News - April 2010

April 30, 2010

163 factors.
10^14558+1: 53835804130421.
10^14575+1: 13934971144051.
10^14617+1: 10831479985121.
10^14651+1: 13662032681207.
10^14652+1: 30751411885921.
10^14682+1: 25096766700661.
10^14684+1: 11140907008393.
10^14705+1: 61997114802851.
10^14759+1: 12873994600087.
10^14783+1: 84569166226757.
10^14794+1: 15508883242529.
10^14794+1: 30738403483061.
10^14894+1: 68089717097249.
10^14968+1: 23085420823313.
10^14520+1: 31499039827201.
10^14522+1: 36700688688749.
10^14600+1: 39206514420001.
10^14606+1: 14029060078801.
10^14724+1: 11662762490209.
10^14745+1: 65339099034241.
10^14755+1: 94413329377121.
10^14762+1: 41994177209381.
10^14772+1: 11448708859417.
10^14779+1: 12108897489607.
10^14808+1: 28867935408817.
10^14828+1: 22548876432721.
10^14900+1: 11462164422001.
10^14996+1: 94441419923729.
10^14562+1: 188034844867561.
10^14575+1: 669480676682401.
10^14589+1: 168358839332797.
10^14642+1: 757712275940629.
10^14662+1: 938671707788281.
10^14686+1: 507238294182229.
10^14711+1: 105615615359887.
10^14786+1: 751698601694449.
10^14806+1: 174646028606369.
10^14966+1: 222647820692641.
10^14977+1: 555546476252413.
10^14724+1: 250832917373041.
10^14728+1: 212981685086353.
10^14731+1: 192456638390041.
10^14757+1: 111976430560213.
10^14758+1: 383216338705801.
10^14765+1: 426905679251561.
10^14776+1: 573744976112929.
10^14779+1: 146044824208757.
10^14785+1: 728405649982811.
10^14797+1: 700651219920007.
10^14899+1: 152346330567397.
10^14975+1: 787557056235601.
10^14516+1: 1607383876887281.
10^14601+1: 1628224818857881.
10^14616+1: 9083700161693137.
10^14653+1: 3595161211256287.
10^14659+1: 2723428689143653.
10^14778+1: 2191994413525009.
10^14804+1: 1265433898441409.
10^14916+1: 6266321132692633.
10^14988+1: 1472129965719913.
10^14519+1: 5569924803129259.
10^14547+1: 1162506017964019.
10^14557+1: 3177725715792571.
10^14602+1: 7195597335414461.
10^14604+1: 1668248341429249.
10^14673+1: 7288187964416011.
10^14706+1: 4217405932624609.
10^14722+1: 8719640633429521.
10^14740+1: 3576769627668161.
10^14824+1: 1194510508000001.
10^14860+1: 1311677749601041.
10^14866+1: 2726628574668709.
10^14927+1: 3180207324042277.
10^14979+1: 3116177151717601.
10^14654+1: 39334115138720081.
10^14780+1: 12185789334598001.
10^14900+1: 71225688101818801.
10^14505+1: 37037515988379211.
10^14604+1: 50753288362268929.
10^14684+1: 64274901207802001.
10^14691+1: 61388405708754133.
10^14699+1: 20376713051712943.
10^14723+1: 14572718561313769.
10^14775+1: 61909448836185001.
10^14799+1: 12100700942201089.
10^14819+1: 11910858233380681.
10^14821+1: 51475328791710121.
10^14849+1: 58750962727182527.
10^14856+1: 20323918645256977.
10^14888+1: 10638348423430577.
10^14917+1: 78746102859601087.
10^14657+1: 290896827199018099.
10^14707+1: 312758581957048921.
10^14787+1: 103763606148357769.
10^14509+1: 201719923068657401.
10^14573+1: 198783287348116277.
10^14595+1: 544179298295199001.
10^14613+1: 373201646372630401.
10^14617+1: 102966576901243733.
10^14663+1: 339139665258451927.
10^14717+1: 217392237940370609.
10^14943+1: 413611765296086557.
10^12114+1: 8536929337905139909.
10^12148+1: 6574649383851637513.
10^12235+1: 9202634866612863931.
10^12659+1: 2407922396914904407.
10^12708+1: 6874689131182895977.
10^14581+1: 7541825264317869449.
10^14923+1: 3667226768603649859.
10^14719+1: 6406130925147443419.
10^14772+1: 5193133574147569657.
10^14926+1: 1634515849657893901.
10^15042+1: 3555763405852807381.
10^15074+1: 2994464466014045509.
10^15132+1: 2117390103853584457.
10^15277+1: 1033719623104726903.
10^15373+1: 1001286796357303571.
10^17499+1: 1204183308674526769.
10^37036+1: 3213064977587514073.
10^14688+1: 36174860377106204161.
10^14502+1: 78321716879385332281.
10^14548+1: 10580762860406844953.
10^14681+1: 53646011428541785807.
10^14697+1: 85769441155634078503.
10^14821+1: 18054766028179196887.
10^15125+1: 29982052483605296251.
10^15131+1: 40168081000195788931.
10^15198+1: 10538483326268429641.
10^15246+1: 46206432737344033309.
10^15293+1: 19858294826978460539.
10^15422+1: 93221223219443763181.
10^15318+1: 29125792650081367621.
10^17012+1: 82917580812899008801.
10^17307+1: 64455204068459040601.
10^17440+1: 20345803976000146561.
10^14625+1: 356634511889543316001.
10^14659+1: 669757184878212970129.
10^14706+1: 180096427232253396541.
10^14737+1: 850586462564090455729.
10^14742+1: 178392590311313015821.
10^14864+1: 660002659679659823777.
10^14978+1: 286102573631080548841.
10^14989+1: 113655264598535103133.
10^15105+1: 650498560092951415171.
10^15173+1: 252165375483791392121.
10^15201+1: 184344638909509234801.
10^15242+1: 380419427082561605929.
10^15354+1: 101193529985202216421.
10^15374+1: 144672767185852182941.
10^15240+1: 500926914028180261441.
10^14577+1: 1133769233553675967543.
10^14540+1: 2241516922985917081441.
10^14627+1: 5017971416301945169223.
10^14658+1: 5088056538376265057101.
10^15056+1: 8154396082921348634369.
10^15320+1: 2775340259982535120481.
10^15025+1: 1468055646958731632051.
10^15118+1: 33495901972674530351321.
10^14898+1: 66765402016512912736921.
10^14641+1: 353547857553631711963477.
10^14815+1: 211580599157397527703761.
10^14735+1: 42492042669264833294309171.
10^14719+1: 778037739945330106419618842411.



April, 29, 2010

10^24261-1: 2782736755848870523.
10^24343-1: 3881463684770671693.
10^24523-1: 2135562024378408289.
10^25639-1: 1556232281053506841.
10^25737-1: 2242396988007492289.
10^24505-1: 28531644569590330351.
10^24567-1: 90043438016385169609.
10^24885-1: 29248724051666439391.
10^24901-1: 48128506435424823671.
10^24143-1: 112546434051418088443.
10^24527-1: 579996680483528030689.
10^24655-1: 225111200322285664801.
10^24783-1: 458811022057005098911.
10^24857-1: 158069389455094147759.
10^24463-1: 4101301346823626155043.
10^24949-1: 7051160605585356687923.
10^4565-1: 270935411026310849916438438241.

10^15770M+1: 1047546609351847721.
10^18330M+1: 1202819134842733201.
10^18350L+1: 1727912616093996301.
10^27490M+1: 17409228951015488941.
10^15510M+1: 8251894774309126926481.
10^15710M+1: 2975172717388528656221.

10^6854+1: 98581337218367849.
10^6568+1: 662852584716794143649.
10^6834+1: 1897897878488091648661.
10^6864+1: 5367040793067463072993.
10^6885+1: 31724754367176043045291.
10^6569+1: 562289793935277154246531.
10^6867+1: 2862847749871640077397299.
10^6969+1: 1614157519262210847977420089.



April 28, 2010 (Juno Fernadez)

(131L^2·41)^41-1: c104 = p51 · p54, where
                  c104 = 28535225132810724772177941176022465627525019177956594285538218980444664892740094752772472461010018907673,
                  p51 = 233201120578639328066193573847547007527543420150329 and
                  p54 = 122363156154681376808029012178697705988423552234189537.

gnfs and Msieve.



April 27, 2010 (Juno Fernadez)

(337M^2·41)^41-1: c99 = p44 · p55, where
                  c99 = 235736532629200491970067477093992466695597598869140251723740844113170644503203073806679269998565697,
                  p44 = 86296084507930784189180866433048006484022649 and
                  p55 = 2731717597309247898032038161625730539437304488423839753.

gnfs and Msieve.



April 26, 2010 (2nd)

231 factors with 16 digits.
10^17210M+1: 6911648831479181.
10^22030M+1: 4446878617871381.
10^22070L+1: 3351967532532581.
10^25890L+1: 2380156012136281.
10^26610M+1: 4550996688931921.
10^26810M+1: 5695859137216921.
10^28430M+1: 1410543517982681.
10^29490M+1: 2818610429290561.
10^29770M+1: 3340881728975701.
10^30090L+1: 7182296153918341.
10^30590L+1: 7669972832458301.
10^30890M+1: 5436200977110601.
10^30950M+1: 1514834327108801.
10^31830L+1: 1566637438035601.
10^32490L+1: 8135043545429641.
10^33110L+1: 4830224044062341.
10^33570L+1: 4835516923901701.
10^33690L+1: 2549058452385301.
10^33710M+1: 1431111387606701.
10^34530L+1: 2090004492861541.
10^34810M+1: 5964075283659461.
10^35110M+1: 5939253864657661.
10^35810L+1: 9970944359775181.
10^36310M+1: 8174271125198621.
10^37050M+1: 3092733772389301.
10^37210L+1: 1769589470008361.
10^40150L+1: 1795047545827801.
10^40490L+1: 6469690445113501.
10^40670L+1: 2867306289792281.
10^41430M+1: 3356251315921921.
10^41590L+1: 4105673264901721.
10^41770L+1: 1727309456255561.
10^41890L+1: 9560474249919881.
10^42050L+1: 2745385968838901.
10^42070M+1: 5236711863231241.
10^42110L+1: 1585557205899661.
10^43150L+1: 2213288100889301.
10^43150M+1: 1609222885485101.
10^43230L+1: 1225818783550681.
10^43850M+1: 7761466430068801.
10^43950L+1: 7547510313562201.
10^44610L+1: 1551962949047461.
10^44670M+1: 2954003507628841.
10^45190L+1: 1925164273794061.
10^45290M+1: 2560956974474501.
10^45410L+1: 2719113601853581.
10^45670L+1: 8842506447369961.
10^46990M+1: 2151229588967321.
10^47250M+1: 1100441647242001.
10^10442+1: 3783717510701461.
10^12208+1: 8572658018491841.
10^12272+1: 3263000712162881.
10^12437+1: 2859275811892223.
10^12545+1: 1438331403844921.
10^12554+1: 1245165819663769.
10^12589+1: 1802416755233729.
10^12615+1: 7940229782219611.
10^12648+1: 2861234713628497.
10^12741+1: 1321406007375397.
10^12747+1: 5973612892061011.
10^12847+1: 4371466956378481.
10^12873+1: 1297581936153889.
10^12875+1: 2766851622433001.
10^12877+1: 1268920658052253.
10^12902+1: 1992494310204949.
10^12914+1: 3770965811654009.
10^12926+1: 1564136735194489.
10^12963+1: 3322408900143811.
10^12980+1: 1026201163242641.
10^13078+1: 6697384584617689.
10^13200+1: 1001858479670401.
10^13421+1: 8205774306900931.
10^13424+1: 2666294453158529.
10^13571+1: 5427072169254251.
10^13656+1: 1073938485183793.
10^13678+1: 4624180734980801.
10^13771+1: 3998084065597121.
10^13869+1: 4044580456062583.
10^13962+1: 5550350646937981.
10^14066+1: 1077547735929029.
10^14156+1: 2472978122238401.
10^14188+1: 5081209274653753.
10^14286+1: 1740350548143409.
10^14288+1: 6007240825571329.
10^14292+1: 7817693817639889.
10^14468+1: 1674878018560961.
10^15006+1: 1163608454098729.
10^15032+1: 7353176166299969.
10^15056+1: 1030130445423169.
10^15062+1: 1769546975214001.
10^15067+1: 9332414998464169.
10^15093+1: 2921227191373609.
10^15138+1: 1437059642906521.
10^15144+1: 5837067980587201.
10^15145+1: 1034372313173681.
10^15169+1: 6212066703772931.
10^15180+1: 5483308442457121.
10^15219+1: 7422913476523927.
10^15249+1: 3945979972646401.
10^15259+1: 1370466539733077.
10^15260+1: 1083854057209841.
10^15294+1: 3581552921828041.
10^15300+1: 4548844405090801.
10^15317+1: 1245887821159717.
10^15318+1: 5032898579630521.
10^15440+1: 2140994497233281.
10^15451+1: 5175326293941491.
10^15474+1: 8277668701096261.
10^15491+1: 1070791339784041.
10^15511+1: 1253403118117453.
10^15536+1: 1200706260293473.
10^15682+1: 3069981683281489.
10^15707+1: 1644573764135171.
10^15765+1: 5122556011704091.
10^15832+1: 1699865252180321.
10^15838+1: 2721981029549629.
10^15879+1: 1438318516524649.
10^15920+1: 2238485923306561.
10^15927+1: 6438566970849049.
10^16115+1: 1231902870747121.
10^16187+1: 8502662628196721.
10^16220+1: 2320740757281761.
10^16261+1: 1327263107960903.
10^16357+1: 3194436211519411.
10^16395+1: 1577199447091651.
10^16436+1: 8781301767070057.
10^16455+1: 3177459155527771.
10^16497+1: 1594256546620063.
10^17047+1: 1114616401721491.
10^17224+1: 5481258122263489.
10^17240+1: 7837930815919681.
10^19576+1: 2086608733724321.
10^19586+1: 9992092317887989.
10^19601+1: 2404325142671801.
10^19705+1: 5343727671064091.
10^19740+1: 5635715437060801.
10^19767+1: 6439252325240131.
10^19822+1: 1614821563130249.
10^19889+1: 7417409414563927.
10^19926+1: 8438975954341201.
10^19956+1: 2408528175834241.
10^19994+1: 5559248357210341.
10^19994+1: 8875384804174409.
10^20117+1: 1673825152615081.
10^20143+1: 5269450072523569.
10^20187+1: 1849716511251607.
10^20253+1: 1745373061300807.
10^20263+1: 5641731597005687.
10^20309+1: 1363737936991889.
10^20329+1: 5765687721469127.
10^20347+1: 1906843121581451.
10^20400+1: 2183076518899201.
10^20407+1: 5074307923960969.
10^20433+1: 5854867275210409.
10^20488+1: 6084180036644321.
10^20521+1: 4172154887892973.
10^20569+1: 1549925777943173.
10^20575+1: 2669880227358401.
10^20606+1: 3406894134428209.
10^20608+1: 2415223231131649.
10^20620+1: 7233867926734081.
10^20626+1: 7745551131574589.
10^20628+1: 2143069356349729.
10^20646+1: 1385379256397581.
10^20649+1: 3918792980618653.
10^20699+1: 1265448011157023.
10^20726+1: 1375589591296909.
10^20742+1: 5053571933560561.
10^20813+1: 2160087671524693.
10^20844+1: 2203876616556961.
10^20883+1: 8654387679629173.
10^20931+1: 2493032264059303.
10^20935+1: 1984075448915801.
10^20951+1: 6379579449508091.
10^20958+1: 1279878458848921.
10^20989+1: 7263503431549819.
10^21086+1: 9133749461237389.
10^21201+1: 2597844539192047.
10^21223+1: 1202599807692161.
10^21446+1: 1663458378317189.
10^21481+1: 2795950582026361.
10^37067+1: 1323710185897531.
10^37123+1: 8466623244267329.
10^37171+1: 5381451983918401.
10^24175-1: 2281160286586751.
10^24409-1: 2968687123254161.
10^24517-1: 2777012262813031.
10^24535-1: 7941651366799991.
10^24563-1: 8086604492503769.
10^24689-1: 1859719656600191.
10^24839-1: 1886026616373157.
10^24861-1: 4027558851964027.
10^24875-1: 1976877739806001.
10^24947-1: 6023810827363031.
10^24947-1: 8779436589002197.
10^25045-1: 6195446567441441.
10^25127-1: 1495506312397613.
10^25167-1: 6582664720308403.
10^25413-1: 3500067503876401.
10^25415-1: 1401887402779631.
10^25423-1: 2850686171512477.
10^25523-1: 4971901984852147.
10^25655-1: 3342615409252351.
10^25833-1: 2604954233098603.
10^25869-1: 1673952677171443.
10^25995-1: 1484531341815631.
10^28067-1: 1485994133894791.
10^28231-1: 3876062588998027.
10^28291-1: 7583173754119489.
10^28369-1: 3109931152284199.
10^28379-1: 1102267551906431.
10^28399-1: 2013875734209641.
10^28431-1: 1682321405570209.
10^28467-1: 2266231684573117.
10^28503-1: 1907894743569757.
10^28511-1: 1048578198014929.
10^28523-1: 6506132039319001.
10^28539-1: 1960426168815871.
10^28573-1: 5620409528837569.
10^28725-1: 1221062490687601.
10^28727-1: 4166652356921921.
10^28775-1: 1374465769485001.
10^28777-1: 2124778447280483.
10^28829-1: 3429914577667159.
10^28851-1: 3255382470082801.
10^28897-1: 2151994027826369.
10^28937-1: 1701830666152921.
10^99375-1: 2411636137920001.
10^99515-1: 1768976032707001.
10^99797-1: 1518292272229751.
10^99919-1: 2714506024089317.

197 factors with 17 digits.
10^17410L+1: 24748949783816341.
10^17810L+1: 25173981644419661.
10^17890L+1: 12531101080790581.
10^20610L+1: 12180297398410621.
10^20910M+1: 42224480025028921.
10^23530M+1: 79918571584365281.
10^23830L+1: 24043114455137881.
10^25250L+1: 23828676653317001.
10^27870M+1: 57217869555992581.
10^28730M+1: 20052063694182781.
10^29250L+1: 33433713470547001.
10^30570M+1: 69448319958187321.
10^30810L+1: 85040869938721321.
10^32030M+1: 20154695522067481.
10^32950M+1: 16953668679653201.
10^34030L+1: 15053591196759781.
10^34370L+1: 93300578480135461.
10^34450L+1: 13958158590604801.
10^34690L+1: 54849761058792001.
10^35330M+1: 38131092136706201.
10^35790M+1: 23587437364102081.
10^37470M+1: 15871394611560541.
10^37810M+1: 45368593885545041.
10^37990L+1: 83286164385513461.
10^38510L+1: 35696570246028701.
10^39990L+1: 12388428771136801.
10^42030L+1: 25752451362276421.
10^42670M+1: 49788491768554321.
10^42770L+1: 22010889229618381.
10^42810L+1: 24464479030334641.
10^43770M+1: 44846346065158921.
10^43870M+1: 10310685070442941.
10^46510M+1: 73591719751748701.
10^46950M+1: 32449073834549101.
10^47390M+1: 18057565628440801.
10^10118+1: 30407434946255321.
10^10172+1: 52896896305881569.
10^12182+1: 14781310864994249.
10^12246+1: 13461907828362709.
10^12356+1: 13089379669670929.
10^12380+1: 43406967911381681.
10^12401+1: 19492371690549731.
10^12439+1: 73315551349178503.
10^12586+1: 18635408977589741.
10^12587+1: 26725657391660093.
10^12636+1: 33384289500439489.
10^12655+1: 26542455941801801.
10^12656+1: 75125242033482593.
10^12883+1: 14898036812796437.
10^12939+1: 55470383939610247.
10^12996+1: 34922646551494153.
10^13029+1: 27670101670667881.
10^13074+1: 11098502298578509.
10^13108+1: 67668778665854777.
10^13127+1: 53016006787382731.
10^13138+1: 68858307471716809.
10^13304+1: 45777450163787857.
10^13357+1: 16546185120986849.
10^13358+1: 13051780314216221.
10^13449+1: 97255953201695917.
10^13462+1: 26183971483113589.
10^13487+1: 81688131550945903.
10^13524+1: 25494039120200449.
10^13555+1: 67756152661382681.
10^13579+1: 91207909863789731.
10^13711+1: 19008803797178053.
10^13737+1: 17972158540270531.
10^13853+1: 24864190860559961.
10^13893+1: 46683592917456463.
10^14027+1: 67701760662976051.
10^14039+1: 14965582909963663.
10^14098+1: 13576007824046221.
10^14125+1: 13832005324332001.
10^14131+1: 53936139257034607.
10^14157+1: 31034192892720733.
10^14228+1: 61778420757263489.
10^14499+1: 11262756096801127.
10^15028+1: 60132768971012401.
10^15052+1: 47793961698974401.
10^15136+1: 18471653778743617.
10^15202+1: 82746847231252249.
10^15225+1: 49040550768556201.
10^15258+1: 28041797806472869.
10^15316+1: 49761582196385921.
10^15329+1: 81770729168953499.
10^15345+1: 17724337809483691.
10^15384+1: 21549317843575201.
10^15397+1: 32961078942125881.
10^15417+1: 26216414058298447.
10^15438+1: 14126565879845401.
10^15438+1: 19471484300701669.
10^15465+1: 43599760455092521.
10^15492+1: 61790726091259201.
10^15500+1: 57305889695388001.
10^15537+1: 56211936858159367.
10^15580+1: 12871129780830401.
10^15581+1: 21690248094631451.
10^15607+1: 78439966157653091.
10^15634+1: 32004236678076529.
10^15637+1: 71975089182623357.
10^15646+1: 40305372603608621.
10^15755+1: 38484663832486051.
10^15797+1: 63584453356053503.
10^15947+1: 23585731190712091.
10^15976+1: 91817958259773121.
10^16147+1: 28633010994529561.
10^16180+1: 11781823614125041.
10^16205+1: 58111136993818721.
10^16282+1: 25254402970951001.
10^16380+1: 67577157682332481.
10^16392+1: 23837031466456801.
10^16439+1: 17605011765252091.
10^16441+1: 22519795563714133.
10^17060+1: 83588274802868401.
10^17083+1: 31147583441848721.
10^17119+1: 22567359781340929.
10^17386+1: 22061698582894829.
10^19531+1: 63487645068053681.
10^19636+1: 71344053576077257.
10^19651+1: 75096967001473877.
10^19672+1: 19768066240944289.
10^19686+1: 17567873043558709.
10^19715+1: 27130412813493361.
10^19717+1: 19025572444891811.
10^19745+1: 23289678659665441.
10^19749+1: 23538404759396731.
10^19872+1: 11177469337317121.
10^19906+1: 65809422966308761.
10^19957+1: 21202781927421361.
10^20082+1: 52750519813450489.
10^20168+1: 68606155169452129.
10^20174+1: 67914493938189361.
10^20407+1: 13181332668474613.
10^20417+1: 30906395149774223.
10^20424+1: 13199437806291697.
10^20463+1: 87296672562192211.
10^20500+1: 56843013468076001.
10^20636+1: 19044987507367361.
10^20665+1: 39351456669005491.
10^20681+1: 82732009121149931.
10^20698+1: 84327667754469109.
10^20744+1: 12043696725510721.
10^20772+1: 99342167002593337.
10^20814+1: 27142922557811869.
10^20879+1: 88024188379907609.
10^20882+1: 10286703004614149.
10^20893+1: 16273195560419207.
10^20949+1: 88132689073113007.
10^20986+1: 99663901913517061.
10^20994+1: 55577425775615329.
10^21025+1: 88075913560875601.
10^21057+1: 39833919611870809.
10^21096+1: 18457515656876017.
10^21200+1: 93245818918014401.
10^21304+1: 70394791129370209.
10^21399+1: 42202900374186049.
10^21468+1: 17862409322593009.
10^37173+1: 15580238015705521.
10^24349-1: 14243657572148083.
10^24495-1: 10043249373235951.
10^24635-1: 14468576117717671.
10^24713-1: 13322218646189311.
10^24733-1: 19459131196168357.
10^24737-1: 20356151647251397.
10^24881-1: 68609844728748923.
10^24783-1: 16350011606368837.
10^25173-1: 21031914471050827.
10^25409-1: 11319433350363563.
10^25469-1: 32729129151225959.
10^25563-1: 33785553670559707.
10^25593-1: 15210065546794213.
10^25607-1: 24330896055023689.
10^25673-1: 27634259308020587.
10^25701-1: 11567682044209591.
10^25721-1: 71260290491623267.
10^25727-1: 50743995166450249.
10^25775-1: 13497188496908551.
10^25849-1: 33677420885354599.
10^25983-1: 32252022819359677.
10^28123-1: 89889282764392081.
10^28199-1: 19281627389796721.
10^28313-1: 61357385885442919.
10^28319-1: 44281417022510597.
10^28405-1: 13731943214254201.
10^28439-1: 31616238545877641.
10^28549-1: 60442279277690923.
10^28569-1: 10484288216260483.
10^28601-1: 19849306979405773.
10^28641-1: 21008264786084533.
10^28685-1: 27915925532106431.
10^28769-1: 44119843626439283.
10^28803-1: 58639098634291603.
10^28803-1: 97008047818086001.
10^28815-1: 40888911494791471.
10^28877-1: 24856963299670631.
10^28899-1: 51076703519022403.
10^99847-1: 14891921469833893.

177 factors with 18 digits.
10^15990M+1: 824706003799180621.
10^17210M+1: 319319630492643761.
10^17770L+1: 340006604683537081.
10^18150M+1: 127502599500503701.
10^22290L+1: 161697758400318661.
10^23550L+1: 709436585213374801.
10^23690L+1: 583380426449975981.
10^24190L+1: 958578249030657881.
10^25050M+1: 707925746040648901.
10^26990L+1: 747806692178578621.
10^30910M+1: 547849667547371641.
10^31150M+1: 147441648593329301.
10^31790M+1: 382469550348121721.
10^34250L+1: 955322319280276501.
10^34390L+1: 657023874115739981.
10^36310L+1: 357466742860240301.
10^36750M+1: 600049189307620501.
10^36870M+1: 363070158763998541.
10^36910L+1: 434817065736177601.
10^39770L+1: 382198931300725841.
10^40510L+1: 453885528388726961.
10^40850L+1: 354561352860369701.
10^41230M+1: 728820790121421761.
10^41430M+1: 111958505723336101.
10^41990M+1: 333075822721279301.
10^42230L+1: 295893902380730501.
10^42870M+1: 316495845646782181.
10^44030L+1: 293117495212670101.
10^44090L+1: 999391125003895081.
10^44410L+1: 276507610468937681.
10^44510L+1: 621198459556265881.
10^46350M+1: 904786158749164201.
10^46790L+1: 865877522087878621.
10^48570L+1: 419217818217548521.
10^12007+1: 804380266856391877.
10^12039+1: 631192618160908957.
10^12243+1: 201997371422612767.
10^12287+1: 626282628996863081.
10^12583+1: 553015733935531847.
10^12716+1: 812469046012454953.
10^12749+1: 214517339412700127.
10^12818+1: 519377652581924449.
10^12819+1: 879181267581670957.
10^12883+1: 342546434464326847.
10^12933+1: 116332222902446521.
10^12959+1: 214760830215865093.
10^12964+1: 962011499873531017.
10^13078+1: 552504200940250261.
10^13192+1: 199201388752579649.
10^13229+1: 175866304358414321.
10^13297+1: 410880084365711287.
10^13713+1: 268587525858656299.
10^13761+1: 519084236222125201.
10^13832+1: 165384284410023953.
10^13939+1: 120119961618783691.
10^13944+1: 187520340564473281.
10^13945+1: 543985918457506451.
10^13960+1: 900748859924361121.
10^13962+1: 665641228987576921.
10^13975+1: 871756318395245401.
10^14061+1: 783395051929903687.
10^14107+1: 147231963895250503.
10^14178+1: 800558074199985589.
10^14253+1: 284800188898795813.
10^14292+1: 393037462994330449.
10^14376+1: 517602670556027857.
10^14406+1: 174757616845609981.
10^14431+1: 704185738908255757.
10^15034+1: 742492638898475449.
10^15068+1: 221949913155878393.
10^15097+1: 872460828386152219.
10^15159+1: 160534930875166207.
10^15167+1: 375351131747112847.
10^15312+1: 394722676894613761.
10^15418+1: 414312316321094881.
10^15481+1: 305005384329879463.
10^15531+1: 149896034047276087.
10^15539+1: 245876275225929979.
10^15566+1: 178729335347723729.
10^15659+1: 243629688965794531.
10^15660+1: 375565703279769361.
10^15714+1: 267545866886260741.
10^15745+1: 277499389899007721.
10^15972+1: 168472967706645097.
10^16142+1: 124491303980200361.
10^16149+1: 497436466542561967.
10^16182+1: 411701572432463581.
10^16226+1: 171044933915036161.
10^16229+1: 363686299471893571.
10^16291+1: 351691979156728211.
10^16327+1: 382150121850639287.
10^16360+1: 866879204311887521.
10^16471+1: 104731998358197211.
10^16499+1: 629336040109203659.
10^17483+1: 113324300221285649.
10^19544+1: 192013999260943217.
10^19574+1: 142103151901786741.
10^19607+1: 271887118560572761.
10^19723+1: 797319640824589081.
10^19836+1: 550268494230862801.
10^19884+1: 181545497589731089.
10^19918+1: 111922537893803341.
10^19945+1: 125921088775925731.
10^20002+1: 226156389267388981.
10^20123+1: 666621139865490049.
10^20124+1: 158742410187598849.
10^20309+1: 404681539740063769.
10^20325+1: 781651088126237401.
10^20356+1: 131472522094043593.
10^20379+1: 264464246717896441.
10^20413+1: 335953304627792503.
10^20420+1: 478828696730358241.
10^20526+1: 465421498250429689.
10^20549+1: 107502776261937059.
10^20573+1: 293451493762293917.
10^20579+1: 378518436356699081.
10^20595+1: 314541317020467001.
10^20629+1: 688939042326420173.
10^20641+1: 293601817890919477.
10^20656+1: 165872407785063457.
10^20678+1: 909089567329431461.
10^20705+1: 102877990797884891.
10^20743+1: 686970915316314653.
10^20767+1: 780611965110172133.
10^20841+1: 878529212293200157.
10^20871+1: 191390610856147561.
10^20894+1: 360870110080542941.
10^20915+1: 639264397812832091.
10^20961+1: 175643741276414623.
10^21054+1: 229968784364944549.
10^21091+1: 408505070815189783.
10^21161+1: 271810731694969853.
10^21171+1: 387453884122820533.
10^21255+1: 169590044804634481.
10^21292+1: 113973539075659441.
10^21407+1: 386641746582296171.
10^37102+1: 865664350403509801.
10^24139-1: 398576989468556957.
10^24379-1: 215453538695288129.
10^24453-1: 235485303855817159.
10^24453-1: 549071336819190043.
10^24625-1: 302369583221884751.
10^24725-1: 265391260241822951.
10^24819-1: 380716968453598759.
10^24891-1: 263777303732603041.
10^24583-1: 687750752667724747.
10^24821-1: 560143453601011561.
10^24921-1: 261685301522219173.
10^25071-1: 690441554898181081.
10^25123-1: 256080962257121471.
10^25301-1: 766963247803733401.
10^25323-1: 820611504610322323.
10^25729-1: 297366355659786293.
10^25783-1: 381729234476877853.
10^25893-1: 424864236988453627.
10^25919-1: 148048795925229809.
10^28107-1: 152839294372990999.
10^28239-1: 104678100823928293.
10^28367-1: 145734848712157871.
10^28387-1: 542798352685789117.
10^28401-1: 151044283699005679.
10^28407-1: 149940639555339679.
10^28445-1: 109620488481219791.
10^28457-1: 200307285618144563.
10^28477-1: 324125678218897627.
10^28497-1: 522151110312492319.
10^28501-1: 136780621812849323.
10^28595-1: 332494604188519711.
10^28645-1: 208684014660023681.
10^28669-1: 277504142574633043.
10^28881-1: 935580597398257627.
10^28891-1: 303076386419102077.
10^28935-1: 730638317088315721.
10^28991-1: 307082254123758277.
10^31933-1: 186717703214937467.
10^99305-1: 267138771401502001.
10^99703-1: 113511093938763013.



April 26, 2010

10^15226+1: 48290188904806481.
The cofactor (14469 digits) is probably prime.

25 factors of repunits.
Each factor is the first yet known factor of the corresponding repunit.
10^11027-1: 2154709582874696383639.
10^13007-1: 5669576766194837.
10^13033-1: 174890459908547.
10^13037-1: 105313216409729.
10^13723-1: 17828943959857985987.
10^14033-1: 1123873788713293.
10^14543-1: 474725021824477.
10^14563-1: 1931675687284121.
10^14813-1: 1523349419727742681.
10^15727-1: 18696472856172443.
10^16223-1: 14916992855111.
10^17189-1: 4358992956757.
10^17393-1: 1374890436229380449.
10^17747-1: 280500643402089997.
10^18121-1: 43783265295893.
10^18521-1: 59595809879677.
10^18541-1: 30478479120169.
10^18593-1: 12629409113533.
10^18839-1: 98999458635830265431249.
10^19429-1: 265532773189825307.
10^19463-1: 2706370201272809.
10^19469-1: 87210930003277.
10^19603-1: 10270187578117.
10^19759-1: 44995090909311973.
10^19819-1: 122445041313827.

273 factors with 14 digits.
10^19450L+1: 83952679689701.
10^20650L+1: 67083367929901.
10^22190L+1: 28419599386361.
10^24110M+1: 47075464787101.
10^25350L+1: 73372632777601.
10^25730M+1: 32749159129241.
10^26850M+1: 90055072967701.
10^26870M+1: 22469939478241.
10^27430M+1: 94709800440061.
10^27770L+1: 29716913655941.
10^29350L+1: 11901591825401.
10^31550L+1: 17484492895501.
10^32150L+1: 22283203322801.
10^32670M+1: 11830415054041.
10^33150M+1: 85017921483301.
10^33190M+1: 30663271852001.
10^33370L+1: 62189177862761.
10^34290L+1: 13913526790621.
10^34730M+1: 59371124139581.
10^35290L+1: 31389946188781.
10^35370M+1: 64503765755641.
10^35770L+1: 96819599679461.
10^37890M+1: 24306488500681.
10^37930L+1: 85048529224501.
10^38610L+1: 16628398275061.
10^39690M+1: 16725891495601.
10^40690M+1: 23860895133401.
10^41130M+1: 61494878036521.
10^41610L+1: 20101179416221.
10^41910L+1: 18259967223961.
10^42190M+1: 72793196096521.
10^42650L+1: 12875477564501.
10^44470M+1: 39828230471881.
10^44850L+1: 30657309801301.
10^45110M+1: 22377119000081.
10^45130L+1: 87960724883401.
10^45230M+1: 41358275454161.
10^45330L+1: 15662470737721.
10^45730L+1: 33321841669841.
10^45750M+1: 40663085773501.
10^45950M+1: 59625289963801.
10^47150M+1: 25939033386901.
10^12211+1: 89186772135361.
10^12213+1: 89009781714361.
10^12436+1: 21421954165993.
10^12503+1: 18728555699863.
10^12563+1: 28764496587647.
10^12625+1: 52186155105001.
10^12693+1: 25953653451997.
10^12728+1: 26191216806353.
10^12738+1: 93495123942001.
10^12763+1: 18015396061891.
10^12786+1: 11047105406461.
10^12821+1: 34358491444859.
10^12852+1: 43900904154241.
10^12893+1: 87338685839521.
10^12953+1: 13278640777447.
10^13003+1: 51500048484601.
10^13073+1: 76841235673051.
10^13118+1: 22469430312869.
10^13255+1: 13577304630011.
10^13259+1: 62690185747463.
10^13428+1: 22198584058633.
10^13451+1: 81343800094757.
10^13469+1: 16645658989727.
10^13515+1: 22080713368081.
10^13546+1: 63969587432089.
10^13571+1: 69719557091677.
10^13595+1: 64238599033241.
10^13600+1: 41628254742401.
10^13768+1: 15718321102193.
10^13798+1: 22523976484421.
10^13831+1: 10597230680087.
10^13837+1: 12474324325237.
10^13889+1: 14086668442447.
10^13936+1: 16011694537697.
10^13956+1: 25939354931977.
10^14020+1: 36241281531041.
10^14054+1: 96633064635641.
10^14152+1: 13843869409729.
10^14204+1: 12426482662697.
10^14267+1: 13971673499477.
10^14268+1: 79414729104793.
10^14417+1: 45790248736597.
10^14445+1: 42259304453131.
10^14451+1: 14024705702407.
10^15022+1: 25545574131169.
10^15059+1: 25508819255503.
10^15077+1: 25702831100533.
10^15078+1: 15180175313101.
10^15113+1: 22838193724081.
10^15126+1: 25679888181601.
10^15132+1: 45182063784001.
10^15159+1: 11539787385691.
10^15175+1: 47677223146801.
10^15226+1: 54717973107001.
10^15235+1: 37745866307491.
10^15257+1: 13309904009579.
10^15273+1: 10530499151089.
10^15279+1: 14319938820133.
10^15284+1: 55568008812793.
10^15294+1: 39547131784249.
10^15299+1: 57988123488037.
10^15313+1: 24498843396739.
10^15362+1: 13196235284101.
10^15374+1: 11274654347701.
10^15374+1: 46972904808749.
10^15375+1: 35716411805251.
10^15375+1: 72828322232251.
10^15386+1: 12795469919429.
10^15388+1: 12362793677921.
10^15397+1: 30477764650693.
10^15416+1: 71844623729441.
10^15420+1: 12208904227441.
10^15473+1: 36422407506167.
10^15473+1: 48098757699611.
10^15474+1: 22386272194849.
10^15488+1: 47816191920641.
10^15491+1: 14740690874477.
10^15067+1: 23734170008641.
10^15508+1: 74157638143409.
10^15561+1: 16801130938411.
10^15620+1: 92509964897681.
10^15646+1: 27757454853581.
10^15649+1: 98873844622933.
10^15661+1: 12024109804237.
10^15678+1: 74271757205881.
10^15708+1: 11566878817033.
10^15718+1: 16328258674589.
10^15734+1: 26737357690349.
10^15743+1: 40179659818663.
10^15749+1: 21063871694903.
10^15753+1: 14955497034103.
10^15800+1: 49098502528001.
10^15827+1: 17067834710837.
10^15865+1: 10953800297851.
10^15866+1: 22090697911349.
10^15886+1: 11003630914901.
10^15913+1: 29171311483529.
10^15924+1: 32766066977113.
10^15927+1: 43123492809493.
10^15961+1: 10528664871451.
10^16015+1: 13252656664691.
10^16089+1: 10311006147493.
10^16089+1: 70785566496289.
10^16091+1: 20366155196011.
10^16092+1: 39813154441201.
10^16127+1: 24691172165423.
10^16172+1: 35371764598769.
10^16185+1: 13905635374801.
10^16198+1: 13137703437041.
10^16216+1: 46110209751169.
10^16220+1: 10231409972081.
10^16259+1: 46656187648927.
10^16323+1: 18349270458931.
10^16377+1: 31141804786459.
10^16383+1: 89433594684397.
10^16386+1: 19441373050261.
10^16417+1: 10638361684459.
10^17042+1: 12161049929129.
10^17042+1: 16836925502009.
10^17054+1: 87413560611269.
10^17073+1: 49815354914641.
10^17124+1: 18111998530537.
10^17138+1: 22912019107121.
10^17216+1: 25770594246401.
10^17275+1: 67625522917201.
10^17317+1: 23642203956601.
10^17496+1: 55420134799537.
10^19555+1: 15557896010651.
10^19569+1: 17250674855371.
10^19594+1: 51941146231369.
10^19602+1: 32178496655449.
10^19662+1: 91017050669749.
10^19665+1: 42052888581841.
10^19699+1: 33648035842171.
10^19707+1: 14025659510641.
10^19751+1: 14902507099619.
10^19753+1: 35711598032681.
10^19976+1: 11386107495313.
10^20077+1: 49011966778441.
10^20081+1: 39999954000943.
10^20120+1: 54975954315521.
10^20120+1: 83741032860161.
10^20353+1: 15436514095957.
10^20398+1: 15968076507209.
10^20412+1: 12576232132129.
10^20462+1: 32784945051821.
10^20469+1: 17539076305423.
10^20545+1: 15603152419331.
10^20551+1: 30620710424197.
10^20578+1: 32925509941001.
10^20621+1: 58438108425241.
10^20712+1: 34736406418513.
10^20758+1: 12102146074441.
10^20824+1: 24243064114417.
10^20833+1: 58750244356051.
10^20866+1: 18936956036101.
10^20901+1: 44190792010801.
10^20908+1: 28142090514953.
10^20911+1: 73826910237037.
10^20914+1: 23417363553721.
10^20928+1: 20231669645953.
10^20943+1: 11145273253453.
10^20953+1: 44353702346819.
10^20972+1: 84756090766313.
10^21005+1: 46842396016601.
10^21303+1: 19642711582693.
10^21426+1: 86193804102169.
10^37058+1: 26585652300481.
10^37115+1: 52585372877441.
10^37161+1: 93516442826761.
10^37337+1: 57982132653167.
10^37347+1: 25491049943641.
10^37357+1: 58404129326539.
10^37395+1: 10248128170201.
10^37486+1: 89155340908481.
10^41339+1: 23249839041001.
10^24423-1: 11237070413311.
10^24559-1: 41682743888689.
10^24579-1: 99410836849453.
10^24667-1: 51742701814919.
10^25291-1: 57710858439613.
10^25295-1: 17953445219951.
10^25487-1: 39934580037199.
10^25623-1: 10113021236917.
10^25641-1: 29691465744403.
10^25733-1: 17500434925093.
10^25855-1: 14280583211311.
10^25871-1: 14233730581321.
10^25903-1: 27784806324601.
10^25921-1: 27782947681231.
10^25951-1: 13400665872911.
10^28029-1: 23450863720759.
10^28035-1: 60862961890711.
10^28079-1: 82346955449597.
10^28159-1: 17278962411973.
10^28161-1: 11071831421071.
10^28175-1: 17540050750601.
10^28295-1: 30316635703631.
10^28321-1: 66096484393001.
10^28361-1: 19380185376803.
10^28377-1: 56658744086401.
10^28389-1: 10461282397639.
10^28395-1: 10156157091721.
10^28407-1: 13427686195009.
10^28407-1: 16759124221759.
10^28449-1: 12225711609253.
10^28449-1: 38971569038671.
10^28473-1: 19875344171401.
10^28535-1: 17424765804161.
10^28555-1: 11015975141471.
10^28557-1: 11278888369237.
10^28637-1: 26069552571427.
10^28657-1: 60183648476089.
10^28659-1: 91563274298077.
10^28665-1: 60570581861791.
10^28719-1: 24458561680159.
10^28757-1: 24317119348721.
10^28779-1: 72517609687681.
10^28891-1: 15203882971801.
10^28933-1: 35630559092693.
10^28935-1: 10014879943711.
10^28991-1: 10468519408573.
10^31111-1: 22142082298631.
10^99323-1: 19563166613761.
10^99337-1: 31957679846359.
10^99425-1: 58598653122001.
10^99437-1: 44710736338711.
10^99613-1: 25775234310361.
10^99695-1: 12274426267711.
10^99751-1: 17875772418443.
10^99845-1: 73451539572391.

258 factors with 15 digits.
10^18070M+1: 218119850250641.
10^18430M+1: 120267095839741.
10^18750L+1: 205247289975001.
10^19110M+1: 682630425629881.
10^22530L+1: 417441802474381.
10^22610M+1: 817815416095021.
10^22750M+1: 185689616794501.
10^23510L+1: 106462104525521.
10^23850L+1: 152473919284801.
10^24170M+1: 283350946892561.
10^25130M+1: 881165735511181.
10^27890L+1: 122721923110861.
10^29030L+1: 308636945753141.
10^29130M+1: 360052992397141.
10^29890L+1: 335988860517241.
10^30190M+1: 525834991112161.
10^30610M+1: 879678261101221.
10^31930M+1: 176794395664021.
10^32750L+1: 168220742651501.
10^33070L+1: 413691938713181.
10^33070M+1: 213083714737121.
10^34870L+1: 169514498642501.
10^35010M+1: 846004937754601.
10^35190L+1: 213164381464201.
10^35230M+1: 265385262424361.
10^35330L+1: 462560200692061.
10^35830M+1: 840466888900081.
10^36070M+1: 538590384752221.
10^38510L+1: 160599624803221.
10^39350M+1: 347059379872501.
10^40050M+1: 619340930531101.
10^40130M+1: 786036291775681.
10^40610M+1: 296549438759941.
10^41150M+1: 442122642904801.
10^41170L+1: 609573178285801.
10^41330M+1: 250819557728941.
10^41370L+1: 149523209651341.
10^41590M+1: 245627116893461.
10^41830M+1: 366082988569601.
10^43070L+1: 779672752010641.
10^43390M+1: 520525220580481.
10^44970M+1: 428163153595921.
10^45450L+1: 849549370112101.
10^45590L+1: 553321842516241.
10^47630M+1: 628071902748841.
10^47990L+1: 368739202461181.
10^48590M+1: 100919412057301.
10^12212+1: 323360732531489.
10^12489+1: 211389563315023.
10^12660+1: 318462901248721.
10^12696+1: 619617867248641.
10^12705+1: 646410223545241.
10^12742+1: 499311778841009.
10^12763+1: 440397404789651.
10^12767+1: 607129614917893.
10^12805+1: 137750259338641.
10^12816+1: 209335431827521.
10^12868+1: 904809172813657.
10^12888+1: 294930863002513.
10^12992+1: 370483580670337.
10^13096+1: 335072772851809.
10^13121+1: 214444930592059.
10^13229+1: 177624644618093.
10^13241+1: 256455739216361.
10^13279+1: 129986463980899.
10^13352+1: 111774374392657.
10^13436+1: 541475221357649.
10^13482+1: 110932350128461.
10^13506+1: 283151860092769.
10^13541+1: 610209527392807.
10^13689+1: 925678538324047.
10^13741+1: 663111803597699.
10^13763+1: 205666240931663.
10^13892+1: 250901338174457.
10^13937+1: 388188805358971.
10^13940+1: 275536595202641.
10^13984+1: 125034098231041.
10^14000+1: 490479436216001.
10^14036+1: 625678253081729.
10^14084+1: 928972576797329.
10^14171+1: 131700864409931.
10^14177+1: 166283260104413.
10^14263+1: 151162622553037.
10^14265+1: 685742558451481.
10^14267+1: 167329851334757.
10^14323+1: 144162702215663.
10^14346+1: 118060585435549.
10^14367+1: 266998828806223.
10^14383+1: 294125156946637.
10^14483+1: 128688747914651.
10^14491+1: 504962315875877.
10^15049+1: 281525584092317.
10^15051+1: 820097305868983.
10^15063+1: 254253250633651.
10^15069+1: 105737490305047.
10^15072+1: 362583272757889.
10^15073+1: 559146860793971.
10^15107+1: 170307406290059.
10^15156+1: 305620236002377.
10^15160+1: 116962845625441.
10^15165+1: 897437024997211.
10^15185+1: 116706908061001.
10^15206+1: 998751962468009.
10^15235+1: 186611642923201.
10^15241+1: 453544472711689.
10^15298+1: 201942657272689.
10^15306+1: 210815287392781.
10^15341+1: 326985692524693.
10^15353+1: 698964816616093.
10^15355+1: 576169655549531.
10^15525+1: 846218985975001.
10^15527+1: 397350225833117.
10^15542+1: 168785798746861.
10^15591+1: 346214078244211.
10^15601+1: 861751801446463.
10^15616+1: 596098086804481.
10^15665+1: 201103548027331.
10^15675+1: 460890149737051.
10^15727+1: 204564872664569.
10^15731+1: 113956708685881.
10^15766+1: 887446631360629.
10^15874+1: 165129747568361.
10^15875+1: 734122250320001.
10^15882+1: 264033889025149.
10^15891+1: 433230423931651.
10^15912+1: 194107921680817.
10^15931+1: 124207689243331.
10^15963+1: 453394800448543.
10^15985+1: 148793045701801.
10^16185+1: 531455955990961.
10^16243+1: 191327010002729.
10^16296+1: 330453699404641.
10^16298+1: 110290431892829.
10^16318+1: 185580914644129.
10^16355+1: 840497774755721.
10^16368+1: 216051607675201.
10^16376+1: 420085843201729.
10^16405+1: 140094523057331.
10^16423+1: 440964250485463.
10^16462+1: 891767286630589.
10^17072+1: 864401589712673.
10^17076+1: 597063415788001.
10^19507+1: 769042758839099.
10^19538+1: 282708453880561.
10^19555+1: 193181476928611.
10^19571+1: 182965838457343.
10^19580+1: 111906800021281.
10^19598+1: 541137371229821.
10^19642+1: 582225277883089.
10^19660+1: 468009065690161.
10^19709+1: 400973293429259.
10^19726+1: 125432099633989.
10^19736+1: 652379222149729.
10^19737+1: 476138755842733.
10^19759+1: 376426297255979.
10^19827+1: 403199203047877.
10^19831+1: 200938419698437.
10^19851+1: 389672603960251.
10^19889+1: 253809050822849.
10^19928+1: 129958901601601.
10^19997+1: 586494142760489.
10^20102+1: 183626405580281.
10^20108+1: 443221168597681.
10^20187+1: 190160924457997.
10^20189+1: 283125174568783.
10^20216+1: 597321509171633.
10^20228+1: 270063573193649.
10^20235+1: 577086809056651.
10^20292+1: 549861000575113.
10^20321+1: 167094549081881.
10^20335+1: 133750441857761.
10^20343+1: 958037625753757.
10^20363+1: 100671976631143.
10^20373+1: 820321783112569.
10^20465+1: 809172183840931.
10^20520+1: 639782611516801.
10^20568+1: 116874753247969.
10^20577+1: 310321918283371.
10^20599+1: 235071995971289.
10^20617+1: 439509610065329.
10^20619+1: 233652188527453.
10^20625+1: 282057627390001.
10^20632+1: 100655064712337.
10^20645+1: 454954514450411.
10^20654+1: 964669611495881.
10^20699+1: 179469449979401.
10^20699+1: 777956009888401.
10^20743+1: 133792811199863.
10^20796+1: 224311377104377.
10^20818+1: 197779760963849.
10^20818+1: 384180142236521.
10^20935+1: 261204899513321.
10^20940+1: 399259394904481.
10^20945+1: 728601450320131.
10^21032+1: 177355322884433.
10^21039+1: 205475213018041.
10^21098+1: 136291799351401.
10^21113+1: 742526561558849.
10^21144+1: 102797691143041.
10^21236+1: 879135151637761.
10^21239+1: 159536010317317.
10^21241+1: 351978310919401.
10^21326+1: 382225963044301.
10^21403+1: 576251722950691.
10^21489+1: 749056142879773.
10^37075+1: 176250453064201.
10^37161+1: 180141203249533.
10^37407+1: 581867849091943.
10^37465+1: 142800112259251.
10^24439-1: 121490763772003.
10^24611-1: 104778423479801.
10^24659-1: 303010857614027.
10^24965-1: 606283022338031.
10^24981-1: 354100948245067.
10^24517-1: 173504708824747.
10^25023-1: 416978012415631.
10^25091-1: 177193695069271.
10^25197-1: 207652590511039.
10^25311-1: 598182916200871.
10^25371-1: 349211747097163.
10^25527-1: 164182884947773.
10^25669-1: 479844647367373.
10^25743-1: 118997621945641.
10^25837-1: 207302227999721.
10^25873-1: 108458250216077.
10^28041-1: 531831954538483.
10^28135-1: 942307193198681.
10^28143-1: 457883541568711.
10^28149-1: 182980454035831.
10^28303-1: 922411485751801.
10^28363-1: 220846100614187.
10^28389-1: 790479938838283.
10^28415-1: 387061723516591.
10^28451-1: 118297965471071.
10^28451-1: 140029700767351.
10^28479-1: 112369222294363.
10^28489-1: 115392221483867.
10^28529-1: 116010401430083.
10^28535-1: 337060787376431.
10^28541-1: 842375873460929.
10^28569-1: 562532463875929.
10^28569-1: 881137032699751.
10^28591-1: 808806474382523.
10^28609-1: 178420197636409.
10^28617-1: 521236380557413.
10^28655-1: 716195526170081.
10^28773-1: 280258015418083.
10^28803-1: 489517769995321.
10^28815-1: 568576831789711.
10^28871-1: 350212224230719.
10^28877-1: 220925165271883.
10^28885-1: 100276693210321.
10^28911-1: 360601300568599.
10^99127-1: 368082091283453.
10^99417-1: 108748689218041.
10^99445-1: 651667704021361.
10^99855-1: 199676235429721.
10^99937-1: 130025023395797.

24 factors with 24 digits.
10^32390M+1: 146517964631922598212881.
10^32810M+1: 480515213946783113831321.
10^34990L+1: 151890112557688063753741.
10^36390L+1: 210743165485653662473981.
10^39270M+1: 289372555153066242973501.
10^41630L+1: 316783763096950237913501.
10^12337+1: 478353921862630010458847.
10^12474+1: 273809949353283902588569.
10^12598+1: 171443370906198328552789.
10^12880+1: 293062213949890803311041.
10^13868+1: 346561124425095313241281.
10^13885+1: 156274670781932402896681.
10^14351+1: 326639236546264904242613.
10^15491+1: 551600906474471800625771.
10^15663+1: 359652902831054429913997.
10^17236+1: 838790828190099453044161.
10^20849+1: 942909011093043405175223.
10^24633-1: 154288326077114409347329.
10^24677-1: 240475956711383955948839.
10^24881-1: 132213678304879363146893.
10^25961-1: 225659549766623540033467.
10^28111-1: 293071879722863836961689.
10^28369-1: 310190778876681950739757.
10^28477-1: 662979987825552878738683.

15 factors with 25 digits.
10^25330M+1: 4065305655586709035137161.
10^27490M+1: 2958329697458858767918721.
10^30990L+1: 1073196527078839433713921.
10^13006+1: 9893202822736764070347389.
10^13860+1: 2829659869486236394404721.
10^14329+1: 1110315712383546540480379.
10^14452+1: 3182462045686600228248481.
10^15048+1: 1109514833519376657841777.
10^16040+1: 8773652742618912424791521.
10^20137+1: 2873736912510959731489969.
10^20179+1: 6172979527863321801359579.
10^20522+1: 2968047612639412848337369.
10^20838+1: 7209117207289041811973881.
10^4189-1: 3078034957208671652164031.
10^4445-1: 3217817843848027063485241.

11 factors with 26 digits.
10^35570L+1: 85147752225884897601723061.
10^40310L+1: 15713688688845961610262181.
10^41570M+1: 35405105952049365304435841.
10^45810M+1: 62235274102803268012421101.
10^49190L+1: 60791077953057909504025301.
10^6745+1: 11537056433294316884423411.
10^13297+1: 24014980493168268468349157.
10^19700+1: 10089756201018821713681201.
10^21211+1: 81234359060445706111159063.
10^21396+1: 11307184312763932853157889.
10^28963-1: 44857815810772266355322677.

10 facors with 27 digits.
10^22330L+1: 212551382445982960079692301.
10^27290L+1: 671512727460387810775715141.
10^13949+1: 302738631435477922038702011.
10^6523+1: 753578033043731682775284649.
10^6573+1: 206765254833786959262710059.
10^6717+1: 341505989319201091447756453.
10^16235+1: 129290478991736373960652891.
10^20758+1: 164573558779747091784698341.
10^21281+1: 194428004256619642634159009.
10^28687-1: 265592220142362875640162751.

7 facors with 28 digits.
10^9410M+1: 1318647438859959399831078541.
10^48930L+1: 4217195062429040666701329121.
10^49690M+1: 6592290434322258947071767721.
10^20040+1: 3616953939219135370652528161.
10^20294+1: 3498864014594702588842671509.
10^20538+1: 2505533034362588149213632241.
10^28289-1: 4564919499135953887964902723.

3 factors with 29 digits.
10^6805+1: 12857293098624563620368908761.
10^15358+1: 33116204680209029770333161409.
10^19992+1: 22937660519702312538889351681.

3 factors with 30 digits.
10^35070M+1: 461904211182554850127110960541.
10^4551-1: 556360658899885338556754176591.
10^28581-1: 180352476837898608191261958919.



April 25, 2010 (Juno Fernadez)

(448L^2·41)^41-1: c97 = p32 · p65, where
                  c97 = 1163209850063788511641922198468630844171837708798096122001958812047452189030275606638902853562569,
                  p32 = 37933849473853652489194100837099 and
                  p65 = 30664165809629851750992923414664572067046856560760996171223637531.

Msieve (QS).



April 23, 2010

10^13649-1: 9227771615347.
The first yet known factor of the repunit (1)13649.

10^19403-1: 316211244324936083.
The first yet known factor of the repunit (1)19403.

10^19603-1: 10270187578117.
The first yet known factor of the repunit (1)19603.

10^24133-1: 42058190363879.
The first yet known factor of the repunit (1)24133.

10^24407-1: 1035270160335054123559.
The first yet known factor of the repunit (1)24407.

10^25943-1: 229529480234873369.
The first yet known factor of the repunit (1)25943.

10^25997-1: 718714296025597.
The first yet known factor of the repunit (1)25997.

38 factors with 23 digits.

10^15970M+1: 11201499608019382160501.
10^20770M+1: 30364206222922802207801.
10^42110L+1: 33514340593909865790161.
10^46650M+1: 36091161371774381815801.
10^48850L+1: 28166725047550854903601.
10^49830L+1: 59258503907227874886121.

10^10273+1: 16155036927187458564613.
10^12508+1: 42316357019968125124937.
10^12689+1: 42822431320187426019641.
10^12818+1: 32042821081458928742821.
10^12868+1: 54212752655630736680153.
10^12879+1: 18076957438658848129009.
10^13386+1: 49894705157849530582861.
10^13443+1: 64115188882901159630533.
10^13454+1: 88539436092364151507089.
10^13843+1: 48770972128676920388813.
10^13911+1: 14602619183478891775699.
10^14128+1: 10745591245242596322049.
10^16063+1: 79284354849984720934613.
10^16480+1: 10287684420488672037121.
10^19838+1: 11052307255399209547021.
10^20044+1: 11364083965052080476961.
10^20178+1: 13218013264149507051109.
10^20263+1: 39043117803178743113929.
10^20411+1: 33563980870295617498171.
10^20711+1: 11863193441469044673329.
10^20880+1: 44377100217988817256001.
10^20902+1: 14235463205010038577041.
10^20992+1: 12178902394859590297601.
10^21198+1: 24474376427686778552341.
10^21457+1: 13688306754779047254371.

10^24753-1: 43362812731301166861721.
10^24971-1: 15668072120934239976637.
10^25145-1: 18646448837535611948521.
10^25961-1: 14019828103334748214963.
10^28035-1: 17240640916782830980231.
10^28069-1: 26730426592795617954733.
10^28759-1: 17166455727486522342439.



April 22, 2010

10^71147-1: 4189320030860729.
P+1 with B1=B2=15e3.
The first yet known factor of the repunit (1)71147.
The remaining cofactor (71131 digits) is composite.

50 factors with 22 digits.

10^16850M+1: 6261359011099311035701.
10^25370M+1: 1654379029303251870181.
10^27310M+1: 5755743989443428017981.
10^29470M+1: 6558518453203115209441.
10^30150M+1: 1153880497331803012501.
10^32350L+1: 1817678353386227276501.
10^34010M+1: 3043991572658775957521.
10^35050L+1: 2053719112847701733101.
10^38730M+1: 4356910613627339139301.
10^40070L+1: 1310008049582854840241.
10^44130L+1: 2437632831340790793121.
10^46530M+1: 1123586380401737109661.
10^49970M+1: 9769320297657246247321.

10^10167+1: 2648490336958395254293.
10^12587+1: 2070017852964653946917.
10^13058+1: 6373981184611414480921.
10^13266+1: 3105646760367562140181.
10^13453+1: 2660006311405536907771.
10^13459+1: 6807844574671046131847.
10^13700+1: 1143586677797654761201.
10^13865+1: 1696830170503234798561.
10^14009+1: 3386914311293381647687.
10^14267+1: 1689811437770841076451.
10^15689+1: 1100212972249877832859.
10^15822+1: 1815489973088317368109.
10^15979+1: 6727616362131020765179.
10^16424+1: 4961670435433024874513.
10^19601+1: 1676463754948298423533.
10^19856+1: 8956774769556206525441.
10^19897+1: 6110456130741954020851.
10^20120+1: 9673820392941200261921.
10^20207+1: 1824522427671786873647.
10^20311+1: 1059771977181307707019.
10^20331+1: 8750837691368237182681.
10^20391+1: 1400463153013209132373.
10^20875+1: 5254726476345994733251.
10^20915+1: 1126703218636416708571.
10^21197+1: 1718271243449508967649.
10^21327+1: 4930398859058295824533.

10^28285-1: 2880261355989017770951.
10^28373-1: 1944777068983371816359.
10^28375-1: 2444710151587044552751.
10^28709-1: 1402894992252623916559.
10^28731-1: 1778351513343299183761.
10^28809-1: 1070530957695060924679.
10^28825-1: 4532358530379267393551.
10^28881-1: 1406828256504849942769.
10^28957-1: 4924803296767904511281.
10^99239-1: 1165017122724738266803. The remaining cofactor is composite.
10^99855-1: 4620479994015490379881. The remaining cofactor is composite.



April 21, 2010

10^88951-1: 2744836736857067.
P+1 with B1=B2=1e4.
The first yet known factor of the repunit (1)88951.
The remaining cofactor is composite.

70 factors with 21 digits.

10^20190L+1: 128031069937415972161.
10^27450L+1: 521363085763507101001.
10^28650M+1: 116966492081195019001.
10^31050L+1: 758426517692973476101.
10^31290L+1: 403716509339602716601.
10^33890M+1: 588302289569823474301.
10^34850L+1: 108477816042048454501.
10^38730M+1: 108274906030776795241.
10^40750M+1: 117287880201077054501.
10^42610L+1: 321771346574158527661.
10^43010L+1: 753414536538233685281.
10^44150L+1: 156278868163542912001.
10^44590L+1: 192863153566924598941.
10^44990L+1: 701370018499261842721.
10^45710L+1: 485874439238499779861.
10^48590L+1: 539335219957415654761.
10^49010L+1: 196007609889741839281.

10^12269+1: 107486772053788752197.
10^12394+1: 179170152569376062929.
10^12424+1: 146340505850811743041.
10^12779+1: 163537511857088771299.
10^13116+1: 713250521958330772057.
10^13182+1: 117847989280944678601.
10^13243+1: 275822464236324249401.
10^13277+1: 308016820977748424807.
10^13279+1: 178192298357561637493.
10^13308+1: 125471662916258772721.
10^13437+1: 161726498359047552241.
10^13626+1: 150453028659000641149.
10^13743+1: 109832872148388187597.
10^13866+1: 127448906805098629381.
10^13898+1: 601320550889955479689.
10^13925+1: 205428977151853291051.
10^13977+1: 286676418087535936609.
10^14304+1: 784600391406956936257.
10^14362+1: 196887395408764109261.
10^15751+1: 563084192473103927971.
10^15800+1: 874221468020284480801.
10^15845+1: 206283913429782005401.
10^15880+1: 472342882790490416801.
10^15929+1: 420136563404442263663.
10^15934+1: 595325774736514723729.
10^16336+1: 989414206757374202369.
10^19569+1: 190366225629468243499.
10^19739+1: 296713401695074304929.
10^19764+1: 109462555455331779361.
10^19793+1: 363815884469380432813.
10^19804+1: 112493373133138090721.
10^19843+1: 153280694066981876819.
10^20200+1: 197118401135254496801.
10^20205+1: 112728049354952150131.
10^20307+1: 245225627950343167051.
10^20340+1: 556640908931364177601.
10^20599+1: 257508760892005003529.
10^20667+1: 150857119541627761063.
10^20714+1: 642065761973420127881.
10^20760+1: 290313085323963075841.
10^20814+1: 150044625397395430201.
10^20911+1: 109410433320818638493.
10^21001+1: 192278302108471359887.
10^21118+1: 109422741587271211349.
10^21186+1: 603559398228621119209.
10^21337+1: 356211609470640869731.
10^21393+1: 206756984834790503527.

10^25083-1: 334964620403788480867.
10^25243-1: 350888366686618237027.
10^28013-1: 296690625529037541391.
10^28621-1: 190453249135899585067.
10^28833-1: 700893429829156264471.
10^99557-1: 166773168946390995601. The remaining cofactor is composite.



April 20, 2010

10^25457-1: 1380779917157453580437.
The first yet known factor of the repunit (1)25457.

10^25609-1: 12814060454317.
The first yet known factor of the repunit (1)25609.

10^25693-1: 73448689477129.
The first yet known factor of the repunit (1)25693.

10^25741-1: 4901432509418923.
The first yet known factor of the repunit (1)25741.

89 factors with 20 digits.
In any case the remaining cofactor is composite.
10^19350M+1: 23863204878961450501.
10^23830M+1: 13418874984796522561.
10^26610M+1: 20716342992268091521.
10^32690M+1: 47356736360236823521.
10^32970M+1: 22671050020711346101.
10^33890M+1: 20936337383912034101.
10^34750L+1: 26087795234086885501.
10^37690L+1: 22379153504098864141.
10^39530L+1: 15845239201997355281.
10^40670M+1: 11639056001378699461.
10^42310M+1: 33918411508642482161.
10^43190M+1: 10064519737421923481.
10^46090M+1: 12547420966688691821.
10^46750M+1: 66579853281632300501.
10^10277+1: 95276253461675504087.
10^10364+1: 50493768131198296129.
10^12711+1: 10537427647199340289.
10^12741+1: 47810792277609464731.
10^12781+1: 33153454836613711543.
10^12821+1: 91812106802608854637.
10^12827+1: 23570795697744450173.
10^12944+1: 59936534262471307873.
10^12963+1: 13681551282549669091.
10^13004+1: 23771994369045445177.
10^13089+1: 39019023811586457451.
10^13122+1: 34767820833243849289.
10^13313+1: 78514167311003190929.
10^13319+1: 12872460973142652247.
10^13546+1: 60338315191829380681.
10^13644+1: 11616443517755492929.
10^13684+1: 69355601324413246217.
10^13745+1: 32150324151678007721.
10^13878+1: 18015561259588130941.
10^13926+1: 13048217384442585841.
10^13974+1: 55549398424300792969.
10^13986+1: 76999174757252858881.
10^14095+1: 60813697113294435731.
10^14113+1: 19915785204674092889.
10^14248+1: 25394636208348419377.
10^14286+1: 55475311333185554401.
10^15529+1: 89877324326935704121.
10^15546+1: 77242683989789062009.
10^15649+1: 13954884827386194371.
10^15651+1: 34207378549847529121.
10^15861+1: 32238307298116722601.
10^15864+1: 10158073171889289457.
10^15932+1: 38544126269140166473.
10^15988+1: 25153414641396935041.
10^16293+1: 24882257746900991053.
10^16461+1: 28231948295259490081.
10^19900+1: 37331333871656064001.
10^19903+1: 12173394900760827397.
10^19996+1: 23106643887436027169.
10^20067+1: 44315145213022761241.
10^20138+1: 13018836946265313469.
10^20141+1: 29922453923192800597.
10^20162+1: 15210296424434202281.
10^20186+1: 12411832812692834881.
10^20242+1: 42457169365170130741.
10^20360+1: 21646220324338867681.
10^20407+1: 70846746477464747401.
10^20453+1: 23226477416117095819.
10^20518+1: 44885798890635894949.
10^20578+1: 41318604627489228449.
10^20667+1: 76594864836896361121.
10^20680+1: 69549958641459959521.
10^20756+1: 35863989635145048241.
10^20856+1: 34889116571748858673.
10^20934+1: 22768713860431055941.
10^20949+1: 25675083822635968813.
10^20967+1: 49558267013296809223.
10^21154+1: 30315512321285373029.
10^21278+1: 29215234887433363589.
10^21395+1: 81354678068829064681.
10^21472+1: 36994686395337456193.
10^24631-1: 45219737797453388837.
10^25171-1: 70777208719684720681.
10^25285-1: 29065023280225402601.
10^28269-1: 12129803370750570877.
10^28365-1: 13821138118896490441.
10^28423-1: 85564165307210956321.
10^28603-1: 12150621396265731241.
10^28619-1: 21964943423772476609.
10^28723-1: 95291613983626635599.
10^28843-1: 20406868280395590997.
10^28847-1: 13150395608231776987.
10^28909-1: 43840979965649059591.
10^28977-1: 46417536091869347809.
10^99701-1: 12549579936240261769.



April 19, 2010 (Kurt Beschorner)

(520M^2·41)^41-1: c96 = p48 · p48, where
                  c96 = 319882447932619009001469115784719620586523846913518746228117794337174177125671035158049765173541,
                  p48 = 360504990438354267930816419063436731596336650311 and
                  p48 = 887317669427154175030006607857365324112669594931.

A very pleasant factorization.



April 19, 2010

10^8589+1: 10318671134400025531.
The remaining cofactor (4869 digits) is probably prime.

10^25229-1: 3895954485323226877.  
10^25229-1: 41334817875491844157.
The first yet known factors of the repunit (1)25229.

10^25247-1: 1575344555238253.
The first yet known factor of the repunit (1)25247.

10^25261-1: 801636190419626893.
The first yet known factor of the repunit (1)25261.

10^25309-1: 86285730660834043483.
The first yet known factor of the repunit (1)25309.

10^74623-1: 1188943559831723.
P+1 with B1=B2=3e3.
The first yet known factor of the repunit (1)74623.
The remaining cofactor is composite.

104 factors with 19 digits.
In any case the remaining cofactor is composite.
10^16510M+1: 4583365839596921521.
10^18830L+1: 7049532157394918941.
10^20490M+1: 4394558425007914321.
10^20850M+1: 2784525474985221601.
10^22490M+1: 1118776468556094661.
10^22810L+1: 1332832486854406141.
10^22990L+1: 6199076811510615341.
10^25830L+1: 3102029695900871821.
10^26030M+1: 2489740502617170841.
10^30270L+1: 1290696354728723821.
10^30410M+1: 8963715541757221741.
10^30550M+1: 2004771716893699001.
10^32590M+1: 1962611926441738321.
10^34650L+1: 1810164716148165301.
10^38830M+1: 8929501191364008421.
10^39370L+1: 4791373074261457601.
10^39870L+1: 4193465729102502121.
10^45090M+1: 1248834409025809321.
10^45310M+1: 4668580509909081781.
10^45990M+1: 2782333097039927341.
10^46450L+1: 9581943456197287501.
10^47090L+1: 7078904679214069201.
10^47490L+1: 1850778610961195581.
10^48670L+1: 2672409580324680041.
10^12696+1: 2832441310152584497.
10^12851+1: 9805162392007973423.
10^13031+1: 2802128694080623447.
10^13135+1: 7180877679187321451.
10^13205+1: 1159007318637179881.
10^13391+1: 4390871912794532369.
10^13394+1: 2097349861531441421.
10^13499+1: 1093928216316378601.
10^13624+1: 1863105372326224001.
10^13689+1: 9906853063891022929.
10^13697+1: 6986148729670241539.
10^13707+1: 1491262195596620851.
10^13726+1: 9294452861151003001.
10^13782+1: 4233751833600354001.
10^13822+1: 3571298783606775649.
10^13838+1: 1540070384310151321.
10^13848+1: 6597952691438385889.
10^13883+1: 1150687632241272641.
10^13952+1: 6181985768072691457.
10^14307+1: 1839110073240056641.
10^14314+1: 7714958983059455401.
10^14326+1: 1094170755362482409.
10^14355+1: 2850138630256966291.
10^14492+1: 1515053162951914057.
10^15586+1: 8423930919846704701.
10^15668+1: 4284134930566295569.
10^15817+1: 9756580715320596281.
10^15827+1: 3443866298178970063.
10^15898+1: 3064439087481659861.
10^15903+1: 1303787462662695277.
10^16038+1: 1419987636423810829.
10^16172+1: 2725699933872723809.
10^16226+1: 3029003183789513141.
10^16302+1: 1228780346823800629.
10^16426+1: 4383129080321220701.
10^16462+1: 3541604135555826649.
10^19554+1: 1478514519309179641.
10^19586+1: 3304056998614857941.
10^19598+1: 1271373272638401521.
10^19836+1: 1951487583872055841.
10^19913+1: 4733341231963382677.
10^19915+1: 1891100457751775971.
10^19964+1: 2411741764868477441.
10^19977+1: 7128166263158033809.
10^19978+1: 2169674534220154501.
10^20085+1: 2178325579582087651.
10^20272+1: 3330551256611056129.
10^20451+1: 3907593300163471459.
10^20502+1: 1783972349191893781.
10^20601+1: 1858634527638866797.
10^20612+1: 3095990974171713809.
10^20640+1: 2820888450504860161.
10^20713+1: 9721368703216902887.
10^20728+1: 3672408479039117137.
10^20872+1: 1244636174017944289.
10^20906+1: 4659502200153766829.
10^20958+1: 3269338027284569269.
10^20972+1: 1536092047930128697.
10^21002+1: 1783360404705082961.
10^21284+1: 1186986303367087513.
10^21349+1: 1115158002630347413.
10^21393+1: 3615331055952967849.
10^21398+1: 6785520736869130621.
10^24341-1: 1245640394698602449.
10^25001-1: 3933155065786835081.
10^25289-1: 5953252505346427271.
10^25481-1: 2944195191010153733.
10^28069-1: 6434823184350558401.
10^28079-1: 1079669799979106129.
10^28251-1: 1440089000291095111.
10^28303-1: 2280932848876885237.
10^28355-1: 1000645751828132831.
10^28493-1: 6086359171251915373.
10^28565-1: 5227734798858964831.
10^28629-1: 6716462459431932001.
10^28713-1: 2175105606636908161.
10^28747-1: 3547543098693750547.
10^28829-1: 4889927068165831481.
10^28969-1: 3879079222587394523.
10^99255-1: 4575728423892760681.



April 15, 2010

10^9597+1: 1486325893149393367.
10^9625+1: 4090343187719251.
10^9646+1: 145720537535210821.
10^9669+1: 271351808310133.
10^9693+1: 484293314039329.
10^9697+1: 1593132440043608161.
10^9739+1: 74322126919910404973.
10^9886+1: 4452584378483545916526601.
10^9923+1: 3159030905206855291.



April 14, 2010

10^7060+1: 7610670519631583670279140089121.
10^7173+1: 15314445505061694514531.
10^7235+1: 6837370756170149891.
10^7395+1: 48292612403920993201.
10^7398+1: 74846828155631562283861.
10^7406+1: 2258235647032079681.
10^7474+1: 66090546657471683041.
10^7494+1: 104470210133171254921.

10^9042+1: 225781171112660993036989.
10^9063+1: 323499154223643547213.
10^9076+1: 952383490589099335009.
10^9084+1: 6940923973453273.
10^9097+1: 177753903581898557.
10^9178+1: 25865757525277541.
10^9197+1: 71967729090644161693.
10^9205+1: 336246308448497410775281.
10^9303+1: 817702116798757.
10^9304+1: 13153798294686343057.
10^9332+1: 33485194113864897577.
10^9354+1: 436569648143609521.
10^9355+1: 1997633434176566371.
10^9466+1: 70858415559301.
10^9469+1: 88775849677896721.

10^11558+1: 644008852816261.
10^11573+1: 410210555272961251.
10^11600+1: 539036980842788521601.
10^11643+1: 273117941953561.
10^11652+1: 4510000289071201.
10^11657+1: 9050714810767529.
10^11689+1: 17130245335888154893.
10^11764+1: 2678417639322289.
10^11819+1: 2722028481324830089.
10^11861+1: 206066430105573127.



April 13, 2010

10^28409-1: 10108778737145437.    The first yet known factor of the repunit (1)28409.
10^28433-1: 19485433360580080147. The first yet known factor of the repunit (1)28433.
10^28837-1: 56955033697961773201. The first yet known factor of the repunit (1)28837.

10^28455-1: 15410775906961.
10^28455-1: 227115917005111.
10^28455-1: 26398324633723561.    The remaining cofactor (12912 digits) is probably prime.



April 9, 2010 (Kurt Beschorner)

(574M^2·41)^41-1: c97 = p37 · p60, where
                  c97 = 2294013266896675657466669155199020923740198900315986526022736453137794247474215448646132918127603,
                  p37 = 2371310115114138117231216276093121249 and
                  p60 = 967403315270832075229611899611050725019615232275415160696147.



April 9, 2010

10^24329-1: 9473958111529649.   The first known factor of the repunit (1)24329.
10^24677-1: 164702542783117.    The first known factor of the repunit (1)24677.
10^24923-1: 114486509231333.    The first known factor of the repunit (1)24923.
10^24953-1: 7815569509942721.   The first known factor of the repunit (1)24953.



April 8, 2010

10^20305+1: 1028282517874156981827943844801.
This p31 is the largest yet known non algebraic prime factor of any number of shape 10^n+1 in the range 11208 ≤ n ≤ 50000 - see Makoto Kamada's list Phin10.txt.

10^12573-1: 3561573930111627474706201.
10^12665-1: 102846145386140797545521.
10^12729-1: 22386800126272573.

10^25599-1: 275835560599865668498722556729.
This p30 is the largest yet known non algebraic prime factor of any number of shape 10^n-1 in the range 10973 ≤ n ≤ 99999 - see Makoto Kamada's list Phin10.txt.



April 7, 2010

10^13093+1: 3728215855099.
10^13537+1: 4407615794161.
10^15764+1: 3190713334313.
10^15859+1: 3771799319677.
10^16103+1: 7428194286917.
10^16246+1: 6026705155589.
10^16267+1: 4985024492449.
10^16292+1: 4851901393193.
10^16434+1: 3231867711601.
10^16446+1: 3728494368721.
10^16449+1: 7753664481961.
10^19696+1: 3593069744129.
10^19769+1: 7030342756939.
10^19785+1: 89592875303401.
10^19799+1: 28169243811463.
10^19840+1: 18664643322881.
10^19847+1: 29889966793637.
10^19915+1: 41508667014851.
10^19953+1: 22968011712853.
10^20101+1: 28694295131053.
10^20231+1: 35115804494401.
10^20341+1: 29685945788117.
10^20452+1: 15349644979673.
10^20461+1: 51740298329063.
10^20580+1: 96361398134401.
10^20669+1: 38446298057047.
10^20695+1: 20164257975331.
GMP-ECM informed of a composite cofactor (each time).



April 6, 2010

10^7087+1: 44493538173902120646571.
10^11331+1: 5185562517218353073653.
10^11340+1: 27988931672369025121.
GMP-ECM informed of a composite cofactor (each time).



April 2, 2010 (Juno Fernadez)

(153L^2·41)^41-1: c95 = p33 · p63, where
                  c95 = 56134213592892619321551902633417214480937762569345506455458393034961315151329553199118708362819,
                  p33 = 527106796961978335009530400448059 and
                  p63 = 106494953046378065865572739652751494561384933103335731256223641.



April 1, 2010

10^7454+1: 196863707847855698281.    p+1, B1 = 3e5, B2 = 3e6.
10^14476+1: 55258270500737009823041. p-1, B1 = B2 = 1e5. This inconspicuous factor is pleasant, since the remaining cofactor (10998 digits) is (probably) prime.
10^16151+1: 44921686053529.          p-1, B1 = B2 = 2e3. This inconspicuous factor is pleasant, since the remaining cofactor (15582 digits) is (probably) prime.



Alfred Reich