News - January 2010
January 28, 2010 (Kurt Beschorner)
(173L^2·41)^41-1: c93 = p27 · p66, where
c93 = 178731916869575830597485633096428302523302251170450063775356889884776519720793408304340747529,
p27 = 184063757442789620840958893 and
p66 = 971032642996701706902472313016846330557830760493263281674775333453.
(185M^2·41)^41-1: c95 = p42 · p54, where
c95 = 92198782452472374987746701860201401239585013325129784121389279717435335311874299447710909003567,
p42 = 208984727151102584567567525159580989704393 and
p54 = 441174738983723588955780863638484628872944393182065719.
(285M^2·41)^41-1: c118 = p24 · p27 · p67, where
c118 = 1391422296613979608086608948185521646374320305770666066595210085857681248271624325036944795249069364729216637026940569,
p24 = 911430577750952860848733,
p27 = 334403146044881263970690381 and
p67 = 4565254666155346655336193720380195285544309241885247883826867438753.
(294M^2·41)^41-1: c126 = p27 · c99, where
c126 = 135768753934551647448386192348984557574614557500617945081054251394282602005972156102548285874233167704935921051559276973202957,
p27 = 305057854902076163459455969 and
c99 = 445059033074672132124193182109767278976066745783573553514441615782924549256942618225039029094721453.
This c99 was reserved by Kurt Beschorner. Done.
(295M^2·41)^41-1: c114 = p23 · c92, where
c114 = 495572454993319926165045376383975731860815325040801840835331538685391401489153339322581839811030486258725358851879,
p23 = 26403923306398178641813 and
c92 = 18768894654122600987051040130822474200888192597482162516496355506081197085203256195410887883.
This c92 was reserved by Kurt Beschorner. Done.
(459M^2·41)^41-1: c99 = p48 · p51, where
c99 = 108736338972966285607934380563507158674922212713484736057305025103627599852758180122023966144792993,
p48 = 130960816713794567704396329634937113769774802251 and
p51 = 830296738379401852307021198269784167931416539346243.
(469M^2·41)^41-1: c98 = p40 · p59, where
c98 = 60898250095015673159406591938100603234514958242394731252055277362068475741290979054951696439648151,
p40 = 1517548115380393855145230501955346135791 and
p59 = 40129370184582719033157707361151458851602394884702107583961.
January 23, 2010 (Robert Backstrom)
(722M^2·41)^41-1: c107 = p54 · p54, where
c107 = 89785639658278837510557473305826968293062510036860388258233724224556748180818209637265425220428851777130579,
p54 = 297478298689656120277855233400103513523320011166846971 and
p54 = 301822486056193291668040095131494375429560820646599049.
Nice split.
(749L^2·41)^41-1: c108 = p52 · p56, where
c108 = 269027263232832618293303652088686029653748079183646014626396928975061836330861122332834545819522112336486739,
p52 = 7069909371916196929376357324605950550741799074253419 and
p56 = 38052434491096830024310328056532807474879798942110404281.
(753L^2·41)^41-1: c106 = p46 · p61, where
c106 = 5171888449773432085754328712686987978299968331292344336517131052541720298192372818893185682698783564282647,
p46 = 4308029788946345361937987743695188050509058517 and
p61 = 1200522907952864600738649655184732512464462827505575871832891.
(786M^2·41)^41-1: c106 = p31 · p75, where
c106 = 1789886248674822562873369295630384690808745716039708697566149184788706634656383079492563295423417034419109,
p31 = 8048482458160552289653729362407 and
p75 = 222388041221362584184149014473267473860908910276288701052882619191192407187.
(808M^2·41)^41-1: c106 = p46 · p60, where
c106 = 5234343580924927137705589350091830095345743238214088290350697691010477360865969748011373129172734998642961,
p46 = 5715588328818506524527064005609054273460735519 and
p60 = 915801362833096216487326243826039710075301098547605859379919.
(895L^2·41)^41-1: c105 = p44 · p62, where
c105 = 305369709231753635739448067967132492460897414882646631331774448905283895916115014527789405372607197393721,
p44 = 10022386473993542821756067250791118137891839 and
p62 = 30468762108120475375638780822782193130503526758251351059108039.
(901L^2·41)^41-1: c107 = p44 · p62, where
c107 = 28114058923324407149312411965158575965928969776817678233333073343018055112654129371152026601454845966616447,
p51 = 867031396142784806650938664996036878885837082450837 and
p56 = 32425652690775821224505574038022610472634232434994606531.
(916L^2·41)^41-1: c106 = p48 · p58, where
c106 = 1342544578070874564869990807938163569227460744902805308899695104125203031360325066530904789199535985034111,
p48 = 895524673894736767319959608517899399159364272647 and
p58 = 1499170952188283475076359314563795496598808524083147175113.
(919M^2·41)^41-1: c108 = p44 · p64, where
c108 = 203555262298108484859448750553200250165469092840868412800533394930125136802424225505585919199180983167268351,
p44 = 70701871755814667331602192292786917862657373 and
p64 = 2879064687298999003893299046232590121800914323240098074984005387.
(951M^2·41)^41-1: c105 = p37 · p68, where
c105 = 150106971267538548460952723922094890776180679584919307985330874935846750592169124401427469218110292190779,
p37 = 2229208139828749963472641363048481059 and
p68 = 67336453956726498702209538783924514250483492000276360140000086275081.
(956L^2·41)^41-1: c105 = p31 · p74, where
c105 = 136861676210045836305809165658213584684923925988236328877400001964207026330796400330320065893911534144223,
p31 = 2662392599402665918660636335283 and
p74 = 51405520072716587859437991045816135390572120443115601231322746062074726181.
(975M^2·41)^41-1: c107 = p35 · p73, where
c107 = 82926549273172161378307685274215611510497036157508416838661146415833730796919377447429078734937722628828087,
p35 = 37078145284763320143504352202569657 and
p73 = 2236534450045685558648408287008523810519672507106972859663970486930314991.
January 25, 2010
10^13050M+1: 45358761118457701.
10^20650L+1: 529453658999311201.
10^20790M+1: 12956022939972421.
January 19, 2010 (Kurt Beschorner)
(269L^2·41)^41-1: c95 = p32 · p64, where
c95 = 27014500108365683573387824233564778850669978525867062114764609999135939280599328715916194817283,
p32 = 17749487498972061957000453226049 and
p64 = 1521987612877847461321856788629873112830774148230420271985728067.
(326L^2·41)^41-1: c95 = p32 · p63, where
c95 = 29879571620200742208419832529418923492770227224083539972170463795050017257899797284227307563649,
p32 = 49263518657396579255705404799389 and
p63 = 606525324104402550183840985097515249028502949330253884952748341.
(420L^2·41)^41-1: c98 = p35 · p63, where
c98 = 12269654931168189753712259269104224379744412912907417579564966399911344727778075843907251058372517,
p35 = 46278910344747667650910740599818999 and
p63 = 265124110307854508393923597887535871201858454970859691730204483.
(506L^2·41)^41-1: c96 = p23 · p74, where
c96 = 625829903559107621957333836412693107730196481861473179985810195504962308939829352461273922573563,
p23 = 10148517603425465215067 and
p74 = 61667124994478901073744760156746852924884447229618881378328628180326737889.
(535M^2·41)^41-1: c97 = p35 · p63, where
c97 = 6398169895926565661657539056313989403638990901792556227519772541447664316140017402613138070635181,
p35 = 55090256484384577262995406509632491 and
p63 = 116139773241755324145339617899466513614098440659012428079963591.
(553M^2·41)^41-1: c99 = p25 · p75, where
c99 = 919104563779307671997423164047374988697962152690235104892739123276111861579229628175847391332119183,
p25 = 5880548435236274663535863 and
p75 = 156295722057491896647594656710422954149145829641034807117820207452154937641.
(574L^2·41)^41-1: c103 = p50 · p53, where
c103 = 1523796934825133293395892740830387863444618603390973601758275584142999879433049960308459967826304801527,
p50 = 17310324240731332682246327755722473632431033560819 and
p53 = 88028214470970266654778908524049839163186556383415533.
(594L^2·41)^41-1: c100 = p29 · p72, where
c100 = 7266640397821326197690429430612520058258049282634756751027727007820176055910812630414594753572271627,
p29 = 63595009175268322689272953861 and
p72 = 114264318726559354858396041450494232734495535229984761532557953576998607.
January 17, 2010 (Juno Fernadez)
(138L^2·41)^41-1: c96 = p40 · p56, where
c96 = 555278714497413696677644011392601598523320617790185332769716342580525674554924764020153374558733,
p40 = 8100299589655587245269283777162022451523 and
p56 = 68550392285061561053004621082046655591557100167057052271.
Here are my results using gnfs:
Number: (138^2*41)^41-1
N=555278714497413696677644011392601598523320617790185332769716342580525674554924764020153374558733 (96 digits)
Divisors found:
r1=8100299589655587245269283777162022451523 (pp40)
r2=68550392285061561053004621082046655591557100167057052271 (pp56)
Version: Msieve v. 1.43
Total time: 27.55 hours.
Scaled time: 58.60 units (timescale=2.127).
Factorization parameters were as follows:
name: n1612812
n: 555278714497413696677644011392601598523320617790185332769716342580525674554924764020153374558733
m: 20357676603612078674214
deg: 4
c4: 3232944
c3: 14525163
c2: -736024065758319262
c1: -919530305715074386647
c0: -3693059476864012007833
skew: 1635.250
type: gnfs
# adj. I(F,S) = 58.413
# E(F1,F2) = 5.133603e-006
# GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect.
# Options were:
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1263676796.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000
type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 4380001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 276926 x 277162
Total sieving time: 27.27 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 27.55 hours.
--------- CPU info (if available) ----------
January 16, 2010 (Juno Fernadez)
(125M^2·41)^41-1: c102 = p25 · p77, where
c102 = 442678692427326879397174263857915215267390932985310874678062963641518014644512889701053795172735553349,
p25 = 7782536703908972049205939 and
p77 = 56881028547540357718422826801329065265988821135996045625995123373982737521191.
Msieve v. 1.43
Sat Jan 16 14:35:11 2010
random seeds: a5621fe0 204e6015
factoring 442678692427326879397174263857915215267390932985310874678062963641518014644512889701053795172735553349 (102 digits)
searching for 15-digit factors
searching for 20-digit factors
searching for 25-digit factors
200 of 214 curves
completed 214 ECM curves
searching for 30-digit factors
ECM stage 1 factor found
prp25 factor: 7782536703908972049205939
prp77 factor: 56881028547540357718422826801329065265988821135996045625995123373982737521191
elapsed time 00:03:05
January 15, 2010 (Kurt Beschorner)
(276M^2·41)^41-1: c95 = p33 · p62, where
c95 = 29305711393793569464623606293207576447028423891771163585518258124624639975208499173407489989207,
p33 = 347904053011498209079025522397379 and
p62 = 84235038770373328697789079246002557691352273067620723005978333.
(344M^2·41)^41-1: c95 = p38 · p57, where
c95 = 37182255562327482441002752718897826808773194739757405852161546329828213209072983800560525867463,
p38 = 83745040466688205251769847136351801661 and
p57 = 443993523140247374450720434666672657673418533732719353683.
(345M^2·41)^41-1: c95 = p40 · p56, where
c95 = 21980546060747609279431256000660788701598624167412518926050180993741216796574824237042795774879,
p40 = 1409176830746384396155251806690416579051 and
p56 = 15598146081571179704392630374007262884964070033772262429.
(367L^2·41)^41-1: c94 = p36 · p58, where
c94 = 2530909842335101867375414375198669484392283723196112032194381434192317695365095628029426024829,
p36 = 737717887686316480245793782213442483 and
p58 = 3430728581453707252557726009006902367048988904785468814863.
(566M^2·41)^41-1: c94 = p32 · p62, where
c94 = 1480288165495905271969062322424758596592579003636618745028695903472834361622800266231564785509,
p32 = 34890126473036402522259411470983 and
p62 = 42427136704130135733165106080120165310667754317188608722726323.
January 12, 2010 (Robert Backstrom)
(606M^2·41)^41-1: c101 = p39 · p63, where
c101 = 64048258863133535832476599081500053522678613939534966663380511653728713565202854633036848243573101839,
p39 = 175251154017373472593108514929142826713 and
p63 = 365465546987406029681068395365531141968064296697765810690660903.
(658L^2·41)^41-1: c100 = p42 · p58, where
c100 = 1756809584644755451578892980252930232138495839434326354441994239226570926050727823911639573959711797,
p42 = 441636290769069423368736033290928024412073 and
p58 = 3977955664797001583060726210234915375458421770482038710189.
(663L^2·41)^41-1: c100 = p48 · p53, where
c100 = 4536622316740118575265655865295760898545917018823944531394556554155524963339182601148673394492673789,
p48 = 191443372556923726824458360596746662763180629551 and
p58 = 23696941064863451334749545078177612580193281984456339.
(708M^2·41)^41-1: c101 = p40 · p62, where
c101 = 13894787774575189223778941636781659403118505619312882401097691236954331237842050230771550938968099679,
p40 = 1365837285557422084679589265596833672849 and
p62 = 10173091569179474635333713918331626983903225350511057600082671.
(715M^2·41)^41-1: c100 = p31 · p31 · p39, where
c100 = 9698087982436844930057592760654288708305790006380462539297892069192270182026290783403218745248486599,
p31 = 1868856979870451460979156727449,
p31 = 7723691042771486400998095828219 and
p39 = 671869860939269501806282359906911970029.
(755M^2·41)^41-1: c102 = p43 · p60, where
c102 = 287900397213860048622881481642288154788432335345190111187594138691449162616342564416591973294682031817,
p43 = 2413866390346953785318931117177077272609937 and
p60 = 119269400479319436836709949662049699143945440951510216301241.
(771L^2·41)^41-1: c105 = p39 · p67, where
c105 = 110044837487601236424400720581719341458599627978846707050440386822148015774725432208396135045087973631571,
p39 = 104680515879299171176006717956920461273 and
p67 = 1051244699772853077871856013772666530537451749607757784800573116427.
(861M^2·41)^41-1: c105 = p45 · p61, where
c105 = 516923563345555595792996320977602134664380644984873218757754864479272813991388677100207973525050320191399,
p45 = 212555948286183555786260394305028920289687619 and
p61 = 2431941178374241599218045452434616394904002829170277892220621.
(865M^2·41)^41-1: c100 = p29 · p71, where
c100 = 2213255949074055868106171177130644097314935293116923782353442604921646541674643200160094373039985103,
p29 = 22214994202196404538872930849 and
p71 = 99628923101642333501158499521360117448576316610062891574045527119844847.
(900L^2·41)^41-1: c103 = p30 · p73, where
c103 = 2919983727447889219540946972038832246826662843900970974014782920817348221039589364985430802601536004759,
p30 = 762392852719859381943987751259 and
p73 = 3830025054708684166451714993246448367504161825407926779754353395694736501.
(935L^2·41)^41-1: c104 = p40 · p64, where
c104 = 36499593722865470905369236674025104337656236609856026066139864448729686168693786771979964195717585044853,
p40 = 5480924398833439062401288014983881689477 and
p64 = 6659386458721096575695713920579994525517956460125565703840618289.
(963M^2·41)^41-1: c99 = p43 · p57, where
c99 = 483670739512101261617719246256200504386961901547897183933971522854007426347738446493304812735260293,
p43 = 3412488426814603934614656838535793265412863 and
p57 = 141735495924768586735374643473889113568043200373388927611.
January 11, 2010 (Kurt Beschorner)
(216L^2·41)^41-1: c100 = p26 · p34 · p41, where
c100 = 5406487782998005812797770921491251119611404269931104832248178388265107690581124202156713247311405601,
p26 = 25757375456880319635645023,
p34 = 4199426190353617861377148066577201 and
p41 = 49983154890614855686311500712646688531887.
(222L^2·41)^41-1: c93 = p38 · p56, where
c93 = 583765429570227526889049178288120090740500228486554736927619253953580978333872019565071114787,
p38 = 11458089186552105732995866945500497213 and
p56 = 50947886690860228268692882379839935030684412266864523999.
(237L^2·41)^41-1: c94 = p31 · p63, where
c94 = 1977232589423880750759972709752468373698357470468791437011706163834082716760165441589905542541,
p31 = 2556529633192097083013429430869 and
p63 = 773404917256952414197449438148282024249079482820715169903500889.
(243L^2·41)^41-1: c91 = p39 · p52, where
c91 = 2240501185968083308048735241000070015411527685629844060144712666239957065386990825393383743,
p39 = 460338908240784384105505746989352049859 and
p52 = 4867068904799524613304081876657897084628952272939477.
(264M^2·41)^41-1: c118 = p24 · p94, where
c118 = 1061265315999142186365598244973795258806336886487839687947590637952797193954610447244752645690316422738865107726077851,
p24 = 829478458470367164941753 and
p94 = 1279436861996646448009699577534865458406860161585115891637998576737520099022013025245412026867.
(276M^2·41)^41-1: c122 = p27 · c95, where
c122 = 21220457388562165190735445867495628711504544703869175849533972679585877676419508743525835589443952038136949944716710259503,
p27 = 724106543718173726181367529 and
c95 = 29305711393793569464623606293207576447028423891771163585518258124624639975208499173407489989207.
This c95 is reserved by Kurt Beschorner. Done.
(391L^2·41)^41-1: c92 = p38 · p54, where
c92 = 66103913554948011774691647150689939147456591964714563678901544291756569205866911710254480799,
p38 = 77093587403438057245940211584594164429 and
p54 = 857450220976486156219919314789610182769789196687061531.
January 11, 2010
2009^n ± 1: Some complete factorizations for n > 130 were appended.
January 6, 2010 (Robert Backstrom)
(140M^2·41)^41-1: c87 = p31 · p57, where
c87 = 308314528222924804728828221769598244136844106222149012159627230539756056299909410022929,
p31 = 2631846978910483100168311674847 and
p57 = 117147589010117557339860338144550573103917366433429717007.
(154L^2·41)^41-1: c87 = p40 · p47, where
c87 = 143831238426762000217665894826689791094049364147456804937670772035185433993515546619007,
p40 = 3161911192722841170994563738455324921647 and
p47 = 45488702768689555605116022121090836086370984881.
(178M^2·41)^41-1: c83 = p27 · p57, where
c83 = 72075559057818334324999477712451036289505859650674043212579195453035701870166557779,
p27 = 243636935610132623136650609 and
p57 = 295831824010270394898512509284323037818538327201087792131.
(184M^2·41)^41-1: c88 = p28 · p60, where
c88 = 1281110129958785786284015581226804232621358994662916313728939287762955061592792711756997,
p28 = 2387819732867082420160091483 and
p60 = 536518780008800004360063461022320720874309470084360422846559.
(294L^2·41)^41-1: c88 = p32 · p57, where
c88 = 4188266823620871164694520649948229501065699636416080582956241161159811653219353656356453,
p32 = 38549672815147991088594695065277 and
p57 = 108645975899829242907406292484412979320870318058217868489.
(415L^2·41)^41-1: c84 = p33 · p52, where
c84 = 722610582861726824283858022647742888521947655043594558427934183685222601772191055343,
p33 = 339445788053421272830576342809619 and
p52 = 2128795254775716563547544127457190511966711454431797.
(442M^2·41)^41-1: c84 = p30 · p54, where
c84 = 216242539590540545529263903914174124379462443342572145901992875853929566193406041291,
p30 = 330381167303104950009361779023 and
p54 = 654524412985534844519077872327486157622535119146917317.
January 6, 2010 (Juno Fernadez)
(132L^2·41)^41-1: c87 = p34 · p53, where
p34 = 4095278094281671799873913348183037 and
p53 = 58512230611395136399948431624597186600923723616212243.
Juno Fernadez used GGNFS and Msieve v1.43:
Number: (132^2*41)^41-1
N = 239623856270403974187799992094755861860335560180243509878327516493579140958260204321991 (87 digits)
Divisors found:
r1= 4095278094281671799873913348183037 (pp34)
r2= 58512230611395136399948431624597186600923723616212243 (pp53)
Version: Msieve v. 1.43
Total time: 3.06 hours.
Scaled time: 6.59 units (timescale = 2.151).
Factorization parameters were as follows:
name: 10000_80919
n: 239623856270403974187799992094755861860335560180243509878327516493579140958260204321991
m: 83183073658385435993
deg: 4
c4: 5004840
c3: 18654305635
c2: -15149550423711812
c1: -62993732460078512
c0: 1603454556780344507160
skew: 1379.250
type: gnfs
# adj. I(F,S) = 51.246
# E(F1,F2) = 4.473859e-004
# GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect.
# Options were:
# lcd=1, enumLCD= 24, maxS1= 56.00000000, seed= 1262652520.
# maxskew=1500.0
# These parameters should be manually set:
rlim: 600000 alim: 600000
lpbr: 25 lpba: 25
mfbr: 43 mfba: 43
rlambda: 2.2
alambda: 2.2
qintsize: 10000
type: gnfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [300000, 1450001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 107122 x 107348
Total sieving time: 3.01 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be: gnfs,86,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,600000,600000,25,25,43,43,2.2,2.2,10000
total time: 3.06 hours.
--------- CPU info (if available) ----------
(133L^2·41)^41-1: c88 = p35 · p54, where
p35 = 17392361770162610536182697572379513 and
p54 = 169247103336575935009349690392679940888376902589980101.
Msieve v. 1.43
Tue Jan 05 17:45:44 2010
random seeds: c9659bb0 4abcff19
factoring 2943606849781824096979547183855411407967465942178188858816722347983384595413645890070813 (88 digits)
searching for 15-digit factors
searching for 20-digit factors
searching for 25-digit factors
200 of 214 curves
completed 214 ECM curves
commencing quadratic sieve (88-digit input)
using multiplier of 53
using VC8 32kb sieve core
sieve interval: 25 blocks of size 32768
processing polynomials in batches of 9
using a sieve bound of 1508723 (57667 primes)
using large prime bound of 120697840 (26 bits)
using double large prime bound of 352418743239120 (42-49 bits)
using trial factoring cutoff of 49 bits
polynomial 'A' values have 11 factors
57995 relations (16470 full + 41525 combined from 600265 partial), need 57763
sieving complete, commencing postprocessing
begin with 616735 relations
reduce to 137409 relations in 9 passes
attempting to read 137409 relations
recovered 137409 relations
recovered 113943 polynomials
attempting to build 57995 cycles
found 57995 cycles in 6 passes
distribution of cycle lengths:
length 1 : 16470
length 2 : 11661
length 3 : 10470
length 4 : 7232
length 5 : 5152
length 6 : 3144
length 7 : 1781
length 9+: 2085
largest cycle: 20 relations
matrix is 57667 x 57995 (14.7 MB) with weight 3394069 (58.52/col)
sparse part has weight 3394069 (58.52/col)
filtering completed in 3 passes
matrix is 53110 x 53174 (13.6 MB) with weight 3135924 (58.97/col)
sparse part has weight 3135924 (58.97/col)
saving the first 48 matrix rows for later
matrix is 53062 x 53174 (10.3 MB) with weight 2608747 (49.06/col)
sparse part has weight 2171964 (40.85/col)
matrix includes 64 packed rows
using block size 21269 for processor cache size 1024 kB
commencing Lanczos iteration
memory use: 9.0 MB
lanczos halted after 841 iterations (dim = 53060)
recovered 17 nontrivial dependencies
prp35 factor: 17392361770162610536182697572379513
prp54 factor: 169247103336575935009349690392679940888376902589980101
elapsed time 00:50:37
January 4, 2010 (Kurt Beschorner)
(169M^2·41)^41-1: c85 = p28 · p57, where
p28 = 6647782498729689151689384287 and
p57 = 618287465271253699293333878605599073952441950459370924171.
(197M^2·41)^41-1: c90 = p28 · p63, where
p28 = 1437909606926362734724101497 and
p63 = 284477388968798009199847363324734697230108363258952341139963121.
(202M^2·41)^41-1: c123 = p27 · c97, where
p27 = 173149203443623277702801789 and
c97 = 2062449977360755507274992069507766655809788292617531988864980216933457270169056191807591521281713.
This c97 is reserved by Kurt Beschorner. Done.
(211M^2·41)^41-1: c118 = p27 · p92, where
p27 = 343289913877169053089516337 and
p92 = 27969032884260036098355328186226727647891331798662424255739742843.
(222L^2·41)^41-1: c120 = p27 · c93, where
p27 = 881483252667973231097215507 and
c93 = 583765429570227526889049178288120090740500228486554736927619253953580978333872019565071114787.
This c93 is reserved by Kurt Beschorner. Done.
(241L^2·41)^41-1: c92 = p30 · p31 · p32, where
p30 = 504305910841509336928760676853 and
p31 = 1849913065611587000824687601821 and
p32 = 17232403913310655623532522233721.
(257M^2·41)^41-1: c92 = p26 · p27 · p41, where
p26 = 10247394888411657467356499 and
p27 = 135954963320708726834483287 and
p41 = 44228999699831129532690644009362109603791.
(440L^2·41)^41-1: c88 = p39 · p50, where
p39 = 226676524925116928053679052089111594161 and
p50 = 19533461539082772501526884590475950657943998496811.
(456L^2·41)^41-1: c128 = p38 · p91, where
p38 = 35016584451555646503448323384972832913 and
p91 = 1413033419285390052131919549856091715728731900143607.
(477L^2·41)^41-1: c89 = p31 · p58, where
p31 = 9529049289376413356414359035571 and
p58 = 8663956768480346525225763199985988477036312148065592390007.
(488M^2·41)^41-1: c89 = p37 · p53, where
p37 = 2126352530868172045240619401754441729 and
p53 = 40517616854680546172708891737827176301221942586632519.
(491L^2·41)^41-1: c89 = p44 · p46, where
p44 = 12099343734872900495164473811949203392077753 and
p46 = 4655302253702812523504410694010466572455727221.
(562M^2·41)^41-1: c89 = p43 · p47, where
p43 = 1631310348597867832392451238158714310250509 and
p47 = 36813023984784300467977471433136523533983032757.
(566L^2·41)^41-1: c87 = p31 · p57, where
p31 = 1990033947194495720080688341109 and
p57 = 225280440478828813344196669188108868563121775574282401473.
January 2, 2010 (Juno Fernadez)
(128L^2·41)^41-1: c93 = p36 · p57, where
p36 = 213036110157050766949144160971316821 and
p57 = 972926547020456961624607579183272812345994951108761133869.
Juno Fernadez used GGNFS and Msieve v1.43:
Number: (128^2*41)^41-1
N=207268487045769101921671013597350688146847062035837211692183826673162516693751844837992510449 (93 digits)
Divisors found:
r1=213036110157050766949144160971316821 (pp36)
r2=972926547020456961624607579183272812345994951108761133869 (pp57)
Version: Msieve v. 1.43
Total time: 7.94 hours.
Scaled time: 16.37 units (timescale=2.063).
Factorization parameters were as follows:
name: 11111_109375
n: 207268487045769101921671013597350688146847062035837211692183826673162516693751844837992510449
m: 2318199081561869302038
deg: 4
c4: 7176792
c3: 29666950
c2: -24055051799750711
c1: 232054448375006387129
c0: -544956391418094095881
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.799
# E(F1,F2) = 7.091470e-005
# GGNFS version 0.77.1-VC8(Sat 01/17/2009) polyselect.
# Options were:
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1262456569.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000
type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 2160001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix: 189036 x 189261
Polynomial selection time: 0.17 hours.
Total sieving time: 7.63 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be: gnfs,92,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 7.94 hours.
--------- CPU info (if available) ----------
Alfred Reich