News - May 2010
May 25, 2010 (Kurt Beschorner)
(947M^2·41)^41-1: c103 = p36 · p68, where
c103 = 2362173398256731063661799434624119504706160667865496429854790305768289058623324319081720258995684966349,
p36 = 126969862074066584512768336334546311 and
p68 = 18604205436395458234128907690400560110263311883610071424811458594059.
May 24, 2010 (Juno Fernadez)
(395L^2·41)^41-1: c102 = p38 · p65, where
p38 = 10122989125662935314419360518126913419 and
p65 = 17290075484724900921563153310191565436471755157776206393493452231.
gnfs.
May 22, 2010 (Juno Fernadez)
(316L^2·41)^41-1: c102 = p34 · p68, where
p34 = 2392227963341773236459132954206971 and
p68 = 48232657290126428854971183175193149234443370457995168132010222990471.
GMP-ECM, B1 = 1e6, sigma = 3605798824.
May 22, 2010
(461M^2·41)^41-1: c101 = p50 · p52, where
c101 = 34289792997885091862651897839385956633946741391337361829800545372340530554939855462531591386174238419,
p50 = 17703135192235200147380706386802004954056973781743 and
p52 = 1936933352512892274176237328425473616520507217226333.
This inconspicuous factorization is pleasant.
P-1 found the 52-digit prime factor, the 7th largest ever found by P-1,
compare Paul Zimmermann's list Record Factors Found By Pollard's p-1 Method.
GMP-ECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [P-1]
Input number is 34289792997885091862651897839385956633946741391337361829800545372340530554939855462531591386174238419 (101 digits)
Using B1=1000000000, B2=205702371522480, polynomial x^1, x0=3377881616
Step 1 took 175985ms
Step 2 took 180930ms
********** Factor found in step 2: 1936933352512892274176237328425473616520507217226333
Found probable prime factor of 52 digits: 1936933352512892274176237328425473616520507217226333
Probable prime cofactor 17703135192235200147380706386802004954056973781743 has 50 digits
Report your potential champion to Paul Zimmermann
(see http://www.loria.fr/~zimmerma/records/Pminus1.html)
May 21, 2010
10^49506+1: 4085275039658161.
May 17, 2010
10^46093-1: 28722364110319757. The first yet known factor of the repunit (1)46093.
10^17553+1: 28187426686731379.
10^17566+1: 3577639781909.
10^17662+1: 8041185952173581.
10^17680+1: 7087736331521.
10^17745+1: 7019386526881.
10^17753+1: 628967015093357.
10^17760+1: 7147159739493121.
10^17802+1: 163493945402401.
10^17939+1: 197312288745161.
10^17943+1: 5393042069058487.
10^17982+1: 1225512162243527329.
May 14, 2010
14 factors, found with P-1 and B1 = 2e5.
The remaining cofactor is composite (any time).
10^49523+1: 224148819137070853.
10^49523+1: 120888653179671996607.
10^49542+1: 263926758199541821.
10^49592+1: 602075402682571314241.
10^49628+1: 334932260109089.
10^49669+1: 263846632461439390826423.
10^49721+1: 125719240715927288543.
10^49740+1: 208909508713681.
10^49809+1: 36560612308093.
10^49825+1: 276465366222401.
10^49869+1: 3021172983166573.
10^49894+1: 104010660441221.
10^49909+1: 301859284500419.
10^49921+1: 26367064037190418089529.
May 12, 2010
10^7059+1: 2022481952519649329047. P-1 with B1 = 1e6.
10^7169+1: 1857854595945664134678338863. P-1 with B1 = 1e6.
10^15010M+1: 486348452021468471747321.
10^15090M+1: 3152213324193437059705520007587221. P-1 with B1 =
1e6. This p34 is
the largest yet known factor of
any Phi(n,10)
in the range 12301 < = n < = 100000, compare Makoto Kamada's list Phin10.txt.
10^15310M+1: 290686957995852421.
10^15430L+1: 494221314024857761.
May 11, 2010
10^49370L+1: 72224828909036886961.
10^49470M+1: 11885524147830721.
May 10, 2010
10^7430M+1: 114228976914226426561953821. P-1 with B1 = 1e6 and B2 = 2e9.
10^10630L+1: 349626930802196507521. P-1 with B1 = 1e6 and B2 = 5e9.
10^10690M+1: 1142990704006493161. P-1 with B1 = 1e6 and B2 = 4e9. The first yet known factor.
10^16030M+1: 4032988138159435421. P-1 with B1 = 1e6 and B2 = 7e9.
10^19510M+1: 695746381540181. P-1 with B1 = 1e6 and B2 = 1e9.
10^19510M+1: 4821958451605162695001. P-1 with B1 = 1e6 and B2 = 1e9.
10^19730M+1: 27680586679708993498841. P-1 with B1 = 1e6 and B2 = 1e9.
10^19930M+1: 6665950662020861. P-1 with B1 = 1e6 and B2 = 1e9.
10^19970M+1: 51582172014330234821. P-1 with B1 = 1e6 and B2 = 1e9. The first yet known factor.
10^21510M+1: 7440924136354921.
10^21630M+1: 2561172901049459504641. The first yet known factor.
10^21710M+1: 83031398901129935881. The first yet known factor.
10^21790L+1: 96039544195701581. The first yet known factor.
10^21810M+1: 86985948090661.
10^21830M+1: 142724114728591181.
10^21890M+1: 5132790922762141.
10^21910L+1: 693511988634192421.
10^21930M+1: 163009509563705080981.
10^21950L+1: 189474432087495101.
May 7, 2010
10^30230M+1: 53068341800195816561. P+1 with B1 = 1e5 and B2 = 1e8.
May 6, 2010
10^12820+1: 4593291081521. <--- corrected (Makoto Kamada)
10^13818+1: 4847456929561.
10^14033+1: 4547772035813.
10^14247+1: 4631345804521.
10^14532+1: 4716252481921.
10^15054+1: 4140579396409.
10^15260+1: 4298778929201.
10^17302+1: 4173067649801.
10^18463+1: 4867103620331.
10^18526+1: 4683855402301.
10^19065+1: 4819666355131.
10^20169+1: 4941067249927.
10^31650L+1: 4115375692201.
10^25117-1: 4995565993643.
10^28179-1: 4811183551711.
10^28207-1: 4781757657359.
10^28411-1: 4321223207597.
10^28737-1: 4341601937773.
10^28749-1: 4540274141929.
10^16110M+1: 3428140028134041541. P-1 with B1 = 1e6 and B2 = 1e7.
10^16150M+1: 66638292042505667408321248801. P-1 with B1 = 1e6 and B2 = 1e9.
10^16370L+1: 38834752572081807785461. P-1 with B1 = 1e6 and B2 = 1e7.
10^16430L+1: 129331820749544679941. P-1 with B1 = 1e6 and B2 = 1e7.
May 5, 2010
10^22019+1: 8574480531277.
10^22033+1: 5965921591169.
10^22186+1: 6877532208641.
10^22219+1: 9544847796361.
10^22278+1: 6231270217801.
10^22299+1: 3873261241567.
10^22078+1: 16454011361089.
10^22111+1: 30950336492557.
10^22226+1: 20116439613469.
10^22296+1: 46375597504801.
10^22353+1: 13024077737329.
10^22367+1: 36722820556801.
10^22369+1: 18195221796649.
10^22062+1: 375113132999221.
10^22138+1: 525015880408741.
10^22211+1: 642385513986077.
10^22221+1: 142991346776689.
10^22271+1: 241245326377771.
10^22387+1: 529730486978023.
10^22236+1: 5270982669277993.
10^22400+1: 23592270259622401.
10^22423+1: 14154244844982721.
10^22333+1: 204193252825381921.
10^22186+1: 8635482814752246949.
10^5429-1: 124918949663365788365911844507. P-1 with B1 = 1e6 and B2 = 3e9.
May 4, 2010
10^12268+1: 3841911090713.
10^14989+1: 3756612938807.
10^17464+1: 3568664908337.
10^18548+1: 3437003048777.
10^18725+1: 3721672881851.
10^19769+1: 3688260459259.
10^19949+1: 3389643950419.
10^12626+1: 5345582243921.
10^12815+1: 5779103147401.
10^13535+1: 5670413726291.
10^14586+1: 5255421857401.
10^14960+1: 5977878427841.
10^15137+1: 5906152238081.
10^15285+1: 5182549127491.
10^15335+1: 5269752400921.
10^15360+1: 5743967723521.
10^15478+1: 5549162499301.
10^16234+1: 5386132786469.
10^17063+1: 5898718754413.
10^17346+1: 5468094237061.
10^18291+1: 5671925732383.
10^19867+1: 5963442185677.
10^19901+1: 5769644784331.
10^19947+1: 5722404056893.
10^20345+1: 5902713079121.
10^20784+1: 5896194088129.
10^20838+1: 5535505633909.
10^20937+1: 5394655056841.
10^12831+1: 6903093217567.
10^12837+1: 6018092480863.
10^13227+1: 6487944369103.
10^13645+1: 6013151327851.
10^14543+1: 6730023447773.
10^14946+1: 6740838803401.
10^17996+1: 6865032378161.
10^18206+1: 6656289797669.
10^18356+1: 6950846842369.
10^18382+1: 6649564972961.
10^18449+1: 6190574495321.
10^19017+1: 6981277318129.
10^19284+1: 8085628856401.
10^19528+1: 6989182392433.
10^20447+1: 6399644861849.
10^20544+1: 6882645785089.
10^20758+1: 6257955568421.
10^12858+1: 7835791671289.
10^13521+1: 7212273549373.
10^14821+1: 7172037164797.
10^15647+1: 7207120451579.
10^15782+1: 7551684538009.
10^15909+1: 7986123782929.
10^17199+1: 7107832484299.
10^18348+1: 7901882409433.
10^18957+1: 7252336268041.
10^20359+1: 7589102072411.
10^20921+1: 7946068860893.
10^24217+1: 7719651152641.
10^12628+1: 8328860060137.
10^13113+1: 8483734919161.
10^13966+1: 8499806591009.
10^14765+1: 8363863668571.
10^15293+1: 8388900673091.
10^12671+1: 9374808127721.
10^15406+1: 9235725192289.
10^15463+1: 9144927523411.
10^15008+1: 9796124114561.
10^17751+1: 9225263076853.
10^20251+1: 9954608088811.
10^33570M+1: 5496790405501.
10^45150M+1: 5364686970301.
10^17510L+1: 5195114566501.
10^37430M+1: 5358422954441.
10^43450M+1: 5552339240801.
10^44850M+1: 5392913350501.
10^46530L+1: 6169509668521.
10^36590L+1: 6458393032681.
10^41690M+1: 8085722470321.
10^48770M+1: 8483866698361.
10^34210L+1: 8563655333641.
10^42270M+1: 8591219410201.
10^25251-1: 5697728866693.
10^24651-1: 5643637409521.
10^25963-1: 5275222106827.
10^28289-1: 5658395200561.
10^28683-1: 6516949009609.
10^28731-1: 6970968569959.
10^25495-1: 6734893813601.
10^99399-1: 6918302998267.
10^99645-1: 6093918317761.
10^25409-1: 7763652311243.
10^25435-1: 7070570247361.
10^25365-1: 8200628027551.
10^28339-1: 8033478564439.
10^24321-1: 8644781930929.
10^25015-1: 8757895986641.
10^24419-1: 9632773177591.
10^28379-1: 9256953899363.
10^99345-1: 9149706091711.
10^17647+1: 13307733746623.
10^17802+1: 11307629771461.
10^17811+1: 68979709869373.
10^17937+1: 76569971423401.
10^17021+1: 26548114628681.
10^18501+1: 12212312509321.
10^18652+1: 60110126436961.
10^18784+1: 18392703320513.
10^18822+1: 46484748247309.
10^18829+1: 22716226036837.
10^18873+1: 70100527442401.
10^18897+1: 15070597038373.
10^18947+1: 19827380199059.
10^18114+1: 19646994558409.
10^18169+1: 15926547898619.
10^18191+1: 10969727934647.
10^18199+1: 32157573125291.
10^18207+1: 18275420048887.
10^18222+1: 53828297013349.
10^18254+1: 18076894945961.
10^18280+1: 44638770686401.
10^18501+1: 12212312509321.
10^19137+1: 23719909814371.
10^19225+1: 94924983651401.
10^19235+1: 15213712742161.
10^19284+1: 60094592283601.
10^19319+1: 32330711242721.
10^19396+1: 36128705137409.
10^19411+1: 10101024204013.
10^19439+1: 54847481403961.
10^17851+1: 420029070278161.
10^17995+1: 195155181165001.
10^17040+1: 138816278003521.
10^18711+1: 189760954010167.
10^18838+1: 207950278082821.
10^19283+1: 232223614674503.
10^19305+1: 642544377686641.
10^19480+1: 602689875945281.
10^17595+1: 4601189334997441.
10^17599+1: 1188417830262851.
10^17808+1: 2835192888677857.
10^17813+1: 3015648053727613.
10^17861+1: 1119749265895409.
10^17864+1: 1547187401157553.
10^17037+1: 7449731995176721.
10^17187+1: 7589163406977001.
10^17224+1: 1033077712071953.
10^17328+1: 1761580611605569.
10^18821+1: 2823634892612623.
10^18866+1: 7187570456762149.
10^18961+1: 7985260353350573.
10^18962+1: 2174447520374729.
10^18054+1: 1311508004486221.
10^18361+1: 7600854525945647.
10^18367+1: 4058372284551691.
10^19161+1: 9812134385793757.
10^19268+1: 5248842796809281.
10^17984+1: 52034665366850561.
10^18568+1: 28690207370033089.
10^17634+1: 244292477944575961.
10^17917+1: 234066287664614401.
10^18107+1: 144959273021002001.
10^18320+1: 271916563114701121.
10^17993+1: 2373666214582855681.
10^18443+1: 1478220062567385853.
10^18446+1: 12557679446000553349.
10^18427+1: 222349679168504554291.
10^6626+1: 51816502002442239409. P-1 with B1 = 1e6 and B2 = 9e9.
10^6694+1: 4451116192445407325149. P-1 with B1 = 1e6 and B2 = 9e9.
10^5961-1: 48476901338918508360349507. P-1 with B1 = 1e6 and B2 = 1e9.
10^5319-1: 797628293919437150299108717. P-1 with B1 = 1e6 and B2 = 1e9.
10^5751-1: 5102655395070987783727931449. P-1 with B1 = 1e6 and B2 = 1e9.
May 3, 2010
10^6558+1: 1523797661845242169.
10^6604+1: 883919705482096490377.
10^6716+1: 11610857333093590244161.
10^6819+1: 15463040107977938034049.
10^10550L+1: 27994690863246361601.
Alfred Reich