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October 31, 2010 2010 年 10 月 31 日 (Juno Fukos)

n=21870: c5793(4201815525......) = 386154744109715673524881 * c5770(1088117028......)

# ECM B1=50000, sigma=1894433935

October 29, 2010 2010 年 10 月 29 日 (Kurt Beschorner)

n=7331: c7325(8420123758......) = 11021319982693638937449920791 * c7297(7639850555......)

n=8807: c8807(1111111111......) = 762506521668989812406612803 * c8780(1457182436......)

n=9011: c9011(1111111111......) = 9028780257957352781209 * c8989(1230632576......)

n=13260L: c1524(7915519839......) = 56769796326238373215869721 * c1499(1394318872......)

October 29, 2010 2010 年 10 月 29 日 (Alfred Reich)

n=14394: c4782(2073119131......) = 1176942435515404703957689 * c4758(1761444798......)

n=14752: c7331(1863687921......) = 5491123068444536129 * c7312(3394001370......)

n=14974: c7481(1124281822......) = 94691446905424441 * c7464(1187310849......)

n=15158: c6232(8639344629......) = 1610492986164319973 * c6214(5364409968......)

n=15230: c6082(5050707313......) = 917743912603852555651 * c6061(5503395058......)

n=15798: c5245(9596684485......) = 1509802108933661855281 * c5224(6356253199......)

n=16144: c8042(7004371326......) = 80345702972914735097233 * c8019(8717792074......)

n=16586: c8269(5273057908......) = 22290933742862294761 * c8250(2365561698......)

n=17898: c5604(1394572187......) = 6829235943138121 * c5588(2042061804......)

n=19570: c7340(4645138214......) = 18910377042970211 * c7324(2456396402......)

n=19768: c8427(2561933384......) = 302691038809433 * c8412(8463856065......)

n=20364: c6765(3639080587......) = 14413394403780118298401 * c6743(2524790820......)

n=20556: c6841(1000000999......) = 405079789650436883161 * c6820(2468651918......)

n=21236: c10566(1461502945......) = 759009741302941 * c10551(1925539115......)

October 27, 2010 2010 年 10 月 27 日 (Serge Batalov)

n=27823: c27823(1111111111......) = 5919041700263843 * c27807(1877180745......)

# ECM B1=20000, sigma=387068013

October 25, 2010 2010 年 10 月 25 日 (Alfred Reich)

n=14004: c4648(1445306138......) = 25418117865051413216461 * c4625(5686125725......)

n=14118: c4293(4618851752......) = 19403875897022484845641 * c4271(2380375847......)

n=14148: c4657(7891646784......) = 336290276866129192834021 * c4634(2346677060......)

n=14252: c6097(1009999999......) = 5442279402932433912382309 * c6072(1855840035......)

n=14924: c5739(3625112261......) = 1104543434341827808852889 * c5715(3282000642......)

n=15200: c5740(1967079223......) = 211509463544791377601 * c5719(9300194849......)

n=15364: c7285(2128625613......) = 10065554525803214869729 * c7263(2114762389......)

n=16262: c7907(2818424295......) = 79183430667597023 * c7890(3559361184......)

n=16658: c8328(9090909090......) = 20134907245402852703 * c8309(4514999239......)

n=16664: c8315(5095874917......) = 1901636837181907513 * c8297(2679730860......)

n=16684: c8065(1009999999......) = 4728587901861203269 * c8046(2135944220......)

n=16882: c8032(1591429317......) = 33377295745155876281 * c8012(4767999568......)

n=16960: c6657(1000000000......) = 261441377122851841 * c6639(3824949252......)

n=17196: c5729(1009998990......) = 1118814135262861381 * c5710(9027406413......)

n=17634: c5865(1288787300......) = 66318467969691143887 * c5845(1943330930......)

n=17674: c8829(1148138934......) = 46993020083754352536449 * c8806(2443211636......)

n=17822: c7128(9090910000......) = 17385295819973663 * c7112(5229079846......)

n=18000: c4777(4404283716......) = 1319954216085857196001 * c4756(3336694305......)

n=18070: c6585(1209268045......) = 587495901467411 * c6570(2058342947......)

n=18394: c8600(1650789606......) = 147074528729475241 * c8583(1122417063......)

n=18438: c5231(6503963358......) = 260819912852384299 * c5214(2493660582......)

n=18454: c9188(6621415805......) = 7353588904229183171 * c9169(9004332294......)

n=18474: c6157(1098901098......) = 16260202639938379 * c6140(6758225117......)

n=18592: c7834(2896858856......) = 30795478320925249 * c7817(9406766884......)

n=18666: c5739(9864676848......) = 18446027800071621583 * c5720(5347859688......)

n=18772: c8209(1000000000......) = 520165855731038401 * c8191(1922463746......)

n=18810: c4321(1000999998......) = 722006751035527651 * c4303(1386413627......)

n=19162: c7909(2236507743......) = 26485996558135973 * c7892(8444114000......)

n=19200: c5092(9666324488......) = 363323163253785601 * c5075(2660530752......)

n=19534: c9766(9090909090......) = 326396915333077 * c9752(2785231313......)

n=19544: c8318(2135006073......) = 88006653308666849 * c8301(2425959848......)

n=19630: c7179(5036160746......) = 9561450461275961 * c7163(5267151429......)

n=19676: c9832(1677309474......) = 4665555906080664809 * c9813(3595090292......)

n=20094: c6226(1062418791......) = 976808552191012543 * p6208(1087642802......)

# Phi_20094(10) is the 1002th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

Primality testing 1087642802...... [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N-1 BLS with factored part 0.16% and helper 0.05% (0.55% proof)
1087642802...... is Fermat and Lucas PRP! (17.9213s+0.1531s)

n=20196: c5735(1342399206......) = 3152104337774468612114569 * c5710(4258739756......)

n=20514: c6288(9100000000......) = 1277481839387340303289 * c6267(7123388935......)

n=21082: c10317(2279061318......) = 3403217147328397249 * c10298(6696784894......)

n=21194: c10596(9090909090......) = 26802896570422903219 * c10577(3391763672......)

n=21438: c7118(8121101010......) = 227294134224410521 * c7101(3572947906......)

n=21606: c6615(4494880598......) = 3077156962670521849 * c6597(1460725160......)

n=23704: c11848(9999000099......) = 163936826117689441 * c11831(6099300771......)

n=23746: c11436(2712499028......) = 4952511127849063 * c11420(5477017534......)

n=21766: c10868(1408085092......) = 2614259389589983 * c10852(5386172077......)

n=23772: c6752(1481442105......) = 13447224507870301 * c6736(1101671281......)

n=21796: c10881(5377304746......) = 11262398642718589 * c10865(4774564386......)

n=23952: c7958(1127610642......) = 268366903105339201 * c7940(4201750026......)

n=21954: c7317(1098901098......) = 374131501011467066521 * c7296(2937205490......)

n=22258: c10722(9414654308......) = 335110827820560797567 * c10702(2809415132......)

n=22732: c11364(9900990099......) = 105208503113171609 * c11347(9410826887......)

n=22836: c6820(4667479491......) = 957944756060954472361 * c6799(4872388999......)

n=22860M: c2969(1636911796......) = 542291467562835923482021 * c2945(3018509222......)

n=23262: c7753(1098901098......) = 28743985396031999226253 * c7730(3823064490......)

n=23288: c11201(1000099999......) = 253340718523880929 * c11183(3947648075......)

n=23364: c6931(6879200170......) = 83434147816735189 * c6914(8245065540......)

# The ratio of the factored part of (10^23365-7)/3-1 was raised from 7.35% to 7.42%.

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

n=23798: c11627(1963597504......) = 781709947152851 * c11612(2511925953......)

n=23862: c7668(1781604306......) = 6392766266921267449 * c7649(2786906688......)

n=23936: c10231(1563954571......) = 2490285587262518884609 * c10209(6280221751......)

October 22, 2010 2010 年 10 月 22 日 (Paul Bourdelais)

n=2237: c2237(1111111111......) = 5007655482377436114944220906050489 * c2203(2218824987......)

October 16, 2010 2010 年 10 月 16 日 (Kurt Beschorner)

n=7237: c7224(8386133407......) = 2284670636020700600693 * c7203(3670609354......)

n=7367: c7171(5090238619......) = 7875195443327394323983951 * c7146(6463634656......)

n=11847: c7134(8101631432......) = 60954821924403209947 * c7115(1329120679......)

n=14000: c4801(1000000000......) = 1161008491856333894004001 * c4776(8613201428......)

October 14, 2010 2010 年 10 月 14 日 (Serge Batalov)

n=9209: c9209(1111111111......) = 198052390085540279237423977869613 * c9176(5610187842......)

# ECM B1=1000000, sigma=6868161888639481

October 13, 2010 2010 年 10 月 13 日 (Serge Batalov)

n=57506: c28729(2394072917......) = 2804361138093811 * c28713(8536963678......)

# ECM B1=50000, sigma=3505403259929040

n=28753: c28745(1099695795......) = 146523363725276443523 * c28724(7505259010......)

# ECM B1=50000, sigma=7378419592171772

n=28753: c28724(7505259010......) = 2403918101970650874689014321 * x28697(3122094302......)

# ECM B1=250000, sigma=5706490999123023

n=28753: x28697(3122094302......) = 256798906093100413738505213 * c28671(1215773988......)

# ECM B1=250000, sigma=7882015947410525

October 12, 2010 2010 年 10 月 12 日 (Raman)

n=1100M: c201(1010050200......) = 126239370797267198368490274128272780260464262689211651471701 * p141(8001071253......)

# snfs

# http://www.mersenneforum.org/showthread.php?p=233145

# n=1100M was the smallest blank Phi_n(10).

# Phi_1100(10) is the 1001th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

October 12, 2010 2010 年 10 月 12 日 (Kurt Beschorner)

n=6220L: c1219(3572892473......) = 650984681718130029836870181208361 * c1186(5488443236......)

n=8177: c6913(1111111111......) = 15174022101675760363 * x6893(7322456127......)

n=8177: x6893(7322456127......) = 68720292131201409573893747 * c6868(1065544964......)

n=8819: c8819(1111111111......) = 1308564568947085796671479340201 * c8788(8491068285......)

n=8821: c8821(1111111111......) = 258688483986989903283209 * c8797(4295170368......)

n=12150: c3168(5773217596......) = 1588120486435702456714183952251 * c3138(3635251636......)

n=12151: c11664(3623494510......) = 6444590420166132547 * x11645(5622536537......)

n=12151: x11645(5622536537......) = 106704055157435942359 * c11625(5269281030......)

October 8, 2010 2010 年 10 月 8 日 (Kurt Beschorner)

n=7193: c7172(9932991316......) = 7122863544251898018161 * x7151(1394522196......)

n=7193: x7151(1394522196......) = 561009819353050058177401 * c7127(2485735808......)

n=7531: c7040(2639463911......) = 15086886821132564923129 * x7018(1749508657......)

n=7531: x7018(1749508657......) = 58623651425594027075560883 * c6992(2984305166......)

n=7799: c7071(6589658072......) = 93596271798845197777859267 * c7045(7040513415......)

n=12149: c12136(1099944930......) = 170665499221213428037 * c12115(6445033916......)

October 7, 2010 2010 年 10 月 7 日 (Maksym Voznyy)

n=4554: c1303(3478979528......) = 734596899604121334094674312265986668491 * c1264(4735902820......)

# P-1

# Phi_4554(10) is a divisor of R_109296 = (R_109297-1)/10

October 7, 2010 2010 年 10 月 7 日 (Kurt Beschorner)

n=3771: c2489(9713840961......) = 1528311466719084712757275149427 * c2459(6355930170......)

n=6045: c2842(2879537730......) = 8347289059369125407252316841 * c2814(3449668161......)

n=7207: c7195(2635543514......) = 28997972284224123229205449 * c7169(9088716580......)

n=7339: c7099(2387873902......) = 142555448486527968431 * c7079(1675049202......)

n=7363: c7112(9916996808......) = 2602437869387746547 * c7094(3810656509......)

October 7, 2010 2010 年 10 月 7 日 (Bo Chen)

n=50957: c50957(1111111111......) = 307270111459079 * c50942(3616072861......)

# ECM B1=2000, sigma=2372431315

n=50971: c50971(1111111111......) = 744485249793401 * c50956(1492455507......)

# ECM B1=2000, sigma=1612717779

October 6, 2010 2010 年 10 月 6 日 (Yousuke Koide)

n=968: c440(9999999999......) = 262533769339473652474903068060921237392956780959193 * c390(3809033795......)

October 5, 2010 2010 年 10 月 5 日 (Kurt Beschorner)

n=11907: c6772(1844032118......) = 835627160840024910969361 * c6748(2206764218......)

October 4, 2010 2010 年 10 月 4 日 (Crunchers For More Power)

n=1001: c713(1154495233......) = 92521253115451330371924584256109612766459318729 * c666(1247816252......)

October 2, 2010 2010 年 10 月 2 日 (Kurt Beschorner)

n=7391: c6976(9875889585......) = 35145963004534571107519 * c6954(2809964144......)

n=8803: c8803(1111111111......) = 1782257487899914145091791 * c8778(6234290604......)

n=9775: c7007(1936728706......) = 107089537019402899565001751 * c6981(1808513473......)

n=12147: c8081(2929237284......) = 13757491497888517 * c8065(2129194326......)

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