News - March 2010

March 30, 2010

10^19944+1: 23853910513432609.

10^31049-1: 40871723427511.
10^31149-1: 25284927573271.
10^31229-1: 7385383684801.
10^31275-1: 4937978975401.
10^31421-1: 3314099873683.
10^31479-1: 6083064099547.
10^31535-1: 4130015143591.
10^31535-1: 5214237070561.
10^31605-1: 1245474164425681.
10^31653-1: 13390437717180532009.
10^31665-1: 529712390413081.
10^31669-1: 21947241195991.
10^31695-1: 9253252558201.
10^31753-1: 84731624160803.
10^31789-1: 19184647258529.
10^31915-1: 3476627548189737241.
10^31983-1: 58271948236867.

GMP-ECM informed of a composite cofactor (each time).



March 29, 2010 (Kurt Beschorner)

(139M^2·41)^41-1: c95 = p46 · p50, where
                  c95 = 24818117659944483004603313012942122453585432729399972006412045441704241164933243668026912622913,
                  p46 = 2326186456905525386094394664424441228608303371 and
                  p50 = 10669014767182282695013584188150413175131663496803.
(230L^2·41)^41-1: c99 = p41 · p59, where
                  c99 = 411191976061506266869785617707929618688971337250934536444085689442374179783414692699264846098113843,
                  p41 = 16311679144221388340020643588983211557147 and
                  p59 = 25208439451629113794507981602457689267357723739509317748169.
(308L^2·41)^41-1: c99 = p30 · p70, where
                  c99 = 265576375559282403253112545858941549484769227906542777811818935680682720498199753579081182522882621,
                  p30 = 180405695794102723436701336807 and
                  p70 = 1472106378849507597973434993464899103113696380171723273819508475084603.



March 29, 2010

10^10251+1: 3011401705124647.
10^14006+1: 55485723697236441041.
10^14011+1: 1292007419044766209.
10^14099+1: 199620165015143.
10^14108+1: 3707692273057951489.
10^14177+1: 4153893323561.
10^14201+1: 3255335681648850599647.
10^14232+1: 4964839001208160899361.
10^16008+1: 36094899806689.
10^16027+1: 1989770494865915081.
10^16032+1: 573185879431681.
10^16048+1: 155534027487073.
10^16077+1: 83560666085878489.
10^16085+1: 55516739408051.
10^19515+1: 5217390473432056651.
10^19525+1: 50316017509451.
10^19531+1: 131264411239343.
10^19541+1: 355535142243881.
10^19560+1: 3503381273884801.
10^19562+1: 76947700949081.
10^19634+1: 131306919613525666321.
10^19785+1: 12111727941362281.
10^19995+1: 409020093926371.
10^20024+1: 1077704108104089889.
10^20028+1: 16791873723311422321.
10^20034+1: 8415663107532409.
10^20043+1: 3153460394251.
10^20048+1: 104139659780412481.
10^20059+1: 56115583659639676303.
10^20508+1: 650171513854040814697.
10^20515+1: 4594522536988050258706291.
10^20545+1: 2538620837898902053571.
10^22710M+1: 279895276980841.
10^22890M+1: 62993166639924425941.
10^23450M+1: 22945281514275315301.
10^25390M+1: 7595473071070526701.
10^25410M+1: 31415203824266058721.
10^25850L+1: 2361959352080454119401.
10^26370L+1: 72640480063425370741.
10^26750L+1: 19482825191956501.
10^29210L+1: 2064189841118690401.
10^30170M+1: 357285215892472001.
10^31630M+1: 13776411570610933921.
10^31710L+1: 35479339478101.
10^31890L+1: 17096629107727846081.
10^31930M+1: 11028589239821.
10^31970M+1: 11933307945701.
10^32190L+1: 45994413604712341.
10^32730M+1: 44009998004981925702001.
10^33290L+1: 36060888129202201.
10^33490L+1: 32431314290970665185361.
10^33510L+1: 283859907063746329441.
10^33610M+1: 45340153701756034501.
10^33650M+1: 150898529176999398701.
10^33750L+1: 19195327004535001.
10^33770L+1: 253642678076520041.
10^33830L+1: 305051946772361.
10^34730M+1: 6238717520915496616061.
10^35730M+1: 65030098864703416921.
10^36010M+1: 233118561792993653401.
10^36590M+1: 1650020887516901.
10^37270M+1: 80749489626581.
10^37350M+1: 27549033785101.
10^37470L+1: 6316762782997573861.
10^49538+1: 16624211528229401.
10^49603+1: 11994988134637.
10^49629+1: 227973928253508967.
10^49687+1: 9675196052084971.
10^49689+1: 7757405636887.
10^49697+1: 7424226027070997.
10^49700+1: 1203753482401.
10^49713+1: 2612091160637154451.
10^49716+1: 769369020481.
10^49742+1: 20443705208417261.
10^49745+1: 137312631684828401.
10^49757+1: 49403257385173.
10^49774+1: 516036524209.
10^49812+1: 4788456712374671113.
10^49828+1: 67536457727257.
10^49842+1: 3773907838235809.
10^49844+1: 4961247717101593.
10^49851+1: 31567140348551371.
10^49853+1: 286558299002077.
10^49856+1: 5384055533569.
10^49866+1: 201526513011529.
10^49885+1: 8609120107606497601.
10^49889+1: 476101281616619.
10^49902+1: 174020655031521841.
10^49903+1: 2465767435197088933.
10^49904+1: 605395404900406849.
10^49919+1: 8378695895020499.
10^49923+1: 93693486983851.
10^49937+1: 20466106492496275108462693.
10^49939+1: 191887316919413.
10^49944+1: 18966980521957921.
10^49960+1: 342044753113601.
10^49962+1: 211836168262489.
10^49981+1: 203463228881767.
10^49985+1: 4920272011039321.
GMP-ECM informed of a composite cofactor (each time).

(225L^2·41)^41-1: 11123480569406841348063030044807877805182655557707.
Msieve v. 1.44 (QS).



March 27, 2010 (Juno Fernadez)

(244L^2·41)^41-1: c95 = p36 · p59, where
                  c95 = 13370081102645507581162174717694708947085281159354708400936692761363352071195831127153972751237,
                  p36 = 217327930766419325113624454883527137 and
                  p59 = 61520307378325257685394600233270878682795238391642890059301.



March 26, 2010 (Kurt Beschorner)

(335L^2·41)^41-1: c99 = p41 · p58, where
                  c99 = 626949067930174245797217241508718796013150866150705844516595988818087103228119278891585383343310077,
                  p41 = 79682014743041869980652307303856307023503 and
                  p58 = 7868137746666624933058196745302720652268052418836415207859.
(347M^2·41)^41-1: c99 = p42 · p57, where
                  c99 = 296437304502334139991186738820400765909986149880763118596903341076686956349403706835008322386866651,
                  p42 = 378860115492878204316569768048566959792001 and
                  p57 = 782445267738684821578925260368949929920804159480554274651.
(467M^2·41)^41-1: c99 = p34 · p66, where
                  c99 = 601205141079213457767661817484820574875331959713600841907691814758038320669704673853447720563391851,
                  p34 = 1270983745089850838201572815425297 and
                  p66 = 473023469735021593468887217599163443398211269978742133861763562683.



March 26, 2010

10^35270L+1: 1412141152824781.
10^35290L+1: 1414991467529681.



March 25, 2010 (Juno Fernadez, Msieve v. 1.44 (QS))

(301L^2·41)^41-1: c94 = p31 · p32 · p33, where
                  c94 = 5144531735283502536415613154019106530181023230478547396450559360188647817726772761737997278093,
                  p31 = 1647669654338727851443677581977,
                  p32 = 11723432570417974282013612198201 and
                  p33 = 266330508043189895184038140690109.



March 23, 2010 (Juno Fernadez, Msieve v. 1.44 (QS))

(158L^2·41)^41-1: c97 = p38 · p60, where
c97 = 2897584941059287127160267490079575027846512907740459592525081431708048898780700253317440670422973
p38 = 21887683092459008103273719681586891649 and
p60 = 132384269674372059600439565937762893499741042823421981334077.



March 23, 2010

10^16610L+1: 69262453452721.
10^16610M+1: 5387661224942461421441.
10^16750L+1: 74185848489238143001.
10^16950M+1: 231128747791801.



March 22, 2010 (Juno Fernadez, Msieve v. 1.44 (QS))

(416L^2·41)^41-1: c94 = p32 · p62, where
c94 = 1126220482366800047778876998303287153365530514819945164975546326096199159570237549360707801651,
p32 = 35874047287774823509798697872001 and
p62 = 31393739137724614903568476340024382020080822059480222905129651.



March 22, 2010

10^6310M+1: 173709770411859051010641304501.
10^17290M+1: 79687092540518119021.
10^17590M+1: 397944353084303488721.
10^49505+1: 1811701689711363161.
10^49537+1: 502821751837.
10^49537+1: 616455593348724090373.
10^49604+1: 182377733172193637521.
10^49618+1: 41517542753969.
10^49641+1: 2853442417807.
10^49642+1: 44767865083974518329.
10^49660+1: 8768795545121.
10^49660+1: 42150205830721.
10^49663+1: 824226715223.
10^49679+1: 1987764758066207.
10^49698+1: 6294225656976725161.
10^49701+1: 2496892754281.
10^49707+1: 8050942176271849.
10^49741+1: 1889085098368877.
10^49743+1: 1293088453475794489.
10^49778+1: 1772996288461.
10^49780+1: 2598721771006241.
10^49785+1: 13615001066881.
10^49789+1: 673324528841.
10^49834+1: 684407065604881.
10^49844+1: 630839916393361.
10^49851+1: 1192600520918671411.
10^49853+1: 395459387927609.
10^49856+1: 31748721350969057173633.
10^49882+1: 49358948322041.
10^49886+1: 5034082463009.
10^49906+1: 4900720355400809.
10^49935+1: 963484539691.
10^49938+1: 116308314931789.
10^49986+1: 356104824222781.
10^49991+1: 7521226067076331.
GMP-ECM informed of a composite cofactor (each time).



March 20, 2010 (Kurt Beschorner)

(277M^2·41)^41-1: c99 = p29 · p70, where
                  c99 = 125675568638281894104263590436491371853600607633667211519397204264161220857702745691472279239501421,
                  p29 = 55488771763757069243392491181 and
                  p70 = 2264882869877611656365123659310183070645220471356727361859795694223041.
(344L^2·41)^41-1: c99 = p45 · p54, where
                  c99 = 145892523625925941888031518622653863776620149018792091839191343849876827620753706517200328135113269,
                  p45 = 662442529332176572022975511174101726143305811 and
                  p54 = 220234234919976414573181886973261945778794688710472279.
(625L^2·41)^41-1: c112 = p29 · p39 · p45, where
                  c112 = 3634081669989593660059093448246058177010336539367093121555632327405501306102165610491219862976607068381458487533,
                  p29 = 71866063411596661163280750893,
                  p39 = 105676229851565531306262881447089767739 and
                  p45 = 478512752176972286570098481720547487972860979.
(980L^2·41)^41-1: c128 = p29 · p99, where
                  c128 = 13417772365128727858750333622412234872066387283821438435497903093134407179586625561635230341928293090940433355736694242941770057,
                  p29 = 35392162711447199262216404323 and
                  p99 = 379117051267084603145546231894321774012736175841947697470035421613331721819537860512298521640105059.



March 18, 2010

10^7681+1: 414497497511605100293.
10^17230M+1: 1438195115941317121.
GMP-ECM informed of a composite cofactor (each time).



March 17, 2010

10^8751+1: 4145745163880435053.
10^8791+1: 73132626827387971.
10^12899+1: 28805733663877.
10^19510M+1: 61211994310960501.
10^19590L+1: 7486709293840863479401.
10^19744+1: 2638492124067239873.
10^19832+1: 574025929136113.
10^37630L+1: 1009015303212235301.
10^49636+1: 5979521256209.
10^49641+1: 6788730707167.
10^49654+1: 16595197394832409.
10^49716+1: 5791044367729.
10^49738+1: 907925144976461.
10^49892+1: 768103205657.
10^49904+1: 32040728059969.
10^49932+1: 17219520059121361.
10^49972+1: 3356250346697.
10^49980+1: 1079176316336161.

10^25589-1: 43766347228363.
10^25793-1: 4189677697113121.
10^65963-1: 235582828382333.

GMP-ECM informed of a composite cofactor (each time).



March 16, 2010

10^10053+1: 593516763152783641.



March 15, 2010

10^11683+1: 3307525113768649997609.
10^11691+1: 23657174221665131427727.
10^11793+1: 245137207918891.
10^11978+1: 610869316232147251969.
10^12247+1: 1467942505985653.
10^12328+1: 4754896763864497.
10^12829+1: 254665712528783.
10^20506+1: 288314088869669.
10^20529+1: 8722864795866499.
10^20538+1: 46544616544956769.
10^20688+1: 5582842578241.
10^20688+1: 36333860231041.
10^20728+1: 69357830130689.
10^20738+1: 24076383538901.
10^20765+1: 46203031878857011.
10^20819+1: 9665032203600899.
10^20837+1: 51379701111139.
10^20872+1: 13103047536641.
10^20895+1: 6993293541230851.
10^20943+1: 854505812615131.
10^20955+1: 1994250212436499051.
10^20988+1: 245464894210537.
10^21001+1: 19869472462303.
10^21013+1: 29904912561851.
10^21020+1: 15220461177041.
10^21035+1: 4436513221561.
10^21047+1: 2747348123779284299.
10^21048+1: 225364302290833.
10^21052+1: 24449684912373569.
10^21053+1: 203626437000289.
10^21059+1: 379477293921762941251.
10^21063+1: 57008469460783.
10^21078+1: 336271324311721.
10^21086+1: 195433830276829.
10^21088+1: 2673791021212097.
10^21093+1: 104638974378071115613.
10^21108+1: 37695861112801.
10^21117+1: 123981072571632739.
10^21120+1: 65534533785601.
10^21123+1: 746754658034653.
10^21125+1: 32973436730013001.
10^21128+1: 284008898638513.
10^21129+1: 61557979186597.
10^21132+1: 579005568764641.
10^21132+1: 125495099537669569.
10^21135+1: 52672237110303931.
10^21143+1: 17249053360150361.
10^21145+1: 40930463279081.
10^21149+1: 91641937604491.
10^21159+1: 1470215747365935769.
10^21163+1: 7200979235697850051.
10^21173+1: 11151258989459.
10^21174+1: 5857192873499221.
10^21175+1: 4823125475560946401.
10^21185+1: 4123366414051.
10^21187+1: 123674124392893721.
10^21196+1: 41853009077993.
10^21204+1: 260821356083569.
10^21211+1: 218683945507717.
10^21212+1: 262654722682277114456713.
10^21228+1: 41847358109686764529.
10^21233+1: 601743477752780183.
10^21234+1: 6890539424809.
10^21238+1: 857557553084429.
10^21239+1: 605276291811037183.
10^21239+1: 4086893418972527850289.
10^21256+1: 34960203222353.
10^21281+1: 14992195635847.
10^21282+1: 47343104860981.
10^21285+1: 168273632138763691.
10^21287+1: 274737399520739.
10^21313+1: 1316319011156579.
10^21334+1: 3860264037310829.
10^21349+1: 72785820541891.
10^21355+1: 221165879744085509111761.
10^21357+1: 2340677154584332679851.
10^21364+1: 23265167277017.
10^21387+1: 208534063943754323007787249.
10^21397+1: 86562916603487.
10^21404+1: 377620206826328426777.
10^21407+1: 144080883646804757.
10^21423+1: 5241949181967294933259387447.
10^21429+1: 10328204609334816049.
10^21439+1: 10352770340287.
10^21441+1: 9942194272921.
10^21452+1: 1342341549193361.
10^21462+1: 384172430897809.
10^21476+1: 45526720312993921.
10^21477+1: 604734109653776569.
10^21486+1: 18918565194349.
10^21487+1: 25033714446388101263.
10^21492+1: 24889388638170248641.
10^21495+1: 15933127308628771.
10^21496+1: 567899231818616177.
10^21497+1: 34741723491906103.
10^23810L+1: 465083568047324567437981.
10^24170L+1: 29410048797341.
10^24290L+1: 30860692674534481981181.
10^24430L+1: 1202744259443918877841.
10^34010M+1: 1210107485923235736101.
10^38570L+1: 83180025979014161.
10^38630L+1: 1820228511555941.
10^38830M+1: 4774742857918441.
10^39670M+1: 265435937396485099120621.
10^39830L+1: 1610615148199885381.
10^39830M+1: 193311168512519833860001.
10^40470L+1: 4868156696881.
10^40650M+1: 381770531544645655201.
10^40670M+1: 108630675519514261.
10^41150M+1: 11325037516819250501.
10^41290L+1: 182030499808822801.
10^41330L+1: 2639538425235447301.
10^41530L+1: 161444307174561181.
10^41710L+1: 5182003082391772831561.
10^41910L+1: 12165971337301.
10^41930M+1: 15356869689569381.
10^42150L+1: 4691396750101.
10^42410L+1: 14991020301121.
10^43090L+1: 200546752471321.
10^43530L+1: 819554673817472821.
10^43670M+1: 1768982624379521.
10^44210M+1: 3245897576230853281.
10^44690M+1: 1047273921854953381.
10^44970M+1: 16469724351853271034421.
10^45010M+1: 739545333973076261.
10^45370M+1: 131688853903094281.
10^45470M+1: 3573812228621.
10^45570L+1: 101346288201061.
10^45590L+1: 285840720149058870121.
10^45670L+1: 1175364581441.
10^45750L+1: 276568690010762100001.
10^45830M+1: 4363786585621.
10^45910L+1: 1810081174301.
10^45910L+1: 231714526207421.
10^46110L+1: 13979857673083581121.
10^47770L+1: 27209838532949607266612501.
10^48530M+1: 238130170643659253081.
10^48850L+1: 2004168968563001.
10^48930L+1: 12513216171476161.
10^49688+1: 120886222197889.
10^49738+1: 20794729436729.
10^49746+1: 976060124856301.
10^49782+1: 224211641106709.
10^49826+1: 71621508755441.
10^49854+1: 65889494331109.
10^49865+1: 2131792567326731.
10^49879+1: 981861730489.

GMP-ECM informed of a composite cofactor (each time).



March 12, 2010 (Kurt Beschorner)

(221L^2·41)^41-1: c98 = p30 · p68, where
                  c98 = 14172213314498629990618411988963143312762654717172315924722743395389826140350775612779186052613447,
                  p30 = 390938977226987887307648194391 and
                  p68 = 36251727609830848176621101638620428655110614471280103458868040956817.
(238L^2·41)^41-1: c98 = p42 · p56, where
                  c98 = 24963660365800096350147808914000388027669102812752606020780799654031527122423565924098881922703423,
                  p42 = 850311745394890501613880675477590180546069 and
                  p56 = 29358244786101130874137503964875210416976476818458187267.
(324L^2·41)^41-1: c98 = p48 · p51, where
                  c98 = 94711275561962220245384675995798606221045756939210379534848769457827453601689105918870042015823071,
                  p48 = 249045491922798055883059753004834414405785263191 and
                  p51 = 380297088819908833540718493896918402737859368490681.
(385M^2·41)^41-1: c99 = p39 · p60, where
                  c99 = 700764775485978749634318106655370655329910081098939282807170885634290690850760197405111502818619637,
                  p39 = 726840215446103122789055828715378887863 and
                  p60 = 964124935018736690792025233236068875521629123930215916952499.
(390M^2·41)^41-1: c98 = p33 · p66, where
                  c98 = 54477497726313339525973323419936687793632731798293400286656943038744920470695620659408043841682707,
                  p33 = 292996277080774848249157952290781 and
                  p66 = 185932388865455375840023863891710190273272815403028039866973936047.



March 12, 2010

10^49530L+1: 4908245490216069301.
10^49570L+1: 7657360545838167481.



March 4, 2010 (Kurt Beschorner)

(174L^2·41)^41-1: c97 = p44 · p55, where
                  c97 = 3180682503107936715481669926770447245738829260714211008448655420861388275386299461984907783971517,
                  p44 = 13540726554180872070019255612400330324185477 and
                  p54 = 234897476910192859256126962287992355706363779230594521.
(320L^2·41)^41-1: c98 = p32 · p67, where
                  c98 = 29934737151722896850414645912957282365422113384478297861725692711931305756862540220905898031826891,
                  p32 = 13609034290186008222279898577603 and
                  p67 = 2199622435613228878966932821102459047467244948541669643768480439897.
(373L^2·41)^41-1: c97 = p42 · p55, where
                  c97 = 1199298028425361760452253693222126955780296983772230421216912949348105299982472659722928475134893,
                  p42 = 625734167213007391023488522714254765946347 and
                  p55 = 1916625447779178684758611554439864386528526428081886919.



Alfred Reich