340(1559847352......)

n=46256: c19482(4503918183......) = 5068349480321 * c19469(8886360739......)

n=46264: c23111(3193800357......) = 6928939849121 * c23098(4609363664......)

n=92533: c79295(1259719339......) = 6691473186917 * c79282(1882573992......)

n=92582: c37238(1998015299......) = 5100955272841 * c37225(3916943380......)

n=15433: c13182(3854889532......) = 7060347948391 * c13169(5459914384......)

n=92632: c46307(3598095733......) = 9506179386553 * c46294(3785007190......)

n=92651: c85503(4769651617......) = 5684225015431 * c85490(8391032382......)

n=92692: c46339(1068159001......) = 5690663036309 * c46326(1877037868......)

n=92696: c46344(9999000099......) = 5897522524241 * c46332(1695457721......)

n=92748: c30150(1546340668......) = 5161216682269 * c30137(2996077793......)

n=23199: c12954(5710821269......) = 6006480650413 * c12941(9507766030......)

n=92825: c71761(1000010000......) = 8347531697801 * c71748(1197970892......)

n=92924: c42859(2173814786......) = 9241125651889 * c42846(2352326836......)

n=92934: c30954(1157024010......) = 5194824732001 * c30941(2227262843......)

n=46487: c38305(1111110999......) = 5577731538121 * c38292(1992048187......)

n=46507: c46488(1969165668......) = 5113262342561 * c46475(3851094539......)

n=93029: c90720(9000000000......) = 5878438506049 * c90708(1531018822......)

n=93030: c21217(1098890000......) = 7627531095451 * c21204(1440688980......)

n=93113: c93100(5620819405......) = 8918359601707 * c93087(6302526088......)

n=93133: c93122(1081119471......) = 9537552529243 * c93109(1133539729......)

n=31049: c30456(3386854255......) = 8695473274933 * c30443(3894962525......)

n=93150: c23760(9999999999......) = 6613405574401 * c23748(1512080256......)

n=93204: c31017(5463978521......) = 5788554373549 * c31004(9439279946......)

n=93252: c29376(9901000000......) = 9154519465621 * c29364(1081542295......)

n=93292: c45914(4510924252......) = 9778125208849 * c45901(4613281335......)

n=93299: c92040(9000000000......) = 5307444606797 * c92028(1695731310......)

n=46652: c22897(1009999999......) = 6764954922889 * c22884(1492988514......)

n=46671: c30353(3670293986......) = 9603006851653 * c30340(3822025791......)

n=93351: c58450(3367143989......) = 7604818491079 * c58437(4427645437......)

November 16, 2010 2010 年 11 月 16 日 (Alfred Reich)

n=89999: c66528(9000000900......) = 528029339442151 * c66514(1704450913......)

n=99999: c64780(6089634565......) = 1756539274631599 * c64765(3466836553......)

# 1756539274631599 is the largest known factor that appears after n=99992.

Largest known factors that appear after the previous one
  1  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
  2  n=1060M: 22534789481525070481066146802824209631029690388674663333618185041786620876200193924826168812981 (Raman / Sep 22, 2010)
  3  n=1220M: 27186363592392725942593454290345801336551729326489701011779461 (Shaopu Lin / Sep 7, 2007)
  4  n=1500L: 36605832263463437733314604426708004731796978480010361966001 (Polybius / Nov 3, 2010)
  5  n=1860L: 1891014345342089253412148254805092014919223493735583702021 (Yousuke Koide / Aug 14, 2010)
  6  n=5100L: 185898550709887865845976723509058449254706894935901 (Frank Boerner / Jun 28, 2010)
  7  n=13020M: 38362725655723071852811291205867646748081 (Kurt Beschorner / Sep 2, 2010)
  8  n=44666: 41824405819036936327873267050242047 (Alfred Reich / Aug 9, 2010)
  9  n=70140M: 461904211182554850127110960541 (Alfred Reich / Apr 26, 2010)
  10  n=99380M: 6592290434322258947071767721 (Alfred Reich / Apr 26, 2010)
  11  n=99874: 20466106492496275108462693 (Alfred Reich / Mar 29, 2010)
  12  n=99940M: 17594820928226575015141 (Alfred Reich / Dec 2008)
  13  n=99992: 371044131599480009569 (Alfred Reich / Jun 17, 2010)
  14  n=99999: 1756539274631599 (Alfred Reich / Nov 16, 2010)
  15  n=100000: 66489400001 (Kurt Beschorner / Mar 13, 2008)

November 18, 2010 2010 年 11 月 18 日 (Kurt Beschorner)

n=7723: c7654(1222279642......) = 591121431651159718318787 * c7630(2067730210......)

n=9005: c7185(3841412183......) = 1936418868436535335915567121 * c7158(1983771303......)

n=9595: c7191(5673517472......) = 28368228586361 * c7178(1999954792......)

n=12159: c6881(4994481441......) = 7822334559009561962838013 * c6856(6384898783......)

November 18, 2010 2010 年 11 月 18 日 (Makoto Kamada)

n=91728: c24179(6737472725......) = 9176884280929 * c24166(7341786732......)

n=91781: c91763(6112417791......) = 8694700486721 * c91750(7030049857......)

n=91787: c91165(6712159213......) = 9547765063283 * c91152(7030084181......)

n=91828: c41721(1009999999......) = 9438013060829 * c41708(1070140498......)

n=45921: c30612(9009009009......) = 7152732658333 * x30600(1259519884......)

n=45921: x30600(1259519884......) = 8982597993169 * c30587(1402177727......)

n=45938: c22636(3092911073......) = 7769917304609 * c22623(3980622898......)

n=91888: c45918(7513770302......) = 9314195602417 * c45905(8067009350......)

n=46015: c36802(1358266121......) = 8818852883471 * c36789(1540184578......)

n=92037: c55761(1109999999......) = 9024652876867 * c55748(1229964204......)

n=92094: c30686(2442383227......) = 5586620778853 * c30673(4371843595......)

n=92149: c89959(2441691060......) = 9832773051649 * c89946(2483217143......)

n=46097: c44574(7509242626......) = 7335975596357 * c44562(1023618812......)

November 16, 2010 2010 年 11 月 16 日 (Alfred Reich)

n=99003: c64801(1109999999......) = 236607740954281 * c64786(4691308895......)

n=99005: c79191(5916009941......) = 4142811101293121 * c79176(1428018270......)

n=99011: c89989(9014376654......) = 295303889057180587 * c89972(3052576342......)

n=99063: c65980(4802372133......) = 55060464584431 * c65966(8721997116......)

n=99077: c90060(9000000000......) = 36727920585599 * c90047(2450451824......)

n=99083: c99076(2002489454......) = 34714947331962311 * c99059(5768378202......)

n=99085: c63936(9000090900......) = 154913309519431 * c63922(5809759618......)

n=99095: c79263(1553005142......) = 78698145542791 * c79249(1973369425......)

n=99111: c66065(2065867563......) = 38280413774666554333 * c66045(5396669888......)

n=99135: c52849(1001000999......) = 1262269938768433921 * c52830(7930165880......)

n=99155: c67947(5829769702......) = 1046409055525751 * c67932(5571214881......)

n=99159: c66086(1964578457......) = 347403606470064891067 * c66065(5655031843......)

November 17, 2010 2010 年 11 月 17 日 (Makoto Kamada)

n=45573: c27574(3141676230......) = 7018348276237 * c27561(4476375504......)

n=91176: c29115(1566669241......) = 7708295303281 * c29102(2032445800......)

n=15201: c10112(3289149093......) = 9529079569489 * c10099(3451696535......)

n=91236: c30409(1009998990......) = 7135148330581 * c30396(1415526269......)

n=91245: c37408(5170064750......) = 8039388181441 * c37395(6430918167......)

n=45655: c34849(1111099999......) = 9661863647911 * c34836(1149985179......)

n=91339: c90712(1289037577......) = 9183426563293 * c90699(1403656433......)

n=91359: c60876(9204266394......) = 8675694751249 * c60864(1060925569......)

n=18277: c15613(2635961348......) = 9377384045401 * c15600(2810977278......)

n=91401: c60921(1797303177......) = 5720783654347 * c60908(3141708000......)

n=45705: c22070(1038513843......) = 6783033984871 * c22057(1531046204......)

n=91437: c58779(3640370864......) = 9055929440827 * c58766(4019875473......)

n=91454: c41554(3644818410......) = 7452853322773 * c41541(4890500661......)

n=45747: c25344(9990000009......) = 6372410709601 * c25332(1567695565......)

n=15249: c8441(2965830372......) = 7156869743791 * c8428(4144032906......)

n=45753: c30001(1109999999......) = 8535418247359 * c29988(1300463513......)

n=91627: c90010(2888949735......) = 7778120737921 * c89997(3714200168......)

n=45825: c22080(9999900000......) = 5231649251401 * c22068(1911424011......)

November 15, 2010 2010 年 11 月 15 日 (Alfred Reich)

n=34172: c17079(1931595220......) = 12456395205586731109 * c17060(1550685562......)

n=34510: c10753(1099988890......) = 1791041698862921 * x10737(6141615188......)

n=34510: x10737(6141615188......) = 58289088726037681 * c10721(1053647487......)

n=34772: c17350(1482468910......) = 3634682523576029 * c17334(4078675099......)

n=34822: c16593(1441033682......) = 407206211743333 * c16578(3538830306......)

n=34842: c11606(7884882544......) = 2283974015136097433251 * c11585(3452264558......)

n=34874: c14346(6684065063......) = 309112076259639964827167 * c14323(2162343556......)

n=34926: c11627(5916971258......) = 380173774647910945582520053 * c11601(1556385961......)

n=34998: c10994(1079616124......) = 12311143940123088518569 * c10971(8769421668......)

n=73230: c19509(1622242164......) = 44935390256641 * c19495(3610165963......)

n=73232: c34849(1000000009......) = 30456284604497 * c34835(3283394619......)

n=73242: c22456(3305799448......) = 19958310875514259 * c22440(1656352318......)

n=73244: c36614(2180292631......) = 378846367323864961 * c36596(5755083907......)

n=73250: c29192(1420886460......) = 794764802176667251 * c29174(1787807483......)

n=73270: c27520(9091000000......) = 2729819567910601 * c27505(3330256734......)

n=73290: c16697(1819626616......) = 33046192368697201 * c16680(5506312484......)

n=73292: c35983(2480649153......) = 224770740916829 * c35969(1103635261......)

n=73308: c23663(3490486996......) = 4869545241568621 * c23647(7167993772......)

n=73312: c34936(2937194593......) = 58799411155184449 * c34919(4995278925......)

n=73318: c31417(1099999890......) = 795013032524715813799359041 * c31390(1383624978......)

n=73320: c17649(8360143370......) = 42914795757601 * c17636(1948079496......)

n=73348: c33321(1009999999......) = 32312121659929140355129 * c33298(3125761937......)

n=73360: c24946(3645150527......) = 878464987055041 * c24931(4149454538......)

n=73382: c36690(9090909090......) = 678625831361419 * c36676(1339605519......)

n=73394: c36696(9090909090......) = 6439429340899 * c36684(1411756944......)

n=73408: c34561(1000000000......) = 376102900000769 * c34546(2658846820......)

n=73412: c36697(2062214389......) = 8705113105621 * c36684(2368969092......)

n=73438: c36129(1518735227......) = 85087350529813 * c36115(1784913055......)

n=73440: c18414(1465886021......) = 6520221214130881 * c18398(2248215165......)

n=73442: c36708(6242426581......) = 5139110064043782647 * c36690(1214690190......)

n=73462: c35113(1099999999......) = 401370581442223 * c35098(2740609428......)

n=73520: c29377(1000000009......) = 76733314784405954879041 * c29354(1303214924......)

n=73522: c36731(1550551266......) = 58053062808413 * c36717(2670920691......)

n=73538: c36237(4373757976......) = 12457947271249 * c36224(3510817538......)

n=73556: c30229(1028979670......) = 9429535546369 * c30216(1091230490......)

n=73596: c24514(2162505402......) = 279745880961954481 * c24496(7730249308......)

n=73606: c31953(1302857397......) = 6470778964450809997 * c31934(2013447538......)

n=73622: c36401(1099999999......) = 8868513923933 * c36388(1240343094......)

n=73634: c33450(1352513143......) = 20182301646765721 * c33433(6701481163......)

n=73654: c31552(1109726047......) = 13324602766819 * c31538(8328398727......)

n=73674: c24553(1000999998......) = 1850153215841533 * c24537(5410362722......)

n=73678: c31360(9090909091......) = 708241656977383 * c31346(1283588588......)

n=73692: c23220(2845682377......) = 16245149299669 * c23207(1751712049......)

n=73718: c33600(9090909090......) = 5087788866253 * c33588(1786809423......)

n=73726: c36476(1491990722......) = 369066347552179 * c36461(4042608415......)

n=73754: c36876(9090909090......) = 35418378500117 * c36863(2566720859......)

n=73762: c34033(1099999999......) = 1599996850553877049 * c34014(6875013532......)

n=73768: c36862(1056355525......) = 28454106023720129 * c36845(3712488890......)

n=73792: c36864(9999999999......) = 26796909748417 * c36851(3731773586......)

n=73796: c34908(2713186812......) = 8242515814961 * c34895(3291697430......)

n=73816: c36904(9999000099......) = 36097305901795249 * c36888(2770012844......)

n=73822: c31628(1490050377......) = 17749313801927 * c31614(8394974554......)

n=73840: c26880(9999999900......) = 20432418510401 * c26867(4894183179......)

n=73858: c36924(1230846490......) = 13475481246607 * c36910(9133970561......)

n=73872: c23319(1350532627......) = 11759763683377 * c23306(1148435176......)

n=73890: c19680(9990010000......) = 19300384325750041 * c19664(5176067912......)

n=73902: c24173(9770221758......) = 8147664462572079435019 * c24152(1199143853......)

n=73908: c24625(1000000999......) = 147110130929341 * c24610(6797635170......)

n=73914: c24192(9100000000......) = 5286097402321009 * c24177(1721496844......)

n=73930: c29562(2479797899......) = 31029263932412521 * c29545(7991803816......)

n=73936: c36960(9999999900......) = 417649189632907725569 * c36940(2394353957......)

n=73958: c36970(1124507254......) = 1231770521872643849 * c36951(9129194399......)

n=73960: c28891(2253465266......) = 12383769336871601 * c28875(1819692538......)

n=73972: c36964(8772950002......) = 528629916817764701 * c36947(1659563661......)

n=73984: c34816(9999999999......) = 192243852274433 * c34802(5201726807......)

n=74004: c21120(9901000000......) = 34763117395861 * x21107(2848133522......)

n=74004: x21107(2848133522......) = 135843629131981 * c21093(2096626496......)

n=74032: c31672(2115863481......) = 673296894463201 * c31657(3142541572......)

n=74036: c36400(9168018730......) = 2754078256156061 * c36385(3328888244......)

n=74040: c19712(9999000100......) = 96861104571841 * c19699(1032302919......)

n=74042: c36991(8470230690......) = 41704088053427983 * c36975(2031031269......)

n=74048: c33784(3445090210......) = 52305056729537 * c33770(6586533743......)

n=74062: c35065(1099999999......) = 41425289465899 * x35051(2655382772......)

n=74062: x35051(2655382772......) = 66847333305203797 * c35034(3972309202......)

n=74064: c24673(1000000009......) = 8408630492929 * c24660(1189254315......)

n=74068: c37012(6101059579......) = 5217345646267215569 * c36994(1169379986......)

n=74070: c19728(9990010000......) = 29003364430921 * c19715(3444431429......)

n=74072: c36046(3112604341......) = 6079949978857 * c36033(5119457154......)

n=74074: c25921(1099999889......) = 9522450591836183 * c25905(1155164712......)

n=74094: c24109(9805461954......) = 883696207973629849 * c24092(1109596472......)

n=74122: c37048(3000098028......) = 35769622449392307622441 * c37025(8387278989......)

n=74126: c34187(2979067379......) = 172444670293013 * c34173(1727549696......)

n=74170: c29649(1681882568......) = 6161328601201 * c29636(2729740089......)

n=74178: c22752(9990010000......) = 30241335746060011 * c22736(3303428818......)

n=74204: c34175(3741194879......) = 17784249858893129 * c34159(2103656273......)

n=74224: c37096(4971487450......) = 75304901992018850561 * c37076(6601811195......)

n=74226: c24288(9100000000......) = 18015816364687 * c24275(5051117204......)

n=74228: c28793(3368338012......) = 51875559942084341 * c28776(6493111623......)

n=74234: c37116(9090909090......) = 714537090037698166069487 * c37093(1272279524......)

n=74236: c36421(8657702347......) = 13133734014941 * c36408(6591958035......)

n=74238: c24735(1979407759......) = 219888599078014579 * c24717(9001866252......)

n=74250: c18000(9999999999......) = 5487364872001 * c17988(1822368337......)

n=74256: c18428(1346674401......) = 39331867437409 * c18414(3423876080......)

n=74278: c37132(5563193511......) = 4672438779393613 * c37117(1190640214......)

n=74292: c23995(3331774175......) = 1499007668533069 * c23980(2222653189......)

n=74296: c35982(4349210500......) = 123022291611841 * c35968(3535302784......)

n=74302: c36673(1099999999......) = 154649983460801 * c36658(7112836195......)

n=74312: c31825(1000099999......) = 102646126888637417 * c31807(9743183014......)

n=74316: c22474(1040846579......) = 8351707221130549 * c22458(1246268040......)

n=74324: c34937(5662145602......) = 142345623359509 * c34923(3977744779......)

n=74328: c23328(9999000100......) = 16763096990617 * x23315(5964888293......)

n=74328: x23315(5964888293......) = 4315277427158473 * x23300(1382272262......)

n=74328: x23300(1382272262......) = 4663173035455201 * c23284(2964231119......)

n=74332: c37147(5474533248......) = 12414482789701 * x37134(4409795672......)

n=74332: x37134(4409795672......) = 51170996110469 * c37120(8617763983......)

n=74342: c37131(1152994136......) = 3819592943890201 * x37115(3018630920......)

n=74342: x37115(3018630920......) = 5785257571125889 * c37099(5217798660......)

n=74360: c24954(2169046363......) = 66379544293062001 * c24937(3267642745......)

n=74366: c34885(1000000000......) = 25987082837773 * c34871(3848065618......)

n=74372: c37165(1611621659......) = 2537975619466663501 * c37146(6350028137......)

n=74376: c24741(1903661133......) = 1372015529955440187409 * c24720(1387492409......)

n=74382: c18471(8787002716......) = 28213856501131687 * c18455(3114428088......)

n=74386: c34305(1402402455......) = 39437314213727 * c34291(3556029318......)

n=74400: c19194(3200203788......) = 1745437380691201 * c19179(1833468117......)

n=74416: c37189(2957819870......) = 176454287586097 * c37175(1676252762......)

n=74428: c35540(2735714256......) = 19738266599729 * c35527(1385995190......)

n=74436: c24809(1009998990......) = 2164885507637320261 * c24790(4665369075......)

n=74444: c36145(1009999999......) = 121755074499255338914301 * c36121(8295342137......)

n=74448: c22070(2294023240......) = 583877811816289 * c22055(3928944026......)

n=74450: c29751(1496681459......) = 1252182167500651 * c29736(1195258564......)

n=74464: c34159(3361496867......) = 16348981436324161 * c34143(2056089476......)

n=74468: c37217(1197504963......) = 33014896211412881 * c37200(3627165616......)

n=74470: c27030(2444140193......) = 4254425193811799024700001 * c27005(5744936347......)

n=74478: c24825(1098901098......) = 715972215630103 * x24810(1534837630......)

n=74478: x24810(1534837630......) = 650482612077314521 * c24792(2359536753......)

n=74482: c36828(8242815750......) = 5840527268020927 * x36813(1411313631......)

n=74482: x36813(1411313631......) = 41291010132599413 * c36796(3417968287......)

n=74502: c24813(2013057137......) = 659986205529583477 * c24795(3050150322......)

n=74506: c37252(9090909090......) = 36736857673339 * c37239(2474601712......)

n=74516: c34363(4518025130......) = 254061851550781 * c34349(1778317013......)

n=74522: c31915(8022250395......) = 20515514986891 * x31902(3910333423......)

n=74522: x31902(3910333423......) = 36275758739723539 * c31886(1077946694......)

n=74534: c36737(1099999999......) = 122114156575648571 * c36719(9007964603......)

n=74546: c37272(9090909090......) = 805804139653509041 * c37255(1128178504......)

n=74574: c24841(1000000000......) = 783464591954287 * x24826(1276381870......)

n=74574: x24826(1276381870......) = 1306361165367293432533 * c24804(9770512962......)

n=74578: c31921(1000000099......) = 267505659382738053936207361 * c31894(3738239042......)

n=74594: c32400(9090909090......) = 202746989430982201982921 * c32377(4483868843......)

n=74598: c24865(1098901098......) = 5529233056947139 * c24849(1987438560......)

n=74602: c33875(2453952784......) = 8337277809521 * c33862(2943350144......)

n=74606: c31509(1388200381......) = 5195903535481 * x31496(2671720851......)

n=74606: x31496(2671720851......) = 23188419629957 * c31483(1152178929......)

n=74610: c19834(9707744304......) = 2001840001403469193801 * c19813(4849410691......)

n=74614: c37306(9090909090......) = 141141228578893 * x37292(6441001812......)

n=74614: x37292(6441001812......) = 1998272809183181441 * c37274(3223284519......)

n=74628: c24841(1000000000......) = 7957069900849 * c24828(1256744018......)

n=74636: c36422(2231226424......) = 28818981489241 * c36408(7742211241......)

n=74644: c37320(9900990099......) = 2851995031355320181 * c37302(3471601454......)

n=74658: c23760(9100000000......) = 372611152817192927089 * c23740(2442224268......)

n=74666: c36289(1099999999......) = 740458240994677 * c36274(1485566557......)

n=74670: c18689(5700510402......) = 17101839034036679286121 * c18667(3333273334......)

n=74672: c34353(1074538124......) = 6221183730529 * c34340(1727224545......)

n=74690: c23022(5935030087......) = 270301790546476921 * c23005(2195705058......)

n=74698: c32425(2299938155......) = 1485933403647733 * c32410(1547807021......)

n=74702: c36401(1099999999......) = 3238167493499893 * c36385(3396983022......)

n=74708: c35343(6774554923......) = 8022037811607601 * c35327(8444930182......)

n=74714: c37333(7085011979......) = 39385240699821899 * c37317(1798900261......)

n=74718: c21312(9990010000......) = 1952759231814133 * c21297(5115843180......)

n=74730: c19119(3001692716......) = 36866488500451 * c19105(8142062991......)

n=74734: c32754(3686166697......) = 2970972734739571 * c32739(1240727205......)

n=74744: c37361(8743569532......) = 239859696582854401 * c37344(3645284996......)

n=74752: c36850(8092941822......) = 4713611808176129 * x36835(1716930063......)

n=74752: x36835(1716930063......) = 56142652717310977 * c36818(3058156286......)

n=74760: c16880(4306235006......) = 5103792383761 * c16867(8437324018......)

n=74788: c32034(8440518164......) = 64213641522549709 * x32018(1314443156......)

n=74788: x32018(1314443156......) = 74342195213064211049 * c31998(1768098389......)

n=74804: c37381(6501941742......) = 8257355215559129 * c37365(7874121401......)

n=74810: c29908(1559903746......) = 107007022928202110281 * c29888(1457758288......)

n=74828: c34500(2059150005......) = 16953975530161489 * c34484(1214552894......)

n=74832: c24929(1000000009......) = 54004713160129 * x24915(1851690253......)

n=74832: x24915(1851690253......) = 23845885141878193 * c24898(7765240176......)

n=74844: c19440(9999999999......) = 57192310915741 * x19427(1748486787......)

n=74844: x19427(1748486787......) = 2017807841175589 * x19411(8665278983......)

n=74844: x19411(8665278983......) = 5970630680852579281 * x19393(1451317196......)

n=74844: x19393(1451317196......) = 2344176544266279863189281 * c19368(6191159963......)

n=74848: c37408(9999999999......) = 81174413620180897 * c37392(1231915274......)

n=74850: c19920(9999900001......) = 1841001294897400201 * c19902(5431772388......)

n=74854: c34537(1099999999......) = 11534467729904081 * c34520(9536634249......)

n=74872: c31909(4459592687......) = 43900587458401448881 * c31890(1015838954......)

n=74874: c24957(1098901098......) = 405286928774826846103 * c24936(2711415100......)

n=74882: c37414(3654015766......) = 31751357335029401809673809 * c37389(1150821909......)

n=74888: c31680(9999000099......) = 318684157007833 * c31666(3137589327......)

n=74894: c37446(9090909090......) = 105725790254099 * c37432(8598572844......)

n=74896: c35996(1335166975......) = 142674388060289 * c35981(9358140547......)

n=74904: c24961(1000099999......) = 193038099123930831409 * c24940(5180842561......)

n=74912: c37435(4449645585......) = 21446647947553 * c37422(2074751073......)

n=74920: c29912(9950999243......) = 43823897494241 * c29899(2270678742......)

n=74928: c21307(2224352635......) = 70092677215888321 * c21290(3173445107......)

n=74938: c36961(1099999999......) = 900824329441681 * c36946(1221103786......)

n=74944: c37430(6184896786......) = 8592825234574657 * c37414(7197745348......)

n=74950: c29953(4222266142......) = 392305694920651 * c29939(1076269398......)

n=74954: c34050(1619585972......) = 5337221567217494131 * c34031(3034511406......)

n=74960: c29942(1112287982......) = 439103749216481 * x29927(2533086962......)

n=74960: x29927(2533086962......) = 3121248527772961 * c29911(8115620847......)

n=74962: c36412(2310174397......) = 56414558040340961 * c36395(4094996890......)

n=74972: c37471(1110532470......) = 17038874379148574509 * c37451(6517639872......)

n=74974: c35487(7692016810......) = 3334616696503414081 * c35469(2306716936......)

n=74984: c29371(6667377991......) = 123278840072013809 * c29354(5408371775......)

n=74986: c37492(9090909090......) = 151773188043958681 * c37475(5989799125......)

n=74992: c36262(5013642807......) = 3505095271822556161 * c36244(1430387027......)

n=75004: c35265(1009999999......) = 3037273614287201 * c35249(3325350719......)

n=75022: c37496(1457822034......) = 1558792149561133 * c37480(9352254149......)

n=75026: c30624(9090910000......) = 4121829378145459 * c30609(2205552235......)

n=75028: c37499(5880438108......) = 11044859590413601 * c37483(5324140212......)

n=75030: c19194(4184572614......) = 292725656045041 * c19180(1429520278......)

n=75040: c25336(2576609817......) = 95854930628801 * x25322(2688030548......)

n=75040: x25322(2688030548......) = 1656130728145601 * c25307(1623078723......)

n=75044: c36854(3104232117......) = 29692405526751449 * c36838(1045463330......)

n=75050: c28080(9999900000......) = 2130134652872801 * c28065(4694491959......)

n=75058: c37516(2390612138......) = 51996695280379 * c37502(4597623224......)

n=75068: c32062(7220028512......) = 2921799464396739361 * c32044(2471089683......)

n=75080: c30003(9642204278......) = 320909907215921 * c29989(3004645248......)

n=75102: c25024(3372232065......) = 7462775807269543 * c25008(4518736931......)

n=75108: c22700(7989140995......) = 16083728140261 * x22687(4967219618......)

n=75108: x22687(4967219618......) = 893755362671029 * c22672(5557694896......)

n=75112: c36481(1000099999......) = 17076110860572697 * c36464(5856720000......)

n=75114: c22896(9999999990......) = 35185596937921 * c22883(2842072001......)

n=75120: c19968(9999999900......) = 61332623637121 * x19955(1630453632......)

n=75120: x19955(1630453632......) = 2758298514458881 * c19939(5911084764......)

n=75124: c32175(2177342789......) = 15419797484561 * c32162(1412043700......)

n=75136: c37504(9999999999......) = 233179326097409 * c37490(4288544858......)

n=75138: c21447(6552889408......) = 17420850643477 * c21434(3761520917......)

n=75142: c37570(9090909090......) = 2408376891658495649 * c37552(3774703669......)

n=75152: c28800(9999999900......) = 9146797080209713 * x28785(1093278861......)

n=75152: x28785(1093278861......) = 933204327352590833 * c28767(1171532138......)

n=75164: c33259(6586214302......) = 8585010722021 * x33246(7671760136......)

n=75164: x33246(7671760136......) = 11620513898009 * c33233(6601911243......)

n=75166: c29228(1330370907......) = 21536380869277 * x29214(6177318814......)

n=75166: x29214(6177318814......) = 1570147275482969 * c29199(3934228916......)

n=75168: c24180(3338197380......) = 5641186182358392762337 * c24158(5917545127......)

n=75176: c37584(9999000099......) = 87872472384721 * c37571(1137899028......)

n=75184: c36283(1330068471......) = 11334558872113 * c36270(1173462934......)

n=75188: c37592(9900990099......) = 14437347880201 * c37579(6857900897......)

n=75194: c31177(4565824362......) = 402731039221127 * x31163(1133715536......)

n=75194: x31163(1133715536......) = 3606426929312579 * c31147(3143597690......)

n=75204: c25051(1899593297......) = 2815769062950229 * c25035(6746268088......)

n=75206: c36355(7313197662......) = 3857797205427731 * c36340(1895692612......)

n=75216: c25052(1329486698......) = 57024759178561 * c25038(2331420101......)

n=75226: c36281(2512474837......) = 21741384541207 * c36268(1155618600......)

n=75240: c17265(1109994990......) = 4735023088158001 * c17249(2344222974......)

n=75256: c35905(1000099999......) = 41642307583913 * c35891(2401644044......)

n=75274: c36961(1099999999......) = 12276784732997921 * c36944(8960000716......)

n=75302: c35985(2803809091......) = 3557210450316314717 * c35966(7882044458......)

n=75322: c34746(1058258374......) = 72138743443729 * c34732(1466976445......)

November 15, 2010 2010 年 11 月 15 日 (Kurt Beschorner)

n=7619: c7186(2817962223......) = 144737797261685740994369 * c7163(1946942869......)

n=7639: c7633(3463142296......) = 546321155997228991 * x7615(6339022858......)

n=7639: x7615(6339022858......) = 20555946606306832871674679 * x7590(3083790291......)

n=7639: x7590(3083790291......) = 6316319463354529297788013163 * c7562(4882258267......)

n=8561: c7309(5287028838......) = 993489286650113398237 * c7288(5321676750......)

n=10641: c7080(4119481988......) = 281355727975207299283 * x7060(1464154299......)

n=10641: x7060(1464154299......) = 458903546581621416157 * c7039(3190549104......)

n=12158: c6074(3738499441......) = 205855888953153293607167 * c6051(1816076022......)

n=13180M: c2628(7142108190......) = 55939894275430908322795329346481 * c2597(1276746816......)

November 15, 2010 2010 年 11 月 15 日 (Serge Batalov)

n=30035: c24024(9000090000......) = 7497089451881 * c24012(1200477873......)

n=30132: c9721(1000000000......) = 39147920737669 * c9707(2554414081......)

n=30305: c20160(9000090000......) = 36250233627191 * c20147(2482767447......)

n=30393: c18361(1001000999......) = 5125650766039 * c18348(1952924703......)

n=30401: c25201(1111110999......) = 35091905491427 * c25187(3166288591......)

n=30457: c24625(1111110999......) = 15496090328881 * c24611(7170266669......)

n=30569: c23761(1111110999......) = 867662228919641 * c23746(1280580118......)

n=30691: c29992(9000000000......) = 5563075519711 * c29980(1617810142......)

n=38947: c34945(1111111111......) = 4391527626718961 * c34929(2530124379......)

November 14, 2010 2010 年 11 月 14 日 (Serge Batalov)

n=57060M: c7585(1105096689......) = 617954534022241261 * c7567(1788313911......)

# ECM B1=20000, sigma=3707336001

n=70620M: c8481(2555255162......) = 6616861364655301 * c8465(3861732960......)

# ECM B1=20000, sigma=1348675515

n=50260L: c8593(2798897498......) = 17053020467645401 * c8577(1641291350......)

# ECM B1=20000, sigma=1166516345

n=55300L: c9361(1010050200......) = 29543868293099097001 * c9341(3418814999......)

# ECM B1=20000, sigma=778225995

n=50020L: c9601(2796099999......) = 17450862877929521 * c9585(1602270340......)

# ECM B1=20000, sigma=4098272965

n=35980M: c6145(2798897498......) = 1567463078772641 * c6130(1785622600......)

# ECM B1=20000, sigma=4010373070

n=32140L: c6424(3576409999......) = 242410896607451458921 * c6404(1475350345......)

# ECM B1=20000, sigma=2336008583

n=60420M: c7489(2555229612......) = 12892550968426681 * c7473(1981942610......)

# ECM B1=20000, sigma=3184341552

n=54340L: c8641(2824086419......) = 23392545050494621 * c8625(1207259155......)

# ECM B1=20000, sigma=2657456716

n=49820M: c9552(3470608536......) = 1109826344891821 * c9537(3127163589......)

# ECM B1=20000, sigma=933055318

n=39420L: c5185(1000100005......) = 5989519820162881 * c5169(1669749888......)

# ECM B1=20000, sigma=3519377039

n=33740L: c5761(2798897498......) = 2400576836228170601 * c5743(1165927062......)

# ECM B1=20000, sigma=579818464

n=51900L: c6880(9900498997......) = 2139055914581155201 * c6862(4628443291......)

# ECM B1=20000, sigma=305485749

n=15580L: c2881(2796100002......) = 23450518368492991632421 * c2859(1192340381......)

# ECM B1=50000, sigma=4173991782

n=38940M: c4640(3952634573......) = 16320111321264112371901 * c4618(2421940938......)

# ECM B1=50000, sigma=486992047

n=26700L: c3520(9900498997......) = 38601661487793685774501 * c3498(2564785715......)

# ECM B1=50000, sigma=3044987442

n=26740M: c4539(4574991644......) = 48589398682675901889301 * c4516(9415616921......)

# ECM B1=50000, sigma=1009588846

n=38940L: c4625(1012940998......) = 111458284043415921481 * c4604(9088072792......)

# ECM B1=5000, sigma=702023669

n=71100L: c9360(9999999000......) = 151307250897027601 * c9343(6609067933......)

# ECM B1=20000, sigma=2061350365

n=58100M: c9840(9900498006......) = 19614198239066512901 * c9821(5047617999......)

# ECM B1=20000, sigma=253277566

n=56100L: c6401(1010050099......) = 3510226052085472501 * c6382(2877450297......)

# ECM B1=20000, sigma=1945224630

n=22980L: c3057(2529932837......) = 2226625792562220349100641 * c3033(1136218239......)

# ECM B1=50000, sigma=3922754277

n=26780M: c4896(3541003541......) = 1527096335898928601 * c4878(2318782029......)

# ECM B1=50000, sigma=1827071552

November 13, 2010 2010 年 11 月 13 日 (Kurt Beschorner)

n=7627: c7307(2805084138......) = 1746498928750246310839 * c7286(1606118442......)

n=10671: c7082(1054378088......) = 1926157246383763313859096841 * c7054(5473997985......)

n=10713: c7088(3619066117......) = 47544393671347955555671 * c7065(7611972386......)

n=15000: c3969(2883949573......) = 129142848769917176556570001 * c3943(2233146938......)

November 13, 2010 2010 年 11 月 13 日 (Serge Batalov)

n=72180L: c9600(9048972901......) = 81999321378187141 * c9584(1103542413......)

# ECM B1=10000, sigma=234875533

n=60340L: c10321(2798897498......) = 6242829137161 * c10308(4483379950......)

# ECM B1=10000, sigma=1965944107

n=81460M: c16289(2824060999......) = 1235431534188121 * c16274(2285890331......)

# ECM B1=10000, sigma=3987412581

n=85460M: c17089(2824060999......) = 227576997275081 * c17075(1240925503......)

# ECM B1=10000, sigma=2509309392

n=90140M: c18024(3576409999......) = 620867165096041 * c18009(5760346497......)

# ECM B1=10000, sigma=404612477

n=92780L: c18553(2824060999......) = 1012053646238845961 * c18535(2790426189......)

# ECM B1=10000, sigma=3892894994

n=42780M: c5281(2555229610......) = 278989047601262521 * c5263(9158888608......)

# ECM B1=5000, sigma=2966113891

n=47700M: c6241(1000000100......) = 487168198696801 * c6226(2052679347......)

# ECM B1=5000, sigma=522835906

n=55980M: c7441(1105096689......) = 3736154948851029421 * c7422(2957844910......)

# ECM B1=5000, sigma=1466319901

n=37580M: c7512(3576409999......) = 15233073844385861 * c7496(2347792727......)

# ECM B1=5000, sigma=1099995456

n=58860L: c7777(1000100005......) = 92198111771303821 * c7760(1084729378......)

# ECM B1=5000, sigma=1789753467

n=60660L: c8065(1105096689......) = 81400896778847221 * c8048(1357597684......)

# ECM B1=5000, sigma=1349271918

n=62340L: c8304(3913542626......) = 45803574274997881 * c8287(8544186100......)

# ECM B1=5000, sigma=3904694587

n=31220L: c5328(3537460769......) = 1304904857237381 * c5313(2710895549......)

# ECM B1=5000, sigma=498737806

n=49820M: c9568(3540999999......) = 10202821675058161 * c9552(3470608536......)

# ECM B1=5000, sigma=1059397187

n=28660L: c5728(3576409999......) = 8279899225270961 * c5712(4319388319......)

# ECM B1=5000, sigma=1969060391

n=25980L: c3457(2529932837......) = 191381370494090521 * c3440(1321932657......)

# ECM B1=250000, sigma=326047009

n=29460M: c3920(3913542626......) = 141768538359991447141 * c3900(2760515606......)

# ECM B1=250000, sigma=694925556

n=30300M: c4000(9900498997......) = 50449606777806001 * c3984(1962453154......)

# ECM B1=250000, sigma=827941391

n=24380L: c4577(2796100000......) = 726100491356612441 * c4559(3850844384......)

# ECM B1=250000, sigma=3483702338

n=38940L: c4641(2555255162......) = 25226100687320941 * c4625(1012940998......)

# ECM B1=250000, sigma=2379489246

n=21460L: c4033(2796100000......) = 47336521953124045121 * c4013(5906855604......)

# ECM B1=50000, sigma=1877101128

n=21820L: c4360(3576409999......) = 3351341417547990756121 * c4339(1067157759......)

# ECM B1=50000, sigma=2786210493

n=26740M: c4560(3537460769......) = 773216880938507212621 * c4539(4574991644......)

# ECM B1=50000, sigma=398933154

November 12, 2010 2010 年 11 月 12 日 (Serge Batalov)

n=14337: c9396(9999999999......) = 177620639147929 * c9382(5629976363......)

n=15499: c14080(9000000000......) = 393984570700601 * c14066(2284353416......)

n=15885: c8449(1001000999......) = 124865689583881 * c8434(8016621726......)

n=16115: c11681(1111099999......) = 910722335835401 * c11666(1220020588......)

n=16133: c13825(1111111111......) = 53742944448311 * c13811(2067454849......)

n=16185: c7872(9009099100......) = 332819078004271 * c7858(2706905852......)

n=16227: c10800(9999999990......) = 75351826302013 * c10787(1327107846......)

n=16275: c7200(9999900000......) = 12423972151251151 * c7184(8048875092......)

n=16537: c15796(9000000000......) = 1398716104622797 * c15781(6434472278......)

n=16897: c16560(9000000000......) = 1675521506016889 * c16545(5371461940......)

n=17097: c11041(1109999999......) = 34758484365679 * c11027(3193464905......)

n=17163: c11436(9990000009......) = 294766125015889 * c11422(3389127570......)

n=17187: c10753(1109999999......) = 60602202581797 * c10739(1831616595......)

n=18449: c17460(9000000000......) = 5047526327340157 * c17445(1783051620......)

n=22355: c16769(1111099999......) = 7006508213321 * c16756(1585811314......)

n=23755: c19000(9000090000......) = 1164574311474641 * c18985(7728223018......)

n=23775: c12641(1000010000......) = 105671065554151 * c12626(9463423074......)

n=27634: c13441(1099999999......) = 170619754989899 * c13426(6447084630......)

n=27693: c17281(1001000999......) = 460363425160987 * c17266(2174371258......)

n=28472: c14232(9999000099......) = 79404919126537 * c14219(1259241897......)

n=29183: c22681(1111110999......) = 125462824986054557 * c22663(8856097414......)

n=29529: c18433(1001000999......) = 40446579464479 * c18419(2474871826......)

n=42060M: c5600(3913542626......) = 30156233244524941 * c5584(1297755789......)

n=73060M: c13441(2796097203......) = 334162003782361 * c13426(8367489936......)

# ECM B1=300, sigma=2954984924

n=42500L: c8000(9999999999......) = 8134006018675001 * c7985(1229406515......)

# ECM B1=10000, sigma=2975242507

n=43100M: c8600(9900498007......) = 15187409530116601 * c8584(6518885257......)

# ECM B1=10000, sigma=2827915047

n=12757: c12757(1111111111......) = 1517635725253098067 * c12738(7321329437......)

n=12593: c10752(9999999000......) = 8822514833959 * c10740(1133463551......)

n=13137: c8401(1109999999......) = 269835362521905409 * c8383(4113619466......)

n=18091: c17784(9000000000......) = 7989852629267 * c17772(1126428786......)

n=18359: c16680(9000000000......) = 5480411650370911 * c16665(1642212405......)

n=18405: c9793(1001000999......) = 6756594727591 * c9780(1481517007......)

n=18880: c7425(1000000000......) = 19339020821722018561 * c7405(5170892617......)

n=19187: c16440(9000000900......) = 589089896882551 * c16426(1527780555......)

n=19587: c13056(9009009009......) = 341610869147209 * c13042(2637213807......)

n=19601: c18432(9000000000......) = 3337775698771249 * c18417(2696406473......)

n=19623: c12601(1109999999......) = 96766032092449 * c12587(1147096740......)

n=19745: c14308(1251537281......) = 29866298847001 * c14294(4190466611......)

n=20075: c14401(1000010000......) = 937275489531151 * c14386(1066932840......)

n=20355: c10194(2192103693......) = 222844191073711 * c10179(9836934421......)

n=20505: c10929(1109988900......) = 58879176060005911 * c10912(1885197746......)

n=21361: c20800(9000000000......) = 40345883353136597 * c20784(2230710856......)

n=21931: c17281(1111110999......) = 14212256955443 * c17267(7817977141......)

n=21999: c14664(9009009009......) = 85315648087717 * c14651(1055962090......)

n=22525: c16641(1000010000......) = 13674272608151 * c16627(7313076378......)

n=22919: c20161(1111111111......) = 11921628860831 * c20147(9320128348......)

n=33060M: c4032(3952674096......) = 2728317841166341 * p4017(1448758658......)

# ECM B1=250000, sigma=3000047341

Primality testing 1448758658...... [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 43, base 2+sqrt(43)
Calling N-1 BLS with factored part 0.35% and helper 0.04% (1.11% proof)
1448758658...... is Fermat and Lucas PRP! (5.4006s+0.0574s)

n=14075: c11240(9999900000......) = 265886823759001 * c11226(3760961095......)

n=14145: c7027(3268668149......) = 807195649651591 * c7012(4049412494......)

n=14271: c9241(1109999999......) = 70358358199483 * c9227(1577637722......)

n=14475: c7681(1000010000......) = 28317046900102801 * c7664(3531477006......)

n=15041: c13728(9999999999......) = 72580708409249 * c13715(1377776577......)

n=15243: c10160(9009009009......) = 4484204352312721 * c10145(2009054070......)

n=15285: c8145(1109988900......) = 2052778596741001 * c8129(5407250941......)

n=18109: c14257(1111110999......) = 82479851568479 * c14243(1347130212......)

n=19809: c12601(1001000999......) = 139702417649911 * c12586(7165237487......)

n=20343: c13560(9009009009......) = 116018896055063431 * c13543(7765122161......)

n=20839: c16417(1111110999......) = 525383983167317 * c16402(2114855107......)

n=21003: c14000(9009009009......) = 955250453098321 * c13985(9431043952......)

n=21285: c10080(9990000009......) = 23511962153791 * c10067(4248901025......)

n=21639: c14424(9009009009......) = 63348049417369 * c14411(1422144658......)

n=21931: c17267(7817977141......) = 10211122111373 * c17254(7656334980......)

n=22137: c14353(1109999999......) = 98126782527133 * c14339(1131189642......)

n=22325: c16561(1000010000......) = 322853183067001 * c16546(3097414095......)

n=22627: c19345(1557940781......) = 41009844785471 * c19331(3798943374......)

n=22857: c14401(1109999999......) = 19548440747197 * c14387(5678202237......)

n=23335: c17185(1111099999......) = 97150280303441 * c17171(1143692016......)

n=23435: c18145(1111099999......) = 312985482242311 * c18130(3550004914......)

n=23733: c15768(9999999999......) = 33992161025437 * c15755(2941854738......)

n=23743: c23743(1111111111......) = 777854575276722114923 * c23722(1428430385......)

n=25111: c25111(1111111111......) = 110761706366231 * c25097(1003154562......)

n=25645: c19537(1111099999......) = 30712244531951 * c19523(3617775310......)

n=26267: c26267(1111111111......) = 530296810477289 * c26252(2095262670......)

n=26290: c9520(9091000000......) = 746901096292891 * c9506(1217162492......)

n=26401: c24832(9000000000......) = 22754327236889 * c24819(3955291627......)

n=26579: c22776(9000000900......) = 2087489469486961 * c22761(4311399425......)

n=26735: c21384(9000090000......) = 9847447962734401 * c21368(9139515166......)

n=27007: c26642(5094967529......) = 418853136967961 * c26628(1216409065......)

n=27167: c23280(9000000900......) = 88120722307591 * c23267(1021326274......)

n=27205: c21760(9000090000......) = 254622930724991 * c21746(3534673792......)

n=27592: c13792(9999000099......) = 23081047923617249 * c13776(4332125704......)

n=27631: c27631(1111111111......) = 15470595321606757 * c27614(7182083740......)

n=27645: c13824(9009099100......) = 46756271117875951 * c13808(1926821554......)

n=27717: c18476(9009009009......) = 2175779153557003 * c18461(4140589817......)

n=27746: c13872(9090909090......) = 556859688989958373 * c13855(1632531366......)

n=27889: c27723(1000000000......) = 33389020758347 * c27709(2994996490......)

n=28454: c13841(1099999999......) = 1984440613368361 * c13825(5543123803......)

n=28472: c14219(1259241897......) = 21330378433858633 * c14202(5903514093......)

n=29415: c14976(9009099100......) = 23232009592921 * c14963(3877881964......)

n=29977: c28980(9000000000......) = 5257537677658963 * c28965(1711827960......)

November 11, 2010 2010 年 11 月 11 日 (Alfred Reich)

n=73444: c30240(9900990099......) = 8829699140641 * x30228(1121328138......)

n=73444: x30228(1121328138......) = 8408768466750961 * c30212(1333522432......)

n=73902: c24186(5863617413......) = 6001519268419 * c24173(9770221758......)

n=75064: c34069(7405456477......) = 7642781454617 * c34056(9689478263......)

n=75082: c30937(4921782029......) = 15911748645409 * c30924(3093174822......)

November 11, 2010 2010 年 11 月 11 日 (Serge Batalov)

n=13021: c12544(9000000000......) = 1510769082585616067 * c12526(5957230726......)

n=13211: c12000(9000000000......) = 9786011203684207361 * c11981(9196801242......)

n=13847: c13560(9000000000......) = 3124391853011683 * c13545(2880560577......)

n=14351: c14112(9000000000......) = 12661411679159 * c14099(7108212123......)

n=16473: c9793(1000000000......) = 266199856320187 * c9778(3756576032......)

n=17195: c12961(1111099999......) = 37330786464431 * c12947(2976363760......)

n=20447: c16633(1111110999......) = 3147855649443751 * c16617(3529739364......)

n=20463: c12889(1109999999......) = 5403086862289 * c12876(2054381186......)

n=21843: c14544(9999999990......) = 8512333793387911 * c14529(1174765961......)

n=23489: c23124(9000000000......) = 312120913627079 * c23110(2883497903......)

n=24727: c24336(9000000000......) = 156322605038969 * c24322(5757324730......)

n=25812: c8569(1000000000......) = 23153366813509 * c8555(4319026291......)

n=25879: c22176(9000000900......) = 303043473298837769 * c22159(2969871220......)

n=26049: c16417(1109999999......) = 151289872223911 * c16402(7336908833......)

n=26165: c20928(9000090000......) = 61257390147871 * c20915(1469225179......)

n=26247: c16129(1109999999......) = 9257286033529 * c16116(1199055528......)

n=26271: c14905(1000000001......) = 30133772784841951 * c14888(3318535678......)

n=26286: c8064(9100000000......) = 63091038453847 * c8051(1442360154......)

n=26631: c16081(1001000999......) = 7980433279015627 * c16065(1254319114......)

n=27981: c18648(9990000009......) = 130754398193281 * c18634(7640278375......)

n=14043: c9001(1109999999......) = 362116580229277 * c8986(3065311174......)

n=16723: c14328(9000000900......) = 49857232885774637 * c14312(1805154514......)

n=19359: c12852(9999999999......) = 37675664939683 * c12839(2654233181......)

n=19435: c13729(1000000000......) = 8900121310991 * c13716(1123580190......)

n=19555: c15640(9000090000......) = 192892875243311 * c15626(4665848849......)

n=20339: c18060(9999999999......) = 157022088112649 * c18046(6368530771......)

n=20785: c16624(9000090000......) = 59196063301464391 * c16608(1520386576......)

n=20925: c10801(1000000000......) = 120268310371201 * c10786(8314742236......)

n=21213: c14136(9990000009......) = 156027125628289 * c14122(6402732838......)

n=21663: c13777(1001000999......) = 7330065193127197 * c13761(1365609955......)

n=22017: c14241(1109999999......) = 229461541860037 * c14226(4837411929......)

n=22299: c14864(9009009009......) = 328812364347289 * c14850(2739863212......)

n=22801: c22651(1000000000......) = 12629155598041 * c22637(7918185758......)

n=22947: c15296(9009009009......) = 33883674348163 * c15283(2658805215......)

n=23979: c15984(9009009009......) = 5287513956306037 * c15969(1703826993......)

n=25554: c8517(1098901098......) = 474400411355413 * c8502(2316399970......)

n=26483: c26040(9000000000......) = 1012301747425643 * c26025(8890629718......)

n=26621: c22812(9000000900......) = 1398504821616827 * c22797(6435445027......)

n=26643: c17385(1109999999......) = 125561061198049 * c17370(8840320314......)

n=26693: x26678(2615731101......) = 436333346266009 * c26663(5994799902......)

n=26703: c16633(1000000001......) = 892407943565569 * c16618(1120563760......)

n=26843: c25248(9000000000......) = 31295533260239827 * c25232(2875809760......)

n=26869: c26496(9000000000......) = 191873156511969853 * c26479(4690598812......)

n=27172: c13584(9900990099......) = 3072309110080289 * c13569(3222654278......)

n=27455: c19585(1000000000......) = 2855769888007991 * c19569(3501682695......)

n=27577: c23761(1111111111......) = 59813649784747 * c23747(1857621320......)

n=27716: c12481(1000000000......) = 23840648998132409 * c12464(4194516684......)

n=27793: c27793(1111111111......) = 443336189669227 * c27778(2506249516......)

n=27843: c18560(9009009009......) = 32077079886889 * c18547(2808550229......)

n=28028: c10080(9999999999......) = 117454458421301 * c10066(8513938197......)

n=28315: c19393(1111099888......) = 2237014019279551 * c19377(4966888357......)

n=28437: c18956(9009009009......) = 149164370998003 * c18942(6039652062......)

n=29189: c27200(9999999999......) = 414253203047053 * c27186(2413982541......)

n=27961: c27961(1111111111......) = 197459648720034803 * c27943(5627028703......)

n=13213: c12960(9000000000......) = 1543986892026791 * c12945(5829065030......)

n=13823: c13200(9000000000......) = 22070342659515439 * c13184(4077870533......)

n=13875: c7201(1000000000......) = 9672912543751 * c7188(1033814784......)

n=14061: c9073(1109999999......) = 265303629480427 * c9058(4183885468......)

n=14145: c7040(9009099100......) = 27561987601231 * c7027(3268668149......)

n=14199: c9464(9009009009......) = 19029695846132563 * c9448(4734184446......)

n=14289: c8641(1109999999......) = 303096017546371831 * c8623(3662205821......)

n=15209: c14916(9000000000......) = 155823966730643 * c14902(5775748229......)

n=15549: c10081(1109999999......) = 126037837735639 * c10066(8806879108......)

n=16211: c14113(1111111111......) = 311505826922707 * c14098(3566903136......)

n=18421: c16848(9999999999......) = 7771662179399 * c16836(1286726027......)

n=18729: c12480(9990000009......) = 55966171492747 * c12467(1785006861......)

n=19131: c10921(1109999889......) = 1701176978545409191 * c10902(6524893664......)

n=19517: c18816(9000000000......) = 61486959539529533 * c18800(1463725002......)

n=20395: c16312(9000090000......) = 2384513194046761 * c16297(3774393038......)

n=20469: c13644(9009009009......) = 79825031640142279 * c13628(1128594480......)

n=20629: c17640(9999999000......) = 11882422451719 * c17627(8415791511......)

n=21029: c19776(9000000000......) = 54096953152043 * c19763(1663679648......)

n=21267: c13249(1001000999......) = 39870112253329 * c13235(2510655083......)

n=21415: c17128(9000090000......) = 61783459849121 * c17115(1456715118......)

n=21799: c21799(1111111111......) = 5267428575994133 * c21783(2109399482......)

n=21825: c11521(1000000000......) = 8021048179951 * c11508(1246719852......)

n=21957: c13489(1109999999......) = 233954273017453 * c13474(4744516890......)

n=23393: c23088(9000000000......) = 65373034612559 * c23075(1376714428......)

n=25946: c12972(9090909090......) = 437818918977876809 * c12955(2076408464......)

n=26221: c24192(9000000000......) = 9537348912053 * c24179(9436584613......)

n=26405: c21120(9000090000......) = 1459643592819361 * c21105(6165950404......)

n=26407: c26407(1111111111......) = 507685479929093 * c26392(2188581621......)

n=26621: c22797(6435445027......) = 83622045724631 * c22783(7695871311......)

n=26694: c8893(1000999998......) = 3172281368590729 * c8877(3155457800......)

n=27003: c18000(9009009009......) = 5029631586418729 * c17985(1791186661......)

n=27035: c21624(9000090000......) = 61931385668081 * c21611(1453235690......)

n=27523: c25888(9000000000......) = 28666120080119 * c25875(3139594746......)

n=27553: c27028(9000000000......) = 10817218719112079 * c27012(8320068433......)

n=27605: c22080(9000090000......) = 22034310944791 * c22067(4084579737......)

n=27697: c27697(1111111111......) = 524122654946333 * c27682(2119944827......)

n=27785: c22224(9000090000......) = 66572877282271 * c22211(1351915429......)

n=29035: c23224(9000090000......) = 101736169527991 * c23210(8846499767......)

n=29225: c19921(1000010000......) = 7899829330751 * c19908(1265862790......)

n=29497: c27216(9000000000......) = 292565497416557 * c27202(3076234237......)

n=29757: c15552(9009009909......) = 16549222238641 * c15539(5443766347......)

n=29774: c14886(9090909090......) = 21428984514995143 * c14870(4242342461......)

n=29867: c29867(1111111111......) = 424428255239759 * c29852(2617900899......)

n=99933: c66620(9009009009......) = 242235628098320711653 * c66600(3719109810......)

n=99985: c79984(9000090000......) = 4919525397084511 * c79969(1829463062......)

November 10, 2010 2010 年 11 月 10 日 (Kurt Beschorner)

n=7597: c7403(7132284440......) = 267903384646237932789521 * p7380(2662259922......)

# Phi_7597(10) is the 1007th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

Primality testing 2662259922...... [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 29, base 2+sqrt(29)
Calling N-1 BLS with factored part 0.15% and helper 0.04% (0.48% proof)
2662259922...... is Fermat and Lucas PRP! (25.7138s+0.0039s)

n=10683: c7105(2816403885......) = 2078571510923991231549493 * c7081(1354970887......)

n=10713: c7110(5912826965......) = 16337991000539321501239 * c7088(3619066117......)

November 10, 2010 2010 年 11 月 10 日 (Alfred Reich)

n=28537: c28513(1202138483......) = 56671787993053 * c28499(2121229144......)

n=28771: c28759(3168879481......) = 7121713448277107 * c28743(4449602618......)

n=66026: c33012(9090909090......) = 25519641024884915534179 * c32990(3562318561......)

November 10, 2010 2010 年 11 月 10 日 (Serge Batalov)

n=13911: c9272(9009009009......) = 19271795821801 * c9259(4674711735......)

n=14045: c11024(9999999999......) = 5185279729801 * c11012(1928536264......)

n=14225: c11360(9999900000......) = 12471589714151 * c11347(8018143820......)

n=15357: c10236(9009009009......) = 6205192235317 * c10224(1451850106......)

n=26300M: c5241(1010050200......) = 262831437505399901 * c5223(3842958096......)

n=27445: c19921(1111099999......) = 17055194598311 * c19907(6514730709......)

n=27461: c23532(9000000900......) = 101274337998961 * c23518(8886753621......)

n=27585: c14689(1001000999......) = 791234985044521 * c14674(1265112158......)

n=29161: c26400(9999999999......) = 7890461764769 * c26388(1267352950......)

n=29239: c25056(9000000900......) = 8967294992237 * c25044(1003647243......)

n=29309: c24337(1111110999......) = 37586534358787 * c24323(2956141125......)

n=29511: c19656(9999999990......) = 66625660777519 * c19643(1500923198......)

n=29902: c14950(9090909090......) = 4481129397961306823 * c14932(2028709346......)

n=14215: c11368(9000090000......) = 4534977931031 * c11356(1984594001......)

n=15517: c15196(9000000000......) = 7798811003209507 * c15181(1154022067......)

n=13395: c6624(9009099100......) = 12509321570621041 * c6608(7201908632......)

n=13579: c13176(9000000000......) = 9279807506213 * c13163(9698477036......)

n=13637: c12576(9000000000......) = 40087257424111 * c12563(2245102453......)

n=13689: c8424(9999999999......) = 708410891478889 * c8410(1411610143......)

n=13741: c10801(1111110999......) = 75551976369871 * c10787(1470657755......)

n=14225: c11347(8018143820......) = 51149932120951 * c11334(1567576629......)

n=14469: c7488(9009009909......) = 14351365930357 * c7475(6277458155......)

n=14781: c9073(1109999999......) = 5702688975283 * c9060(1946450183......)

n=18475: c14760(9999900000......) = 5011886176001 * c14748(1995236852......)

n=18997: c17160(9999999999......) = 3972552601799 * c17148(2517273149......)

n=19865: c15233(1111099999......) = 13410313504111 * c15219(8285414055......)

n=20197: c19116(9000000000......) = 46934446820231 * c19103(1917568142......)

n=24681: c15553(1109999999......) = 52340341468813 * c15539(2120735113......)

n=24911: c24024(9000000000......) = 66578706149587 * c24011(1351783553......)

n=25856: c12800(9999999999......) = 1058066556180411255809 * c12779(9451201289......)

n=26809: c23617(1111111111......) = 9104647116311 * c23604(1220378007......)

n=27007: c26656(9000000000......) = 176644894150237 * c26642(5094967529......)

n=27079: c24984(9000000000......) = 15892052410547 * c24971(5663208103......)

n=20581: c18700(9000000000......) = 262893395699639 * p18686(3423440887......)

# Phi_20581(10) is the 1005th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

Primality testing 3423440887...... [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.11% proof)
3423440887...... is Fermat and Lucas PRP! (159.2644s+0.0677s)

n=19549: c19264(9000000000......) = 595339990329547 * c19250(1511741214......)

n=15257: c12961(1111111111......) = 5673857744809 * c12948(1958299205......)

n=15293: c14880(9000000000......) = 2845263757213201 * c14865(3163151386......)

n=15563: c15288(9000000000......) = 3155202756931801 * c15273(2852431584......)

n=16269: c8960(9009009009......) = 40147828296643 * c8947(2243959235......)

n=16565: c13248(9000090000......) = 6135150525071 * c13236(1466971342......)

n=20093: c19740(9000000000......) = 250786427958991 * c19726(3588710949......)

n=20355: c10208(9009099100......) = 410979604906831 * c10194(2192103693......)

n=21085: c16864(9000090000......) = 23475280446041 * c16851(3833858352......)

n=21411: c12961(1000000001......) = 278210255397049 * c12946(3594403806......)

n=21525: c9600(9999900000......) = 14043076990951 * c9587(7120875294......)

n=22563: c14257(1001000999......) = 8688301513147 * c14244(1152125071......)

n=22627: c19360(9999999999......) = 6418729209504481 * c19345(1557940781......)

n=23613: c14785(1109999999......) = 193309376110231 * c14770(5742090851......)

n=23959: c20737(1111111111......) = 1149721282437521 * c20721(9664177988......)

n=25637: c24780(9000000000......) = 4151210394551881 * c24765(2168042364......)

n=26117: c20161(1000000100......) = 47149300074241 * c20147(2120922470......)

n=26361: c16801(1001000999......) = 6980155181947 * c16788(1434066971......)

n=28500M: c3600(9999999999......) = 2107540421233917001 * c3582(4744867476......)

n=19729: c19440(9000000000......) = 67924458722388272399 * c19421(1325001357......)

n=20971: c20592(9000000000......) = 441895211609303951 * c20575(2036681947......)

n=21145: c16912(9000090000......) = 21517641675911 * c16899(4182656322......)

n=21257: c20496(9000000000......) = 1926602368892879 * c20481(4671436174......)

n=21923: c19920(9000000000......) = 172669494575040013 * c19903(5212269846......)

n=23659: c23200(9000000000......) = 9233215329839 * c23187(9747416992......)

n=26143: c24120(9000000000......) = 756245730560893 * x24106(1190089363......)

n=26143: x24106(1190089363......) = 89482119398513791 * c24089(1329974492......)

n=26503: c24928(9000000000......) = 18167732662643 * c24915(4953837755......)

n=26693: c26693(1111111111......) = 424780326407117 * x26678(2615731101......)

n=27483: c18320(9009009009......) = 408727897593649 * c18306(2204158087......)

n=27502: c13750(9090909090......) = 3763524418463 * c13738(2415530784......)

n=13317: c8449(1109999999......) = 16976108228071 * c8435(6538601103......)

n=13531: c11592(9000000900......) = 16821537452791 * c11579(5350284375......)

n=16419: c10081(1109999999......) = 189303379964323 * c10066(5863603704......)

n=16479: c10980(9990000009......) = 25095375873049357 * c10964(3980813063......)

n=17423: c14041(1111110999......) = 15707694046283 * c14027(7073673555......)

n=17577: c9721(1000000000......) = 27960305222809 * c9707(3576498868......)

n=17653: c17388(9000000000......) = 82223906849801 * c17375(1094572168......)

n=17759: c14617(1111110999......) = 2601054724895173 * c14601(4271770944......)

n=17889: c11617(1109999999......) = 138896387377569079 * c11599(7991568542......)

n=18225: c9720(9999999999......) = 22532072369642551 * c9704(4438118179......)

n=18865: c11761(1000000000......) = 6846194939431 * c11748(1460665389......)

n=19155: c10209(1109988900......) = 49588205215951 * c10195(2238413137......)

n=19295: c14465(1111099999......) = 108175103007675391 * c14448(1027130984......)

n=19505: c15089(1111099999......) = 41341126616551 * c15075(2687638414......)

n=19509: c11137(1109999889......) = 791760445807843 * c11122(1401939052......)

n=19617: c12049(1109999999......) = 5103570058627 * c12036(2174948099......)

n=19743: c13160(9009009009......) = 228423262315987 * c13146(3943998048......)

n=19745: c14321(1111099999......) = 8877881758351 * c14308(1251537281......)

n=19829: c19500(9000000000......) = 3445266977759 * c19488(2612279413......)

n=19947: c12961(1109999999......) = 44375107592689 * c12947(2501402385......)

n=20119: c17401(1111111111......) = 8615937084107 * c17388(1289599843......)

n=20135: c16104(9000090000......) = 1720671938307601 * c16089(5230567082......)

n=20277: c13500(9999999990......) = 804265713367147 * c13486(1243370172......)

n=20371: c18792(9000000000......) = 681237286952197 * c18778(1321125571......)

n=20417: c19200(9000000000......) = 589471845653843 * c19186(1526790476......)

n=20845: c15121(1111099999......) = 360049203038801 * c15106(3085967113......)

n=20885: c16704(9000090000......) = 28443820667161 * c16691(3164163530......)

n=21045: c10560(9009099100......) = 14442089286271 * c10547(6238085723......)

n=21417: c12761(1000000000......) = 470029215603289 * c12746(2127527325......)

n=21653: c21228(9000000000......) = 3924487115540449 * c21213(2293293297......)

n=22131: c14748(9990000009......) = 84966507656119 * c14735(1175757399......)

n=22385: c15841(1000000000......) = 10253458562161 * c15827(9752806762......)

n=22803: c13801(1109999999......) = 18960148140121 * c13787(5854384637......)

n=22809: c15204(9009009009......) = 643459954547170249 * c15187(1400088528......)

n=22969: c22644(9000000000......) = 21919184122933 * c22631(4105992243......)

n=23109: c15404(9009009009......) = 28323833094871 * c15391(3180716740......)

n=23301: c15516(9999999990......) = 64057380545413 * c15503(1561100361......)

n=23317: c19980(9000000900......) = 7391006605499357 * c19965(1217696232......)

n=23425: c18720(9999900000......) = 5316616145801 * c18708(1880876806......)

n=23481: c15648(9990000009......) = 3480991709307391 * c15633(2869871819......)

n=24448: c12160(9999999999......) = 3441233174657 * c12148(2905935021......)

n=26072: c13032(9999000099......) = 155128982634634081 * c13015(6445604122......)

n=26087: c24696(9000000000......) = 29608997678683 * c24683(3039616571......)

n=26341: c21841(1111110999......) = 5294621392733 * c21828(2098565539......)

n=26390: c8065(1099988890......) = 1977315319226521 * c8049(5563042370......)

n=26889: c17924(9009009009......) = 1111192088976763 * c17909(8107517231......)

n=27885: c12480(9999999999......) = 14638213070911 * c12467(6831434924......)

n=27923: c23928(9000000900......) = 6105551871791 * c23916(1474068370......)

n=28500L: c3601(1000000000......) = 20501360882353396501 * c3581(4877724975......)

n=29263: c27000(9000000000......) = 11374784853563 * c26987(7912237563......)

n=29730: c7920(9100090999......) = 30490192443211 * c7907(2984596117......)

n=29935: c23944(9000090000......) = 5351872936681 * c23932(1681671091......)

n=12415: c9121(1111099999......) = 12280760975081 * c9107(9047484942......)

n=13097: c11220(9000000900......) = 17722684612067 * c11207(5078237917......)

n=13569: c9044(9009009009......) = 53989853590027 * c9031(1668648534......)

n=14555: c11201(1111099999......) = 181289145661961 * c11186(6128883204......)

n=14895: c7921(1001000999......) = 4648311873991 * c7908(2153472114......)

n=15865: c11953(1111099999......) = 6866824469801 * c11940(1618069611......)

n=16533: c9961(1001000999......) = 449802900760159 * c9946(2225421397......)

n=17021: c17021(1111111111......) = 6295656694885085321 * c17002(1764885166......)

n=17445: c9297(1109988900......) = 212163691521841 * c9282(5231757102......)

n=17574: c5600(9100000000......) = 1982644060537487047 * c5582(4589830409......)

n=17787: c9241(1000000000......) = 1925902697594107 * c9225(5192370316......)

n=18459: c10513(1001000999......) = 75740450323609 * c10499(1321620079......)

n=23349: c15121(1109999999......) = 5561737521952639 * c15105(1995779188......)

n=23507: c21360(9000000000......) = 14175838616809 * c21347(6348830741......)

n=23771: c21600(9000000000......) = 34541192539613 * c21587(2605584618......)

n=23895: c12529(1000000000......) = 5066261341111 * c12516(1973842114......)

n=24086: c12042(9090909090......) = 7517384533327264331 * c12024(1209318088......)

n=27384: c7776(9999000100......) = 393358323174937 * c7762(2541957170......)

n=27887: c27456(9000000000......) = 9974907276689 * c27443(9022640261......)

n=28252: c12097(1009999999......) = 15418874098181 * c12083(6550413432......)

n=29031: c19352(9009009009......) = 42881886988243 * c19339(2100889126......)

n=29969: c28644(9000000000......) = 16326970405639 * c28631(5512351511......)

n=14287: c11233(1111110999......) = 14973045681413 * c11219(7420741401......)

n=24134: c10961(1099999999......) = 382105948208557 * c10946(2878782717......)

n=24188: c12092(9900990099......) = 12426555694448089 * c12076(7967606102......)

n=28254: c8832(9100000000......) = 109760476869733 * c8818(8290780305......)

n=29153: c29153(1111111111......) = 1690692597206681 * c29137(6571928645......)

n=29141: c23761(1111110999......) = 2395186275012049 * p23745(4638933562......)

# Phi_29141(10) is the 1006th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

Primality testing 4638933562...... [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 8+sqrt(7)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.14% proof)
4638933562...... is Fermat and Lucas PRP! (255.9760s+0.0697s)

November 9, 2010 2010 年 11 月 9 日 (Kurt Beschorner)

n=7613: c7256(5910553621......) = 607254142399203891437 * c7235(9733245455......)

n=12153: c8100(9009009009......) = 24216916036135321 * x8084(3720130587......)

n=12153: x8084(3720130587......) = 42608769180525637 * c8067(8730903660......)

n=12155: c7644(9772476586......) = 2410496847106921 * x7629(4054133735......)

n=12155: x7629(4054133735......) = 20779683532762433228951 * c7607(1951008411......)

November 9, 2010 2010 年 11 月 9 日 (Alfred Reich)

n=18007: c16344(1584274983......) = 11896280396837 * c16331(1331739779......)

n=70201: c70201(1111111111......) = 23728981809233206790107 * c70178(4682506481......)

n=12114: c4021(2810771816......) = 995539901827070009162143 * c3997(2823364298......)

November 8, 2010 2010 年 11 月 8 日 (Alfred Reich)

n=14076: c4224(9999990000......) = 156238450624729908181 * c4204(6400466696......)

n=14154: c4025(4394585287......) = 122284157927089915051 * c4005(3593748660......)

n=99480: c26470(1449508063......) = 155524609662001 * c26455(9320120247......)

November 8, 2010 2010 年 11 月 8 日 (Serge Batalov)

n=14837: c14366(1514785536......) = 72584260788443 * c14352(2086933889......)

n=15837: c10529(1374043612......) = 14440710342786643 * c10512(9515069409......)

# P-1/P+1

November 7, 2010 2010 年 11 月 7 日 (Serge Batalov)

n=14507: c14256(9000000000......) = 25710833431159271 * c14240(3500469957......)

# ECM B1=20000, sigma=2983464440

n=14671: c13784(1531723132......) = 39919311874483 * c13770(3837047935......)

# ECM B1=5000, sigma=1102835741

n=14587: c14056(9000000000......) = 32768257717759 * c14043(2746560429......)

# ECM B1=5000, sigma=766153854

n=14417: c13287(9487856741......) = 47822672163293 * c13274(1983966247......)

n=14439: c9614(1800430068......) = 6867977491351 * c9601(2621485103......)

n=14477: c13975(4440519244......) = 12290307839759 * c13962(3613025241......)

n=14491: c14093(1592671466......) = 4034017665488929 * c14077(3948102360......)

n=14509: c13173(7455583979......) = 93344947447362161 * c13156(7987131798......)

n=14531: c13190(9775154106......) = 327682255416810361 * c13173(2983119758......)

n=14567: c12469(6477726120......) = 373995378564347 * c12455(1732033734......)

n=14631: c9747(1184129215......) = 410193719072923 * c9732(2886756087......)

n=14581: c12492(9000000900......) = 123512508634568723544303773 * c12466(7286712090......)

# ECM B1=20000, sigma=4012735522

n=14403: c9600(9009009009......) = 117680887045815832573 * c9580(7655456408......)

n=14635: c11698(2562375423......) = 14370518196716681 * c11682(1783077957......)

n=14639: c14639(1111111111......) = 3146931249825562547 * c14620(3530776565......)

n=14647: c14400(9000000000......) = 281970171679831 * c14386(3191826974......)

n=14677: c13529(8111167699......) = 64482252551159 * c13516(1257891493......)

n=14687: c13896(9000000000......) = 5070408706819373 * c13881(1775004840......)

n=14689: c14251(3403894812......) = 25721452374287341391 * c14232(1323368044......)

n=14709: c9804(9009009009......) = 3542771370014347 * c9789(2542927010......)

n=14711: c14344(4164650069......) = 8464966695391 * c14331(4919865865......)

n=14727: c9816(9009009009......) = 235505432568613 * x9802(3825393287......)

n=14727: x9802(3825393287......) = 5308202383591 * c9789(7206570154......)

n=14791: c12659(8092968080......) = 12073439068391 * c12646(6703117508......)

n=14803: c14545(3426720866......) = 133161097221637 * c14531(2573364847......)

n=14809: c14494(4279846819......) = 5702843925227 * c14481(7504758810......)

n=14837: c14395(4332776491......) = 50500575177253 * x14381(8579657709......)

n=14837: x14381(8579657709......) = 5663942188623281 * c14366(1514785536......)

n=14855: c11875(3365891148......) = 17751020397641 * c11862(1896167698......)

n=14869: c14869(1111111111......) = 12002311900856227 * c14852(9257475728......)

n=14907: c9929(1362984993......) = 5309509043107 * c9916(2567064078......)

n=14917: c12780(9000000900......) = 34393420855294056395729 * c12758(2616779801......)

n=14959: c12816(9000000900......) = 242327996398307 * c12802(3713974874......)

n=14989: c13813(2708362191......) = 21802721473963 * c13800(1242212902......)

n=15109: c14560(9000000000......) = 158370646020803 * c14546(5682871306......)

n=15133: c14688(9000000000......) = 6312391683273001 * c14673(1425767039......)

n=15163: c14848(9000000000......) = 653370370591853 * c14834(1377472931......)

n=15223: c14040(9000000000......) = 49459375531151 * c14027(1819675218......)

n=15245: c12192(9000090000......) = 44671781624521 * c12179(2014714809......)

n=15537: c10356(9009009009......) = 109699611067591 * c10342(8212434776......)

n=15599: c14760(9000000000......) = 6606792504511 * c14748(1362234396......)

n=15811: c15552(9000000000......) = 4689918693442643 * c15537(1919009814......)

n=15821: c14592(9000000000......) = 109815926334427 * c14578(8195532561......)

n=15837: c10556(9009009009......) = 23721539992399 * x10543(3797817937......)

n=15837: x10543(3797817937......) = 276397190260957 * c10529(1374043612......)

n=15977: c14736(9000000000......) = 6324500562641 * c14724(1423037267......)

n=16053: c10700(9009009009......) = 57613240710510187 * c10684(1563704609......)

n=16106: c8052(9090909090......) = 12225798088689023887 * c8033(7435841018......)

n=16157: c15900(9000000000......) = 66220716118163 * c15887(1359091312......)

n=16207: c15336(9000000000......) = 26304618258679 * c15323(3421452427......)

n=16255: c13000(9000090000......) = 21406902093041 * c12987(4204293531......)

n=16309: c15916(9000000000......) = 145789597776679 * c15902(6173279944......)

n=16355: c13080(9000090000......) = 179946226364086081 * c13063(5001544173......)

n=16449: c10964(9009009009......) = 4415637301291639 * c10949(2040251133......)

n=16571: c16272(9000000000......) = 10133633305898551 * c16256(8881316037......)

n=16669: c16380(9000000000......) = 9554994178601 * c16367(9419158014......)

n=16769: c16320(9000000000......) = 210755420574289 * x16306(4270352798......)

n=16769: x16306(4270352798......) = 251079182258347 * x16292(1700799229......)

n=16769: x16292(1700799229......) = 15782636754917 * c16279(1077639469......)

n=16777: c15876(9000000000......) = 25131788900173 * c15863(3581121915......)

n=17223: c11480(9009009009......) = 64844741981083 * c11467(1389319894......)

n=17373: c11580(9009009009......) = 34954919880151 * c11567(2577322173......)

n=17495: c13992(9000090000......) = 26530743876071 * c13979(3392324784......)

n=17521: c15012(9000000900......) = 5090146009187 * c15000(1768122345......)

n=17607: c11736(9009009009......) = 37979102299760803 * c11720(2372096353......)

n=17735: c14184(9000090000......) = 17153978273561 * c14171(5246648828......)

n=17785: c14224(9000090000......) = 6145229719346831 * c14209(1464565266......)

n=17861: c17472(9000000000......) = 180737032339769 * c17458(4979610367......)

n=18035: c14424(9000090000......) = 741276286968071 * c14410(1214134346......)

n=18197: c17580(9000000000......) = 137363153034681523 * c17563(6551975403......)

n=18302: c9150(9090909090......) = 261104490665561 * c9136(3481713036......)

n=18339: c12224(9009009009......) = 32662429730587 * c12211(2758217647......)

n=18419: c18144(9000000000......) = 27254652771447043 * c18128(3302188465......)

n=18499: c17064(9000000000......) = 13919377940521 * c17051(6465806186......)

n=18563: c17568(9000000000......) = 70397166047045483 * c17552(1278460555......)

n=18611: c18072(9000000000......) = 340707941303929 * x18058(2641558622......)

n=18611: x18058(2641558622......) = 8143864798955267 * c18042(3243617971......)

n=18727: c18360(9000000000......) = 2056415372885351 * x18345(4376547714......)

n=18727: x18345(4376547714......) = 946926698731801 * c18330(4621844246......)

n=18781: c16092(9000000900......) = 37351470474053 * c16079(2409543931......)

n=18817: c18180(9000000000......) = 902611905617951 * c18165(9971062805......)

n=18829: c17820(9000000000......) = 4994461701976244270369 * c17799(1801995998......)

n=18847: c18400(9000000000......) = 14146012315493 * c18387(6362216997......)

n=18967: c17496(9000000000......) = 39663848590757 * c17483(2269068766......)

n=19033: c16308(9000000900......) = 361604029338763 * c16294(2488910567......)

n=19193: c18048(9000000000......) = 4340524918039601 * c18033(2073481933......)

n=19255: c15400(9000090000......) = 98412440901791 * c15386(9145276672......)

n=19277: c18720(9000000000......) = 2821921124310413 * c18705(3189316640......)

n=19321: c19183(1000000000......) = 39755052901093 * x19169(2515403519......)

n=19321: x19169(2515403519......) = 547078474421960881 * c19151(4597884284......)

n=19679: c17880(9000000000......) = 6255134869487923 * c17865(1438817897......)

n=19735: c15784(9000090000......) = 18820750706321 * c15771(4782003726......)

n=19739: c19739(1111111111......) = 10343933571483163 * c19723(1074166905......)

n=19999: c17136(9000000900......) = 81009554759729 * c17123(1110980171......)

n=14485: c11584(9000090000......) = 4606991307341767711 * p11566(1953572169......)

# Phi_14485(10) is the 1004th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

Primality testing 1953572169...... [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 23, base 3+sqrt(23)
Calling N-1 BLS with factored part 0.08% and helper 0.07% (0.31% proof)
1953572169...... is Fermat and Lucas PRP! (62.4372s+0.0783s)

November 6, 2010 2010 年 11 月 6 日 (Alfred Reich)

n=14194: c6867(1031120534......) = 4394001804830499637 * c6848(2346654780......)

n=14618: c7291(1216426068......) = 2436052512587885912915699 * c7266(4993431227......)

n=15010: c5594(1443525407......) = 3156875107699511443081 * c5572(4572640214......)

n=12010: c4749(5637556467......) = 2442638856271163903621761 * c4725(2307977887......)

n=14256: c4315(2597989675......) = 384968604460972625281 * c4294(6748575456......)

n=14332: c7164(9900990099......) = 22513288673933375800025821 * c7139(4397842644......)

n=14362: c6956(3837965408......) = 6173117789805541903545241 * c6931(6217223677......)

n=14724: c4875(2172675737......) = 77867204524505205255469 * c4852(2790232101......)

n=14738: c7350(7411915458......) = 197311855283869947402373 * c7327(3756447096......)

n=15022: c6033(1211982495......) = 8974327105215919414380211 * c6008(1350499575......)

n=15044: c7484(4645451141......) = 1436076295276259330239781 * c7460(3234821963......)

n=15048: c4267(2410492881......) = 9356104244617585012801 * c4245(2576385233......)

n=15068: c7523(2313801423......) = 147558060456282171692111809 * c7497(1568061694......)

n=15116: c7537(7393946972......) = 151099594304313503010961 * c7514(4893426092......)

n=15132: c4600(7162657306......) = 83026979924678346339121 * c4577(8626903342......)

n=15140L: c2982(5730421724......) = 381277271849181567593656104821 * c2953(1502953925......)

n=15174: c5041(1000000000......) = 4224281125236884368201 * c5019(2367266693......)

n=15176: c6451(3495032963......) = 12416444050991264173009 * c6429(2814842115......)

n=15188: c7559(7149204564......) = 25055811155392021750745189 * c7534(2853311960......)

n=15236: c6987(1080313164......) = 16968225776179351179169 * c6964(6366683109......)

n=15258: c5063(2283402380......) = 41642545231979343861594481 * c5037(5483340098......)

n=15274: c6534(2526939799......) = 196343473965722630709961 * c6511(1286999638......)

n=15310: c6086(1827994231......) = 112030732721431002149258790241001 * c6054(1631689972......)

n=15316: c6553(1009999999......) = 57537762082503123290801 * c6530(1755368932......)

n=15408: c5058(2723082278......) = 261467649473976978823842193 * c5032(1041460495......)

November 5, 2010 2010 年 11 月 5 日 (Kurt Beschorner)

n=7549: c7535(7042252843......) = 1729495761991682239 * c7517(4071853194......)

n=7549: c7517(4071853194......) = 385183165849514468160331667935711 * c7485(1057121275......)

n=10611: c7014(3652782561......) = 4750700831758833206506003 * c6989(7688934098......)

n=12152: c5004(1156612303......) = 10700438116221460784297 * c4982(1080901820......)

November 4, 2010 2010 年 11 月 4 日 (Paul Bourdelais)

n=26249: c26249(1111111111......) = 789814730235940481 * c26231(1406799681......)

n=27407: c27407(1111111111......) = 1270953901298947 * c27391(8742339985......)

n=29881: c29881(1111111111......) = 347651754282961 * c29866(3196046323......)

n=30341: c30341(1111111111......) = 176833875434094161 * c30323(6283361196......)

n=33647: c33647(1111111111......) = 1000241258313533 * c33632(1110843110......)

n=34877: c34877(1111111111......) = 913384613482151 * c34862(1216476711......)

n=35279: c35279(1111111111......) = 62390949100358201 * c35262(1780885091......)

n=36017: c36017(1111111111......) = 165717098147643769 * c35999(6704867050......)

n=36721: c36721(1111111111......) = 366602552645776319 * c36703(3030832990......)

n=36923: c36923(1111111111......) = 2055613716136626744026321 * c36898(5405252467......)

n=36947: c36947(1111111111......) = 660266828109089 * c36932(1682821344......)

n=38119: c38119(1111111111......) = 5385648083137501999 * c38100(2063096388......)

n=38317: c38317(1111111111......) = 114791721057865445569 * c38296(9679366254......)

n=38393: c38393(1111111111......) = 8092344087682157 * c38377(1373039874......)

n=38671: c38671(1111111111......) = 282341997069871 * c38656(3935337720......)

n=39451: c39451(1111111111......) = 156262424409622907 * c39433(7110545707......)

n=39887: c39887(1111111111......) = 876036874142333 * c39872(1268338290......)

n=40129: c40129(1111111111......) = 48117574112360243 * c40112(2309158621......)

n=47591: c47591(1111111111......) = 15628211237773843 * c47574(7109649941......)

n=48091: c48091(1111111111......) = 638299254988387 * c48076(1740736970......)

n=49937: c49937(1111111111......) = 1055560852910040803 * c49919(1052626296......)

n=51169: c51169(1111111111......) = 429735588382027 * c51154(2585569222......)

n=51949: c51949(1111111111......) = 1754102947449225049 * c51930(6334355191......)

n=52201: c52201(1111111111......) = 45694662111747385145809 * c52178(2431599359......)

n=52237: c52237(1111111111......) = 271094993892973 * c52222(4098604312......)

n=52489: c52489(1111111111......) = 1270235737368991 * x52473(8747282716......)

n=52489: x52473(8747282716......) = 17308601141010653 * c52457(5053720196......)

n=53279: c53279(1111111111......) = 999005687905163 * c53264(1112217001......)

n=54011: c54011(1111111111......) = 1387876932083818013 * c53992(8005833121......)

n=54541: c54541(1111111111......) = 35853072838166489 * c54524(3099068010......)

n=54713: c54713(1111111111......) = 1046474855099544929 * c54695(1061765703......)

n=54833: c54833(1111111111......) = 6736230891070871 * c54817(1649455205......)

n=55103: c55103(1111111111......) = 315147271581049 * c55088(3525688499......)

n=56237: c56237(1111111111......) = 1626648925292793893 * c56218(6830675592......)

n=56333: c56333(1111111111......) = 776535922553915712319 * c56312(1430856034......)

n=56629: c56629(1111111111......) = 10390176848264293 * c56613(1069386139......)

n=57301: c57301(1111111111......) = 3778396606208773 * c57285(2940694762......)

n=57349: c57349(1111111111......) = 84634626874588734689 * c57329(1312832763......)

n=57389: c57389(1111111111......) = 3218006272977319 * c57373(3452793490......)

n=57527: c57527(1111111111......) = 1255386146451719 * c57511(8850751732......)

n=57637: c57637(1111111111......) = 3442359266708519 * x57621(3227760454......)

n=57637: x57621(3227760454......) = 3398867599750999093 * c57602(9496576020......)

n=58661: c58661(1111111111......) = 74326583744811043 * c58644(1494904050......)

n=59167: c59167(1111111111......) = 4631150469161569 * c59151(2399211855......)

n=59359: c59359(1111111111......) = 864799535224123 * c59344(1284819274......)

n=60169: c60169(1111111111......) = 5284223574377681 * c60153(2102695117......)

n=60217: c60217(1111111111......) = 1075775920854227 * c60202(1032846236......)

n=61057: c61057(1111111111......) = 1314115813014420079 * c61038(8455199306......)

n=62989: c62989(1111111111......) = 158058664532837410723 * c62968(7029738701......)

n=63617: c63617(1111111111......) = 222480780471410400559 * c63596(4994189200......)

n=65839: c65839(1111111111......) = 4025998696200789340609 * c65817(2759839719......)

n=66653: c66653(1111111111......) = 3539170275329431 * c66637(3139467798......)

n=66713: c66713(1111111111......) = 96885178203390151 * c66696(1146832912......)

n=71933: c71933(1111111111......) = 977879989655071 * c71918(1136244859......)

n=73459: c73459(1111111111......) = 491819878765843 * x73444(2259183003......)

n=73459: x73444(2259183003......) = 216585194149721951 * c73427(1043092078......)

n=73751: c73751(1111111111......) = 17761822074527359 * c73734(6255614465......)

n=73999: c73999(1111111111......) = 15577464177642178409203 * c73976(7132811210......)

n=74573: c74573(1111111111......) = 5275826348183650888921 * c74551(2106041855......)

n=77761: c77761(1111111111......) = 15645304436754043 * x77744(7101882328......)

n=77761: x77744(7101882328......) = 222455211166466321 * c77727(3192499870......)

n=79147: c79147(1111111111......) = 2169521335216884401 * c79128(5121457406......)

n=79159: c79159(1111111111......) = 19377630679826311 * c79142(5733988481......)

n=79241: c79241(1111111111......) = 567107203492746557 * c79223(1959261148......)

n=79399: c79399(1111111111......) = 1557577145021917 * c79383(7133586382......)

n=79829: c79829(1111111111......) = 2623401834588967529 * c79810(4235382839......)

n=81077: c81077(1111111111......) = 14642851911517231 * c81060(7588078591......)

n=81533: c81533(1111111111......) = 77210107773644843 * c81516(1439074679......)

n=82361: c82361(1111111111......) = 160468565558302843 * c82343(6924166781......)

n=82889: c82889(1111111111......) = 5609194453764604559496150317 * c82861(1980874651......)

n=83047: c83047(1111111111......) = 9371898206078489 * c83031(1185577442......)

n=83101: c83101(1111111111......) = 2555547146968391187797 * c83079(4347840392......)

n=83233: c83233(1111111111......) = 648719220642319289 * c83215(1712776615......)

n=83357: c83357(1111111111......) = 369734369993184061399 * c83336(3005160464......)

n=83983: c83983(1111111111......) = 15249560468670271 * c83966(7286184499......)

n=84127: c84127(1111111111......) = 27231630649340963 * c84110(4080222464......)

n=84443: c84443(1111111111......) = 85831669960805483141923 * c84420(1294523468......)

n=84827: c84827(1111111111......) = 3562952462946839 * c84811(3118512308......)

n=84947: c84947(1111111111......) = 112487003339638831 * c84929(9877684337......)

n=85363: c85363(1111111111......) = 1123850896209253 * c85347(9886641678......)

n=86689: c86689(1111111111......) = 130740712963241900895707 * c86665(8498585375......)

n=86959: c86959(1111111111......) = 812103448996429290909839 * c86935(1368189129......)

n=87041: c87041(1111111111......) = 938770897720121 * c87026(1183580694......)

n=87187: c87187(1111111111......) = 56979834161587643 * c87170(1950007625......)

n=87683: c87683(1111111111......) = 46441070502416231 * c87666(2392518301......)

n=89087: c89087(1111111111......) = 5816046432775409 * c89071(1910423384......)

n=89681: c89681(1111111111......) = 2503840221864253 * c89665(4437627854......)

n=90271: c90271(1111111111......) = 43331501674368161 * c90254(2564210950......)

n=91583: c91583(1111111111......) = 1592544743512156631 * c91564(6976953807......)

n=92489: c92489(1111111111......) = 128299030081650973 * c92471(8660323545......)

n=92987: c92987(1111111111......) = 511572669648437 * c92972(2171951664......)

n=93323: c93323(1111111111......) = 2060423387557627 * c93307(5392634920......)

n=93487: c93487(1111111111......) = 1749676717147862969 * c93468(6350379474......)

n=94321: c94321(1111111111......) = 5114689935143991203 * c94302(2172391924......)

n=96259: c96259(1111111111......) = 526022379659401 * c96244(2112288666......)

n=97007: c97007(1111111111......) = 243253706998712387 * c96989(4567704742......)

n=98387: c98387(1111111111......) = 542933463037529 * c98372(2046495909......)

n=98627: c98627(1111111111......) = 217765033827093119 * c98609(5102339395......)

# P-1

November 3, 2010 2010 年 11 月 3 日 (Polybius)

n=1500L: c186(2113195014......) = 36605832263463437733314604426708004731796978480010361966001 * p127(5772836960......)

# ECM B1=26e7, sigma=3307707165

# http://www.mersenneforum.org/showthread.php?p=235503

# Phi_1500(10) is the 1003th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

# 36605832263463437733314604426708004731796978480010361966001 is the largest known factor that appears after n=1220M.

Largest known factors that appear after the previous one
  1  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
  2  n=1060M: 22534789481525070481066146802824209631029690388674663333618185041786620876200193924826168812981 (Raman / Sep 22, 2010)
  3  n=1220M: 27186363592392725942593454290345801336551729326489701011779461 (Shaopu Lin / Sep 7, 2007)
  4  n=1500L: 36605832263463437733314604426708004731796978480010361966001 (Polybius / Nov 3, 2010)
  5  n=1860L: 1891014345342089253412148254805092014919223493735583702021 (Yousuke Koide / Aug 14, 2010)
  6  n=5100L: 185898550709887865845976723509058449254706894935901 (Frank Boerner / Jun 28, 2010)
  7  n=13020M: 38362725655723071852811291205867646748081 (Kurt Beschorner / Sep 2, 2010)
  8  n=44666: 41824405819036936327873267050242047 (Alfred Reich / Aug 9, 2010)
  9  n=70140M: 461904211182554850127110960541 (Alfred Reich / Apr 26, 2010)
  10  n=99380M: 6592290434322258947071767721 (Alfred Reich / Apr 26, 2010)
  11  n=99874: 20466106492496275108462693 (Alfred Reich / Mar 29, 2010)
  12  n=99940M: 17594820928226575015141 (Alfred Reich / Dec 2008)
  13  n=99992: 371044131599480009569 (Alfred Reich / Jun 17, 2010)
  14  n=99999: 821893328984521 (Alfred Reich / Jul 28, 2008)
  15  n=100000: 66489400001 (Kurt Beschorner / Mar 13, 2008)

November 3, 2010 2010 年 11 月 3 日 (Kurt Beschorner)

n=7471: c7160(3268054357......) = 94037681301076995827 * c7140(3475260461......)

n=7459: c7454(3723937095......) = 1700043485956980964409 * c7433(2190495199......)

n=7489: c7469(4610393303......) = 2652831840277051776352027 * c7445(1737913890......)

n=9421: c9421(1111111111......) = 4817755062641891803228111 * c9396(2306283936......)

November 2, 2010 2010 年 11 月 2 日 (Alfred Reich)

n=14088: c4689(1000099999......) = 7034806653138011359093033 * c4664(1421645326......)

n=16068: c4877(7127490207......) = 1368296044086465469 * c4859(5209026393......)

n=16266: c5421(1098901098......) = 144765760714756900321 * c5400(7590890922......)

n=17138: c7188(5952265980......) = 263604275213578322167 * c7168(2258030897......)

n=17526: c5523(1705209290......) = 1446911685748693 * c5508(1178516496......)

n=17606: c8802(9090909090......) = 2017926571665167 * c8787(4505074277......)

# The ratio of the factored part of (8*10^17606-11)/3+1 was raised from 0.15% to 0.24%.

# See http://stdkmd.com/nrr/prime/primesize.txt

n=17912: c8924(4875829969......) = 30015759970061753 * c8908(1624423294......)

n=18040: c6394(8660434658......) = 11596509745342721 * c6378(7468138990......)

n=18044: c8305(1009999999......) = 33151171352600549 * c8288(3046649511......)

n=19006: c8046(1280685826......) = 104663459422923639317 * c8026(1223622679......)

n=19160: c7615(6449159367......) = 322409873144081 * c7601(2000298348......)

n=19162: c7892(8444114000......) = 6818255837179821607 * c7874(1238456608......)

n=19572: c5561(2984517555......) = 192314112075597709 * c5544(1551897322......)

n=19586: c8377(2389549815......) = 26932124125301543 * c8360(8872489243......)

n=19712: c7681(1000000000......) = 72399380883225089 * c7664(1381227280......)

n=21910: c7488(9091000909......) = 22942795783072411 * c7472(3962464293......)

n=21950: c8755(3796530764......) = 37465005898485836851 * c8736(1013353841......)

n=22446: c7036(9588767668......) = 1355558247889821913699 * c7015(7073667017......)

n=22960: c7636(5902084276......) = 18125332129564801 * c7620(3256262690......)

n=23132: c11564(9900990099......) = 65599853216661299581 * c11545(1509300648......)

n=17876: c8623(1238886403......) = 930717893422366057402421 * c8599(1331108397......)

n=18114: c6037(1098901098......) = 773103130591216120489357 * c6013(1421415921......)

n=19466: c9732(9090909090......) = 45938080281148881852301573 * c9707(1978948409......)

n=21824: c9586(9885047470......) = 27524562432590198977 * c9567(3591354992......)

n=21898: c10941(2095648196......) = 220356511489392779 * c10923(9510262174......)

n=22204: c8640(9900990099......) = 19975170627732389409341 * c8618(4956648573......)

n=22908: c7210(1309718278......) = 81286041571977481 * c7193(1611246228......)

n=22936: c11017(4990776877......) = 7913885708154126713 * c10998(6306354503......)

n=22950: c5723(2349467113......) = 178308408770295357601 * c5703(1317642353......)

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