News - August 2010
August 30, 2010 (Kurt Beschorner)
(376L^2·41)^41-1: c112 = p51 · p62, where
c112 = 6842797372425805057228739953540473827718543234756775920265047808024485671455954434869652536209255320817744479617,
p51 = 344824376642716162273230913919902653134049453676673 and
p62 = 19844297085515655631654812437842572551372437398660101194345729.
Msieve - QS.
(486M^2·41)^41-1: c112 = p47 · p66, where
c112 = 7642129690963529790912625905072051777803567149201357719288738333272543384524197332407354605479159687892218385923,
p47 = 76325605721511911781046619551963254879985605043 and
p66 = 100125372327174884304468655202003769376036241379805378782596418161.
Msieve - QS.
(501L^2·41)^41-1: c112 = p43 · p70, where
c112 = 4105099148037560370769430568575176470768426194163352282669705320296001012765703240675670510132855364826441488373,
p43 = 3734348907588460061879393268448983088806331 and
p70 = 1099281092801936557471317162037267098173064530715276340930152992915983.
Msieve - QS.
(539M^2·41)^41-1: c113 = p36 · p78, where
c113 = 50390291355116213084188087516789219542998721645231747088911920588911083290069078162920714457160791878870554301919,
p36 = 141523565205013348998925564149593699 and
p78 = 356055836228546204784771072067141769205088416251623049682778816748019833277781.
GMP-ECM, B1=45e6.
(624L^2·41)^41-1: c115 = p39 · p76, where
c115 = 1052497863135872168259172763014361010606725178014975373739525057182194600642227631726264102875761917276443986350903,
p39 = 648196971014807508602272275689840597761 and
p76 = 1623731535628895664150777277180007961409180304421328390239749974621245818423.
GMP-ECM, B1=45e6.
(726M^2·41)^41-1: c113 = p42 · p72, where
c113 = 24001996527495287137333202459361038764991097964890842597871877703861553575844490369483266481431136521657792261661,
p42 = 165424534330602990395739196947734457043027 and
p72 = 145093329865611097307287912135820399676736931027377424885358676345774543.
GMP-ECM, B1=45e6.
(818L^2·41)^41-1: c114 = p38 · p77, where
c114 = 372819948442327025698300336138641346035895904200373345911668967098392827050252695553416961314017623412628153936597,
p38 = 18866871246944325176762319671465110331 and
p77 = 19760560379226040064389021336664506395096924083091557011237957526162895683887.
GMP-ECM, B1=45e6.
(825M^2·41)^41-1: c114 = p45 · p70, where
c114 = 430271315765397233213589315852173510286407385586039830900290199089592111797138208090124233447196334980702182552653,
p45 = 406394088698951318315959347209279459461518311 and
p70 = 1058753873962309750026441946848681142749122013527730685653104760516523.
Msieve - QS.
(854M^2·41)^41-1: c115 = p42 · p73, where
c115 = 1025902250609490618094565206186502988195937273268950402878328036814809586023024563630023106435286038204845211023531,
p42 = 331334183927079668767656661327251490236551 and
p73 = 3096276509867367403240885115210534060380217909687274950149170607487617981.
GMP-ECM, B1=45e6.
(934M^2·41)^41-1: c112 = p43 · p70, where
c112 = 2204312267305708651529297500188038197923041922822341449248114894056438572357475783672178416858926999854280367681,
p43 = 1393011912695850606813620167283742301476041 and
p70 = 1582407334219974385822771963869400310520618945044466505739509885850041.
Msieve - QS.
August 30, 2010
10^6106+1: 6219908629712986001.
10^6206+1: 3311354296550325689.
10^6251+1: 1599065973632069507573.
10^6341+1: 1504654787835811243157.
10^7557+1: 80760988474868456629135346317.
10^10668+1: 14435973064229809.
10^11141+1: 89429221632313652051.
10^11356+1: 27930911704041314849.
10^11529+1: 535296762710263.
10^11601+1: 47847988796874571.
10^11846+1: 13375183750466701.
10^11918+1: 4508533378292205589.
August 20, 2010
10^3892+1: 2834278778744573810273127918507017.
10^6075+1: 33671237692047955201.
10^6146+1: 76450473305598476869.
10^6280+1: 2608819689539633255041.
10^6384+1: 2241549213434896917217.
10^6403+1: 148331454472206557.
10^7081+1: 6175209187858143265139.
10^8621+1: 177185865532965607.
10^8635+1: 95537452043138409481.
10^8636+1: 7007156967305993.
10^8671+1: 330231412514665169.
10^8716+1: 5810083533829160393.
10^8716+1: 1537041717714837899969.
10^8744+1: 2980461002398577.
10^8755+1: 33477647558038732334491.
10^9319+1: 8545227365924055071983849.
10^9323+1: 97537679772491394979.
10^9347+1: 11378838637245899.
10^9358+1: 38410426532221.
10^9367+1: 394163081510222710717.
10^9369+1: 1025326423600125013.
10^9396+1: 260868325359784537.
10^11082+1: 6765340009303356421.
10^11099+1: 9644780571997314437.
10^11161+1: 17033747976200419.
10^11180+1: 90148081811526961.
10^11214+1: 893245096732309021.
10^11246+1: 6848431606685423705221.
10^11274+1: 121494772278064609.
10^11299+1: 16490599799329.
10^11504+1: 2249877971856769.
10^11772+1: 1199409113094697.
10^11785+1: 665241240329568841.
10^11796+1: 266464683185000449.
10^11945+1: 1928678881797881.
10^11967+1: 1626121490595818863.
August 17, 2010 (Kurt Beschorner)
(353M^2·41)^41-1: c112 = p48 · p64, where
c112 = 2738911107311160163069637691533723284105305807693573699862868518694565782048936975682193226627479531191045822413,
p48 = 883962028115340614030052547898453934788593669217 and
p64 = 3098448824946339406628484844371833126135115355617078663241841389.
Msieve - QS.
(848L^2·41)^41-1: c113 = p50 · p64, where
c113 = 48315506325191634264708595273524481883143055620324882285002125232341285343481005123074525732110511775607400431561,
p50 = 26416733982047705520539952562114685755108737454393 and
p64 = 1828973496800395729252415467406416134642221799402924978036028177.
GMP-ECM, B1 = 45e6.
August 16, 2010
10^6089+1: 685222418409111710717. P+1.
10^6109+1: 1137747784110053703343. P+1.
10^7515+1: 19510587138286537994521.
10^7594+1: 8186095371684852403169.
10^9324+1: 5742755777555497. The first yet known factor.
10^9327+1: 15345048435861000847.
10^11030L+1: 21713252105872754461.
10^11030L+1: 564501056655193333578341.
10^11030L+1: 379734028873536797744282021.
10^11150L+1: 16935083847181371753404801.
10^11170L+1: 1017107149496080116361.
10^11270L+1: 65381641598771220819881.
10^11350L+1: 9455294956384426301. The first yet known factor.
10^11560+1: 99491422665121. The first yet known factor.
10^11890L+1: 1918983759848746017881.
10^11929+1: 16603307144257739.
10^11949+1: 28481127972893863.
10^11950L+1: 1768986379915526245352201.
10^11950M+1: 2116084338827167432001. The first yet known factor.
10^11980+1: 651830535365811408961.
10^11990L+1: 45964331469131131465747801.
10^33011+1: 58683403804185931. The first yet known factor.
P-1. B1 = 1e5-3e5, B2 = 203499040, n = 17001..17500.
10^17006+1: 2654925677479354709. The first yet known factor of Phi(34012,10).
10^17067+1: 398527752637181659. The first yet known factor of Phi(34134,10).
10^17080+1: 60008028384161761.
10^17089+1: 13523280810959441.
10^17105+1: 95410033004441.
10^17122+1: 287713024661827864709. The first yet known factor of Phi(34244,10).
10^17123+1: 480184563665322319106722357.
10^17134+1: 1086644258429549.
10^17144+1: 304028203630049. The first yet known factor of Phi(34288,10).
10^17152+1: 643471229453102593.
10^17187+1: 17589772773259.
10^17188+1: 17416128486306377.
10^17196+1: 67113047140081. The first yet known factor of Phi(34392,10).
10^17199+1: 3146740439556949327.
10^17219+1: 2457257975481953213.
10^17247+1: 5211153715988569.
10^17256+1: 70348079570342597204017.
10^17274+1: 431531896318699261.
10^17275+1: 24496198310851.
10^17284+1: 7971926490449.
10^17288+1: 27640231177299188641.
10^17301+1: 384986232993823.
10^17309+1: 693448924283449.
10^17323+1: 260960464902637.
10^17345+1: 1680798706283439061411. The first yet known factor of Phi(34690,10).
10^17348+1: 584874350191580377.
10^17431+1: 1633970918553011. The first yet known factor of Phi(34862,10).
August 15 (Kurt Beschorner)
(265L^2·41)^41-1: c112 = p43 · p70, where
c112 = 6335369431934959625870318702293752479060629392675332976667075901962483591817048384966573450397501542900594816729,
p43 = 1594520793195758811858070979777046988438567 and
p70 = 3973212176956019369293598597635297422548216256662926943131577248044287.
GMP-ECM, B1 = 45e6.
(280L^2·41)^41-1: c112 = p53 · p59, where
c112 = 1143819602719321272170654789191618238929365316757647200308093000311731164998419334280236067852911365393027169477,
p53 = 26962650900853887255739766739534964908667335186079841 and
p59 = 42422371855250232442285682345969351512738171846945505248997.
Msieve - QS.
(443L^2·41)^41-1: c112 = p40 · p73, where
c112 = 3283092528115176670627037306622788082538793261557488518471218953960705274977652867320826230210982105421529556469,
p40 = 1797277561050056968359850492497193088599 and
p73 = 1826703119910446292135530598974471876454177034610811303056924842195050131.
GMP-ECM, B1 = 45e6.
(454M^2·41)^41-1: c112 = p46 · p67, where
c112 = 2223414062060674394512875105048336166816508435944850242438096925107270902884940692856600968454036306006125153861,
p46 = 1759568448496915789622698905603027270152466647 and
p67 = 1263613281972628894698000480198128570227873169465863777257523063363.
GMP-ECM, B1 = 45e6.
(736L^2·41)^41-1: c112 = p44 · p69, where
c112 = 9229035575055402172913797855490998587242567012779347593989014196380643669785627354042350397583850701529321009609,
p44 = 24127492742155350955048603821856642387007111 and
p69 = 382511174023917926113717842347167306840801754376765407486069077129519.
GMP-ECM, B1 = 45e6.
(792M^2·41)^41-1: c112 = p45 · p67, where
c112 = 1196697422113475569014727987430705482101272134783621984044265660579127710719501417020566765809355419699106745843,
p45 = 246815574762364709256672379094061347376592543 and
p67 = 4848549056378074737424567157982288864381610708165102726840510893101.
GMP-ECM, B1 = 45e6.
August 12, 2010
(944M^2·41)^41-1: c113 = p54 · p59, where
c113 = 19688808651777131233222196295818583047930936742269351238628178733774001325229881252582668226056949205839411708563,
p54 = 282449773443966242314208479345499464081643278892893561 and
p59 = 69707291359124041592379686992894265446354987366852095263083.
Msieve - QS.
August 9, 2010 (Kurt Beschorner)
(427L^2·41)^41-1: c109 = p45 · p64, where
c109 = 1122683596702753150819619265215880119322943904751969813460443734653113246042940974599439245616603617922727577,
p45 = 635036645351429271614520736884379205603036443 and
p64 = 1767903639767843731933526270456172093558164497675971803911234139.
Msieve - QS.
(446L^2·41)^41-1: c109 = p44 · p66, where
c109 = 2503667620303036512181618005340237873689645392965440055207333673846684750367541770191613760954465212733322537,
p44 = 22685304126193755538231266867101924851196929 and
p66 = 110365177666371156490480143035781918384572727248784217838048915753.
Msieve - QS.
(485L^2·41)^41-1: c108 = p49 · p60, where
c108 = 886822424176300486237152556481933534839515796639818945061470500922604602316743355930161377890095688095705521,
p49 = 1056952905835856694266528313407394541041557964917 and
p60 = 839036838140849736669110830328401642445326626317403151684813.
Msieve - QS.
(540L^2·41)^41-1: c109 = p52 · p58, where
c109 = 9577912987915105636810589595668115598609873984001366114709471669225753995777674930844949586717805923635434057,
p52 = p52 = 1349553933777643220102218129030624291432771931024377 and
p58 = 7097095379585765345220138716155755201433502995440281029841.
Msieve - QS.
(557M^2·41)^41-1: c112 = p39 · p73, where
c112 = 1174804211120469371528000320322250706753261383374772636642582228507221590650799773911780403884368651482123901691,
p39 = 185872274219489740729480463564585239927 and
p73 = 6320491940251326748600846660357977209738798233320455101880145473116178333.
GMP-ECM, B1 = 45e6.
(862L^2·41)^41-1: c109 = p51 · p58, where
c109 = 3562817756746028445753295761776643853186282197570415983738170949095835533560366142324611864441392201953552047,
p51 = 620491597907150484989983784133179757897056020570837 and
p58 = 5741927479377671810853750635908949294958898986564874665331.
Msieve - QS.
August 9, 2010
10^9890L+1: 561058006145661348309682561. The first yet known factor. P-1 (B1 = B2 = 1e7).
10^11210L+1: 966691211608649341.
441 factors in the range n = 17001..19500 and n = 22001..22500.
In any cases but one the remaining cofactor is composite.
These 441 factors were found by P-1 (extending an earlier search with B1 = B2 = 1e5 to B1 = 1e5 and B2 = 31056462).
10^17020+1: 4013920022534914995521.
10^17025+1: 277279723069801.
10^17037+1: 660388515035113473841.
10^17045+1: 60522592793881.
10^17046+1: 624421880292601.
10^17054+1: 40281410033141.
10^17057+1: 151677153896011.
10^17066+1: 27105203826149.
10^17072+1: 3090025381492897.
10^17073+1: 13599174429290899.
10^17084+1: 5106311908074161.
10^17089+1: 114326014506287.
10^17103+1: 71564145052303.
10^17108+1: 231694595889121.
10^17113+1: 77690218904149807.
10^17125+1: 15071166074070816001.
10^17139+1: 4452517147965157. The remaining cofactor (10955 digits) is (probably) prime.
10^17148+1: 699972508805220793.
10^17152+1: 44654486539777.
10^17167+1: 29330391016450859.
10^17175+1: 99069365741851.
10^17177+1: 209024109438769.
10^17179+1: 271967327766767.
10^17183+1: 768916018466751490207.
10^17187+1: 1522350613987247641.
10^17188+1: 497884268554490953.
10^17193+1: 486232663619463114223.
10^17205+1: 1140366105585691.
10^17220+1: 8094433957681.
10^17236+1: 29805376128785015201.
10^17238+1: 8496378348901.
10^17240+1: 745492229068142561.
10^17241+1: 12369808168579.
10^17248+1: 28435018579969.
10^17254+1: 85819284896549212709.
10^17259+1: 76870656075793455460250851681.
10^17264+1: 45958598180671489.
10^17284+1: 187045213656606295921614241913.
10^17285+1: 259306956546902312401.
10^17293+1: 221091128547486653.
10^17296+1: 4549689844729082561.
10^17314+1: 97232505379021.
10^17316+1: 15650457561649.
10^17323+1: 143797873182629371.
10^17324+1: 33286088603993.
10^17328+1: 6861238096033.
10^17333+1: 284699022498478649.
10^17340+1: 110840882905201.
10^17347+1: 4657613052863.
10^17352+1: 6691813826833.
10^17363+1: 264496034380321087.
10^17374+1: 38803896870132101.
10^17377+1: 6104338923099340691.
10^17384+1: 29793463349186744683199920961.
10^17389+1: 107989792280495144709121.
10^17395+1: 285347100419851.
10^17396+1: 282096285139179602953.
10^17398+1: 539349324172145789.
10^17403+1: 5263673799370099.
10^17407+1: 6434123662878826866407.
10^17408+1: 15828506288129.
10^17411+1: 158210212449642011.
10^17413+1: 6127900301035350289.
10^17418+1: 2610833375122261.
10^17427+1: 10371770664226957.
10^17429+1: 100396650813397.
10^17431+1: 793794371157821237.
10^17434+1: 5896260425989.
10^17439+1: 489040667326327.
10^17443+1: 226299209156228886129371.
10^17445+1: 6353207657850601.
10^17455+1: 7991026875331.
10^17469+1: 1869872186149489.
10^17471+1: 1881355401477264721.
10^17476+1: 67928516846068217.
10^17485+1: 4624977667571.
10^17491+1: 3436517467268201.
10^17515+1: 4802469622211.
10^17524+1: 17610005515982881.
10^17524+1: 149187491102216321.
10^17524+1: 3669670487302050937889.
10^17536+1: 11967768668161.
10^17543+1: 28084383376729.
10^17545+1: 45767649510881.
10^17569+1: 191812258276957.
10^17576+1: 278814160949750255844303953.
10^17588+1: 4687015466683675383064297.
10^17593+1: 1232406011795201428771.
10^17594+1: 351913800180529621.
10^17615+1: 1145641860784257721.
10^17618+1: 14870150966172428381881.
10^17631+1: 15564601643523210253.
10^17635+1: 3404464810812001.
10^17637+1: 9425651068656157.
10^17640+1: 6112993259521.
10^17648+1: 48056649548551489.
10^17657+1: 6545252391587807.
10^17659+1: 55094055642877.
10^17662+1: 6480259331101.
10^17666+1: 91200113049761.
10^17676+1: 42152657204953.
10^17687+1: 133111300052533474536967.
10^17694+1: 1735272824189041.
10^17695+1: 11260570793895961.
10^17698+1: 2095447046164048081.
10^17699+1: 3567457767127.
10^17709+1: 959042679524887.
10^17711+1: 2160630971749958731.
10^17718+1: 2866752005448049.
10^17721+1: 369342552311371.
10^17724+1: 3300293088502537.
10^17726+1: 43246309882889.
10^17744+1: 3235804960417.
10^17751+1: 103980853747059332023.
10^17757+1: 46550926742491.
10^17766+1: 1456687760016889.
10^17768+1: 681730415907649.
10^17774+1: 262956624720589.
10^17781+1: 130387892864423011.
10^17784+1: 61501462122673.
10^17787+1: 12482986147171.
10^17789+1: 234999135274903.
10^17797+1: 47273189130332491053521.
10^17814+1: 3368581010063809.
10^17818+1: 130216488775241369.
10^17831+1: 28215269390419.
10^17838+1: 112235060362429.
10^17844+1: 849397620632740801.
10^17846+1: 1341118623141698689.
10^17874+1: 30704591369521.
10^17886+1: 618989870559721.
10^17888+1: 238704698322689.
10^17898+1: 47860055520329161.
10^17902+1: 33181376584789.
10^17902+1: 901550076605222671421.
10^17909+1: 824464003668571092123961.
10^17917+1: 26221495927000161710863.
10^17922+1: 1592368304679105601.
10^17924+1: 82950374609453041.
10^17927+1: 19411890362411.
10^17929+1: 85464449319459103.
10^17934+1: 631815147833521.
10^17943+1: 43939134950407.
10^17943+1: 5446613442947942917.
10^17949+1: 67487165840658541531.
10^17964+1: 1041561416271765673.
10^17965+1: 2731388316134981851.
10^17973+1: 131551806434131.
10^17984+1: 716972714135809.
10^17997+1: 63297483900633361.
10^18004+1: 957789689843135986537.
10^18009+1: 25933108574251.
10^18026+1: 85761794931221.
10^18033+1: 29210869473785053.
10^18038+1: 407415344721601.
10^18041+1: 5229910923407971.
10^18049+1: 669764200392967.
10^18051+1: 86351532185903183893.
10^18056+1: 3950356418018513.
10^18069+1: 1621032764560903.
10^18071+1: 49883129343973.
10^18081+1: 8529321417373.
10^18084+1: 3165567139265257.
10^18091+1: 29086316863481.
10^18114+1: 8307610078538461.
10^18115+1: 20359731842360358601.
10^18146+1: 62765686801561.
10^18158+1: 2747495417768389.
10^18166+1: 17047831835201.
10^18169+1: 225133835360893.
10^18172+1: 8808332179525649.
10^18174+1: 27566924250529.
10^18187+1: 435799999045340333.
10^18206+1: 255206283522301.
10^18209+1: 83551686289545847.
10^18214+1: 9670573617349.
10^18227+1: 813916499023321.
10^18252+1: 1608299017993513.
10^18255+1: 211772172151067131.
10^18288+1: 999800015990880673.
10^18306+1: 64095428864715049.
10^18313+1: 51324128575372339.
10^18316+1: 50669672425343572849.
10^18317+1: 60492400000198401197.
10^18324+1: 11974167310222947647593.
10^18344+1: 459395020851953.
10^18347+1: 8878309873993478339.
10^18348+1: 64363748438881.
10^18354+1: 7115393740981.
10^18357+1: 96081674849011.
10^18362+1: 574065248339501.
10^18364+1: 28445271857921.
10^18369+1: 610896253647895881823.
10^18376+1: 121674696488593.
10^18377+1: 30652738013837.
10^18378+1: 16827294274575506569.
10^18381+1: 20752800234087703.
10^18386+1: 294421328626781.
10^18387+1: 7600900764727.
10^18389+1: 1247900859061992493.
10^18408+1: 70762252058245298311489.
10^18412+1: 39629366128587362609.
10^18420+1: 54691144161021333587521.
10^18425+1: 27187623887051.
10^18448+1: 32709971699201.
10^18451+1: 35317531304753566006681.
10^18453+1: 7494819968307853.
10^18468+1: 229178752079342473.
10^18472+1: 9688958482120961.
10^18476+1: 25867736074720369.
10^18485+1: 648039485869042832699161.
10^18486+1: 31305455326549.
10^18487+1: 204608186553569.
10^18496+1: 152377720414651777.
10^18512+1: 12267927026476577.
10^18513+1: 3728623702180609.
10^18516+1: 14126617925001957097.
10^18527+1: 644698169142240462653.
10^18534+1: 4520163515029.
10^18546+1: 6151755377929748269.
10^18557+1: 2771530866514103.
10^18564+1: 17095455937057681.
10^18565+1: 178429543505050771.
10^18573+1: 5362309762093327.
10^18580+1: 30892098685601.
10^18582+1: 9880484404621.
10^18583+1: 10115211061593499.
10^18594+1: 6873951190069.
10^18600+1: 182590520378401.
10^18602+1: 361970799869892752969.
10^18605+1: 11557569184081.
10^18611+1: 25610477059051.
10^18615+1: 826905852098731.
10^18629+1: 189016341519539.
10^18629+1: 177402715572409237.
10^18631+1: 169460941351853.
10^18632+1: 9459050123857.
10^18643+1: 179125263491110091.
10^18649+1: 181714071962507622413.
10^18655+1: 134491092210931.
10^18664+1: 1070230210179335537.
10^18666+1: 73552368022561.
10^18667+1: 31689843975967.
10^18677+1: 22128890814454009.
10^18697+1: 44465293014143.
10^18703+1: 5339099021431873170019.
10^18704+1: 17541625592737.
10^18708+1: 440451748648297.
10^18713+1: 79582779807484205167.
10^18715+1: 6320989989357601.
10^18716+1: 2679153627535009.
10^18745+1: 255518835056411.
10^18747+1: 8478838135755289.
10^18758+1: 39750437690989.
10^18760+1: 16246674016921401761.
10^18767+1: 349541162819108874041.
10^18778+1: 9967551682241.
10^18787+1: 13807769231611.
10^18811+1: 64679871556327.
10^18816+1: 29565676912129.
10^18816+1: 694325840063092484353.
10^18817+1: 30976530308767.
10^18823+1: 2814431072036249.
10^18831+1: 4862385045632312899.
10^18844+1: 92143980276253921.
10^18846+1: 335550473996323969.
10^18854+1: 71413729889165220041.
10^18855+1: 42043668540869251.
10^18868+1: 7060118051681.
10^18869+1: 15162411282532671881.
10^18871+1: 60217503589277.
10^18883+1: 1766553048879642931.
10^18891+1: 197635861548337249.
10^18893+1: 94107064028797.
10^18901+1: 25695289592789213.
10^18902+1: 1312348940252741.
10^18907+1: 26878576638103.
10^18916+1: 5812950849577.
10^18919+1: 17098814828093893.
10^18931+1: 6937361207887771.
10^18932+1: 37331456054537.
10^18941+1: 146097883163623.
10^18942+1: 17153609064901.
10^18945+1: 90672346349378011.
10^18957+1: 451372188582103.
10^18967+1: 13853887408256767.
10^18971+1: 415168086297967.
10^18978+1: 16132919013181.
10^18981+1: 81583567230165373.
10^19009+1: 2921074996222531.
10^19020+1: 2252720758420081.
10^19022+1: 1382620522769412389.
10^19025+1: 36123109036801.
10^19032+1: 46515386537569.
10^19035+1: 417545948386081.
10^19054+1: 77889359138044643281.
10^19057+1: 7044592287167.
10^19059+1: 47485675906126577641.
10^19066+1: 1534938098699101.
10^19075+1: 1389406342947001.
10^19086+1: 8073867937621.
10^19120+1: 14670335781121.
10^19121+1: 794492041423481.
10^19131+1: 100727083969576303.
10^19139+1: 9050005448207229689.
10^19146+1: 2657011152572199229.
10^19151+1: 1832772574428280651.
10^19159+1: 82772163132569.
10^19163+1: 37670981820608809.
10^19167+1: 4437482541902299.
10^19174+1: 22392817187133301.
10^19180+1: 48631555085681.
10^19182+1: 7893194082661.
10^19187+1: 937835564425588823.
10^19218+1: 78185994735469.
10^19219+1: 136072985259569.
10^19224+1: 340542336734209.
10^19226+1: 4760202830701.
10^19242+1: 348675488135719064791741.
10^19259+1: 532363487361557983.
10^19262+1: 3809064591520394201.
10^19263+1: 9314836626389647.
10^19269+1: 3170926873297837.
10^19288+1: 3425208470183681.
10^19296+1: 11918001428880769.
10^19300+1: 923232973525201.
10^19307+1: 93557042523797.
10^19323+1: 1294262819104020607.
10^19344+1: 29393042765370337.
10^19357+1: 133463727018142379.
10^19360+1: 241050573202320641.
10^19367+1: 25042589729591561.
10^19371+1: 15413294194723129.
10^19380+1: 357126272801281.
10^19394+1: 4756749861199289.
10^19403+1: 1954348194397178653.
10^19405+1: 3758045767331.
10^19411+1: 938603946106961.
10^19411+1: 17887395598806343.
10^19420+1: 674962125331809121.
10^19423+1: 820644184380767.
10^19432+1: 8087494562504113.
10^19437+1: 253214749826821729.
10^19439+1: 52232657456963663.
10^19444+1: 28021990482721.
10^19445+1: 24861572772844961.
10^19448+1: 2690360449384609.
10^19451+1: 2920110893396256811.
10^19459+1: 77571231505681.
10^19464+1: 542123930940001.
10^19466+1: 18458205762868349.
10^19472+1: 12210352714154482241.
10^19474+1: 923748839273261.
10^19482+1: 13218063423751201.
10^19484+1: 571007050156537.
10^19492+1: 467909171860235674537.
10^19496+1: 41682244817912929.
10^19498+1: 430697489485208149681.
10^22001+1: 16596068106609982879211.
10^22003+1: 186523139077579.
10^22005+1: 866832391509481.
10^22007+1: 1252132842106341016849.
10^22011+1: 554459647370047.
10^22013+1: 170319161594476441.
10^22015+1: 43881529739251.
10^22020+1: 44961806436721.
10^22021+1: 447949772920253.
10^22022+1: 345866908807421.
10^22027+1: 683173457799331.
10^22027+1: 31347309918100447.
10^22043+1: 442924383644597.
10^22044+1: 104080040708170116481.
10^22078+1: 6596014540114609.
10^22089+1: 1096290489066837331.
10^22094+1: 136709303971111463561.
10^22099+1: 1132078260892863131.
10^22112+1: 3737766341675713.
10^22118+1: 224231110418921.
10^22121+1: 14992973312955956693.
10^22123+1: 1462052361296478167.
10^22124+1: 10601128041365041.
10^22145+1: 28144487835131.
10^22148+1: 14203288183169141749897.
10^22160+1: 5965029621781441.
10^22184+1: 56113629587457889.
10^22191+1: 501023367433447.
10^22223+1: 365659876625543.
10^22226+1: 6849569528011961.
10^22242+1: 1833235827360217645861.
10^22245+1: 9800096421684393481.
10^22246+1: 219349975340876129.
10^22260+1: 2942237831178130801.
10^22263+1: 1264956681741127.
10^22268+1: 8199063793841.
10^22275+1: 4484567331540451.
10^22278+1: 1025203882362301.
10^22283+1: 256367864450539.
10^22286+1: 1793620076830621219709.
10^22288+1: 63140681262467346407768641.
10^22292+1: 7187921785274137.
10^22301+1: 2861686339834478047.
10^22302+1: 340417077937824889.
10^22307+1: 7317374132801.
10^22308+1: 6206088735630326401.
10^22312+1: 20721647004337.
10^22315+1: 50176967682731.
10^22324+1: 35111180640565243729.
10^22326+1: 2592160352525089.
10^22333+1: 41824405819036936327873267050242047.
This p35 is the largest yet found factor of any Phi(n,10) in the range n = 12581..100000.
41824405819036936327873267050242047 - 1 = (2)(3)(23)(41)(59)(773)(971)(4153)(5479)(18503)(73477)(5395843).
10^22347+1: 408589381259756282899.
10^22355+1: 19073449817441.
10^22358+1: 1913127631958509.
10^22375+1: 114956047524001.
10^22379+1: 680493139018463.
10^22384+1: 909134255710817.
10^22385+1: 2075758155753811.
10^22391+1: 5801353422973.
10^22394+1: 4401823706459189.
10^22395+1: 38669150077988401.
10^22399+1: 838379285011997.
10^22400+1: 90890992281601.
10^22402+1: 41854260423509.
10^22405+1: 222648154146611.
10^22408+1: 3454086499267096321.
10^22408+1: 10637949108322749929894336497.
10^22411+1: 7400394354491.
10^22418+1: 53460489395378198250701.
10^22419+1: 360069550347277.
10^22420+1: 29233467368047681.
10^22428+1: 468286187654881.
10^22429+1: 30283643291287.
10^22433+1: 855675167391409.
10^22438+1: 862027027002317992458241.
10^22444+1: 754578458691563833.
10^22445+1: 5718914338788377761.
10^22449+1: 28907569718723156917.
10^22451+1: 651359479384477007.
10^22463+1: 14652043800689.
10^22476+1: 23397815577209761.
10^22478+1: 586696292293481.
10^22486+1: 3870432162362581.
19 factors of (yet unfactored) repunits (found by P+1 and P-1).
In any case the remaining cofactor is composite.
P+1.
10^47563-1: 1002898784577169.
10^48271-1: 3260365779804557.
10^70981-1: 148078791365870039.
10^74771-1: 14589598244130493.
10^76801-1: 1106986327783199.
10^83591-1: 34764899693462693.
10^89963-1: 58300513622947009.
10^91703-1: 6136179933781712359.
10^95087-1: 26129267273682431.
10^96001-1: 8314445743843667.
10^96661-1: 385042712574489517.
P-1.
10^46237-1: 5859265756046281.
10^46511-1: 24417250558016201.
10^46591-1: 5223387620151413.
10^46601-1: 31112074036137536715517.
10^46639-1: 9275672865673971558677.
10^46919-1: 3047698156125521.
10^48787-1: 1951903445595613.
10^49739-1: 29833873936798656827.
August 6, 2010
17 factors of (yet unfactored) repunits.
In any case the remaining cofactor is composite.
P+1.
10^40879-1: 523279597422778769.
10^43331-1: 17447852714967253.
10^54269-1: 2804799127279151.
10^54667-1: 22224848623210001.
10^55663-1: 4954888499974636001.
10^56377-1: 6580804448292327468043.
P-1.
10^41879-1: 120506774297744398540841.
10^42239-1: 830873865130679278904803.
10^42283-1: 71401977810305610493.
10^42397-1: 656411131509318083477.
10^42649-1: 11051595938611157.
10^42689-1: 2475228511288674738204551.
10^42737-1: 1826128430342323361.
10^43291-1: 303128236638713294191.
10^44087-1: 439433811747991.
10^44129-1: 3438340331360521.
10^44963-1: 6114727878515689.
August 5, 2010 (Kurt Beschorner)
(134M^2·41)^41-1: c109 = p45 · p64, where
c109 = 3204906056492557716849190643201761590288522424536002598631640533471595182147156963451458561099116758525535239,
p45 = 447700751640014468567091395421183386146013971 and
p64 = 7158589849921776517997688809283499196755420389233962309110744509.
GMP-ECM, B1 = 45e6.
(367M^2·41)^41-1: c108 = p52 · p57, where
c108 = 598181571517426688723122887080892376465175657029116621301109459319102813399039317258434634452252834482022369,
p52 = 1251730820499226433239559665802407638862203404458793 and
p57 = 477883552694543853452115684412041353270578036965111805433.
Msieve - QS.
(450M^2·41)^41-1: c109 = p43 · p66, where
c109 = 1071272954483703263235695656689004633871116255293536544810763507551113599669512878160979386761032227145694057,
p43 = 3591885577734478010729554196438644184212603 and
p66 = 298248073692645530330043662800839821193787704382282151027266778219.
GMP-ECM, B1 = 45e6.
(513M^2·41)^41-1: c110 = p52 · p58, where
c110 = 13555629486836824779455767028499444376953660488192286097998009295868225489429403057135189873230675076859624519,
p52 = 5025003767883029476471614499501196032093788365259889 and
p58 = 2697635686061911155554636823684758268294997374488743151671.
Msieve - QS.
August 5, 2010
10^40879-1: 523279597422778769.
The first yet known factor of the repunit (1)40879.
The remaining cofactor (40861 digits) is composite.
P+1.
10^41879-1: 120506774297744398540841.
The first yet known factor of the repunit (1)41879.
The remaining cofactor (41855 digits) is composite.
P-1.
10^42239-1: 830873865130679278904803.
The first yet known factor of the repunit (1)42239.
The remaining cofactor (42215 digits) is composite.
P-1.
10^42283-1: 71401977810305610493.
The first yet known factor of the repunit (1)42283.
The remaining cofactor (42263 digits) is composite.
P-1.
10^42397-1: 656411131509318083477.
The first yet known factor of the repunit (1)42397.
The remaining cofactor (42376 digits) is composite.
P-1.
10^42649-1: 11051595938611157.
The first yet known factor of the repunit (1)42649.
The remaining cofactor (42633 digits) is composite.
P-1.
10^42689-1: 2475228511288674738204551.
The first yet known factor of the repunit (1)42689.
The remaining cofactor (42664 digits) is composite.
P-1.
10^42737-1: 1826128430342323361.
The first yet known factor of the repunit (1)42737.
The remaining cofactor (42718 digits) is composite.
P-1.
10^43291-1: 303128236638713294191.
The first yet known factor of the repunit (1)43291.
The remaining cofactor (43270 digits) is composite.
P-1.
10^43331-1: 17447852714967253.
The first yet known factor of the repunit (1)43331.
The remaining cofactor (43314 digits) is composite.
P+1.
10^44087-1: 439433811747991.
The first yet known factor of the repunit (1)44087.
The remaining cofactor (44072 digits) is composite.
P-1.
10^44129-1: 3438340331360521.
The first yet known factor of the repunit (1)44129.
The remaining cofactor (44113 digits) is composite.
P-1.
10^54269-1: 2804799127279151.
The first yet known factor of the repunit (1)54269.
The remaining cofactor (54253 digits) is composite.
P+1.
August 3, 2010
10^49667-1: 6887806662970111.
The first yet known factor of the repunit (1)49667.
The remaining cofactor (49651 digits) is composite.
P+1.
August 2, 2010 (Kurt Beschorner)
(449M^2·41)^41-1: c110 = p53 · p58, where
c110 = 82182171801803417359015610173669423665183163642073747210153442224781066619560781727589141730720665510744835111,
p53 = 76524860273889849625781403858160165800346161046219691 and
p58 = 1073927760307768019168787925764989122320556576431268277621.
Msieve - QS.
(451M^2·41)^41-1: c110 = p42 · p68, where
c110 = 64363994892112931405006039199347629220891065703411496625206836711297549785803890012738015422828221515374591201,
p42 = 659282399460945758054632693002716817317737 and
p68 = 97627352019012443894677480515235434198415388808388149701584580377273.
Msieve - QS.
(533M^2·41)^41-1: c110 = p42 · p68, where
c110 = 10386465296115772122597983030873696729356661438407798375824043616268909545880187069681300023228481476059037289,
p42 = 580518372104237623351348552950706596369937 and
p68 = 17891708161564924574239882214612255377219125525498007843844455918297.
GMP-ECM, B1 = 75e5.
(569L^2·41)^41-1: c110 = p52 · p59, where
c110 = 62735509427166177178490211364916159479019368768764739346104437613234980871565311330046196263728121556393850853,
p52 = 2571024079357931438261803979404277543618707799200891 and
p59 = 24400980889620170295445012298149056883752121587895948125983.
Msieve - QS.
(569M^2·41)^41-1: c108 = p54 · p55, where
c108 = 319819310698430164064769236094988954892627616498596167639137954307858373412874680694636523709038978546711281,
p54 = 202302669297206421898106821387245184286508696693423293 and
p55 = 1580895159759745780894958166899131798588728505027202117.
Msieve - QS.
(697L^2·41)^41-1: c110 = p40 · p70, where
c110 = 12170796041400361167560624369729621389891386004645253169116838028858155888151343365086486845795547061813380163,
p42 = 5763179875198379022160937550985403405939 and
p70 = 2111819569223738737885165645663719591996872056002217370920561352152817.
GMP-ECM, B1 = 75e5.
(857L^2·41)^41-1: c110 = p55 · p56, where
c110 = 67668244926279822889899684062832237594750711345441196960318470186257204792377523122174360767362127704644466981,
p55 = 1579400275756117113987543866999614190620914645704939467 and
p56 = 42844265614607760165463249697938297169823834809409729743.
Msieve - QS.
(993M^2·41)^41-1: c113 = p43 · p70, where
c113 = 12121593797610996175335604422794892732257364573450451244389663767636326378802845034161985007793692985233926116563,
p43 = 4189675221379825706764650027527482490057677 and
p70 = 2893206073767903197943593634592852565107930212173123200368589788089119.
GMP-ECM, B1 = 11e6.
Alfred Reich