News - June 2010
June 22, 2010
10^6815+1: 28010436544042930661731.
10^6816+1: 67913977477507190977.
10^6817+1: 36265150972281249276757.
10^49503+1: 666285445518595891.
10^49529+1: 595638986856889.
In any case the remaining cofactor is composite.
June 21, 2010 (Juno Fernadez)
(433L^2·41)^41-1: c104 = p46 · p59, where
c104 = 59336308052344828833743115515072136923213170568207861460431245662551209095328860030380063906704962624761,
p46 = 1307782553345304609984003458874590190948568249 and
p59 = 45371692641534860881298085893887140040023220301554568999489.
GMP-ECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM]
Input number is 59336308052344828833743115515072136923213170568207861460431245662551209095328860030380063906704962624761 (104 digits)
Step 1 took 13260ms
Step 2 took 10421ms
********** Factor found in step 2: 1307782553345304609984003458874590190948568249
Found probable prime factor of 46 digits: 1307782553345304609984003458874590190948568249
Probable prime cofactor 45371692641534860881298085893887140040023220301554568999489 has 59 digits
June 20, 2010 (Juno Fernadez)
(285L^2·41)^41-1: c104 = p42 · p63, where
c104 = 44023012955401678297472475701913902700064044221302235269019408137942048539959472760551797389509883266323,
p42 = 135668536594707510024404819118352400443639 and
p63 = 324489480467492826336218988402892315058888337774698094563785157.
gnfs.
June 18, 2010
10^49594+1: 9846415103590964795789.
10^49628+1: 32113928285475737.
10^49686+1: 1517693967594169.
10^49699+1: 29158715667558413.
10^49707+1: 28597174254811.
10^49757+1: 26327491509521.
10^49758+1: 38964170020101709.
10^49760+1: 3606657180234413441.
10^49761+1: 119311649268062023.
10^49764+1: 24429480998894401.
10^49768+1: 7229569498343457908710849.
10^49774+1: 7829812258066961.
10^49774+1: 10842467724235549.
10^49775+1: 47297154901844834801.
10^49776+1: 35930315406303308057281.
10^49787+1: 24578818042042448580247.
10^49788+1: 7981748037770455513.
10^49801+1: 1820613910743773.
10^49815+1: 136665757594441.
10^49816+1: 19994167685889073.
10^49817+1: 11911712182729.
10^49820+1: 1180060609909193681.
10^49827+1: 67109628821748426967.
10^49829+1: 19268288813933927.
10^49832+1: 28003121467046362577.
10^49834+1: 3767387833200308489.
10^49846+1: 20308114084029781.
10^49846+1: 11103816025907477101.
10^49854+1: 23980455908979138927121.
10^49864+1: 55506378771313.
10^49869+1: 9889873533061579.
10^49874+1: 1019490177725581.
10^49862+1: 22460959679141.
10^49963+1: 34063397485288895081.
In any case the remaining cofactor is composite.
June 17, 2010
10^49501+1: 106044618548249.
10^49599+1: 1949053999146607.
10^49617+1: 209456548953048081444259.
10^49631+1: 846593946591478635576289.
10^49632+1: 10594420117249.
10^49651+1: 1886001050166703.
10^49652+1: 299519836227809.
10^49659+1: 1073471100518281.
10^49662+1: 57427442829181.
10^49680+1: 110256319169281.
10^49683+1: 32338980175921009.
10^49687+1: 19506744399274303601.
10^49696+1: 1589460334870268929.
10^49714+1: 39272484966023401.
10^49947+1: 75249371991776041.
10^49948+1: 4647179270207167025281.
10^49969+1: 75891758579490367.
10^49979+1: 31976565699371.
10^49979+1: 1148175513361127.
10^49996+1: 371044131599480009569.
In any case the remaining cofactor is composite.
June 15, 2010
10^17528+1: 14518814044525185137.
10^17537+1: 2132236545407084784253.
10^17539+1: 131954508649001.
10^17564+1: 346060651271460906049.
10^17574+1: 78564921861413341.
10^17589+1: 891629782855813.
10^17620+1: 2425529085109841.
10^17622+1: 10492857425161.
10^17644+1: 2072421145235761.
10^17647+1: 299870896927246961.
10^17672+1: 2891645691501617.
10^17696+1: 611204140250369.
10^17736+1: 7511071493281.
10^17749+1: 252859989014201.
10^17767+1: 7878829642101853.
10^17861+1: 46993890559717.
10^17873+1: 14751266533693561.
10^17904+1: 3574037995687777.
10^17904+1: 91385547059787553.
10^17906+1: 18429520551149.
10^17956+1: 47564575755577.
10^17958+1: 526364541459317495929.
10^17960+1: 247294449739361.
10^17966+1: 40400892598487149.
10^17997+1: 23565911017447.
10^18011+1: 188190352692780677.
10^18018+1: 24022205525085769.
10^18020+1: 9823994178161.
10^18034+1: 13533083072873449.
10^18035+1: 6847999297081.
10^18055+1: 168448715511451.
10^18068+1: 2162957193650369737.
10^18069+1: 65785889333002327.
10^18077+1: 11500079136221801.
10^18098+1: 1128769365043921.
10^18112+1: 24606928079853953.
10^18155+1: 38122951038001.
10^18172+1: 146194741604297.
10^18186+1: 33744351052441.
10^18187+1: 101767397153579.
10^18192+1: 4459141648993.
10^18209+1: 20510601831007.
10^18222+1: 11714788118989.
10^18274+1: 4225520291108435589409.
10^18329+1: 934365121099051.
10^18334+1: 1907152434479189.
10^18339+1: 2410127261704609477729.
10^18352+1: 2717810868864122161601.
10^18355+1: 14990956942411.
10^18359+1: 10954809825728140637.
10^18378+1: 335032879062781.
10^18387+1: 5551706274600832921.
10^18409+1: 545379998843957.
10^19428+1: 466782882185041.
10^18428+1: 29540023777506116057.
10^18438+1: 68351354367661.
10^19458+1: 40413346220341.
10^18461+1: 1430722311646717.
10^18511+1: 206580344790825053.
10^18517+1: 21094647999533437687.
10^18548+1: 68085708362382478849.
10^18554+1: 20465375228629.
10^18572+1: 49757588029889.
10^18572+1: 35571340596557329.
10^18620+1: 19063775375681.
10^18652+1: 2473902560559601.
10^18668+1: 38720071655201.
10^18707+1: 157404578280769.
10^18718+1: 11276998030120369.
10^18746+1: 5369980472221.
10^18760+1: 760522959631293601.
10^18764+1: 97801266677051621569.
10^18782+1: 17176544315561.
10^18786+1: 94619323151701.
10^18788+1: 51589775859756289.
10^18837+1: 73728002176921.
10^18862+1: 56622652043379349.
10^18909+1: 4424368928167.
10^18933+1: 1438247215012411.
10^18934+1: 2062846871911741.
10^18936+1: 915580303170163633.
10^19007+1: 46000430445481.
10^19009+1: 1465629222599837.
10^19024+1: 786844340006092028929.
10^19034+1: 344476352129681.
10^19037+1: 523572176662663.
10^19040+1: 24114669586561.
10^19048+1: 154500598826369.
10^19055+1: 133374550536477521.
10^19069+1: 1427647782895095474371.
10^19091+1: 154920899803153927.
10^19102+1: 3157898541695861.
10^19106+1: 6133483360192241.
10^19113+1: 34269870198259.
10^19122+1: 5002045579801.
10^19127+1: 5730716737764881.
10^19147+1: 122045316001877.
10^19243+1: 13278476551103.
10^19283+1: 11493317620397647.
10^19293+1: 194206048357813.
10^19301+1: 118574479312693.
10^19322+1: 146172353624555969.
10^19348+1: 35918868954641.
10^19355+1: 25759491953604843491.
10^19359+1: 22152900520783.
10^19366+1: 2878294197866509.
10^19371+1: 55639451381053.
10^19378+1: 25192488268481.
10^19382+1: 4453533730794061.
10^19399+1: 94259445436837.
10^19418+1: 174892925623245901.
10^19454+1: 5358141489341.
10^19465+1: 82880037514801.
10^22011+1: 259529340773368447.
10^22024+1: 15696784064321.
10^22038+1: 4672805890904689.
10^22045+1: 817560007105836091.
10^22085+1: 19310665382891.
10^22089+1: 86919046889503.
10^22103+1: 8341921654459.
10^22106+1: 7223407359589.
10^22115+1: 8569393266128933561.
10^22133+1: 878931198088213.
10^22149+1: 314603474990518144927.
10^22169+1: 4222187893889724767.
10^22184+1: 898122055593281.
10^22219+1: 198515681140727.
10^22222+1: 228923142967901.
10^22255+1: 188502881131001.
10^22280+1: 555047677480481.
10^22309+1: 6987944534117.
10^22331+1: 10554257833129.
10^22347+1: 1958114754151219.
10^22349+1: 6672385759693.
10^22387+1: 137813744850583.
10^22428+1: 6251998643353.
10^22441+1: 1201520456798794973.
10^22474+1: 28361556467115601.
10^49502+1: 1641995690696591761549.
June 12, 2010 (Juno Fernadez)
(910L^2·41)^41-1: c104 = p46 · p58, where
c104 = 18713075263333773090840783636589178149147309529040395344186014247146324198664343107343795876865181637981,
p46 = 5808809213064333650384353416258332615360437997 and
p58 = 3221499377402003558656315424620449941737513672364652378673.
June 1, 2010 (Kurt Beschorner)
(195L^2·41)^41-1: c106 = p42 · p64, where
c106 = 1349479910611062541452135276575546176195147369853167651289649794865561029811668787587766054214936512082121,
p42 = 602468342603481593133994366538431039344613 and
p64 = 2239918374431885140215175519522436670969070105189351133757744917.
Alfred Reich