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July 29, 2011 2011 年 7 月 29 日 (Alfred Reich)

n=86380L: c14784(3537460769......) = 78763617228406181 * c14767(4491237063......)

n=73820M: c14761(2824060999......) = 19505400356021 * c14748(1447835444......)

July 25, 2011 2011 年 7 月 25 日 (Alfred Reich)

n=83780M: c16215(4372818603......) = 156580977178961 * c16201(2792688283......)

July 28, 2011 2011 年 7 月 28 日 (Kurt Beschorner)

n=12221: c10980(1807924962......) = 2237208882788214919 * c10961(8081162989......)

n=14020L: c2800(3576409999......) = 69793802383751048657458916041 * c2771(5124251548......)

July 27, 2011 2011 年 7 月 27 日 (Alfred Reich)

n=15820M: c2677(4773824656......) = 13565052618906622683991961 * c2652(3519208359......)

n=24780L: c2773(3989730683......) = 11974088300884973733121 * c2751(3331970320......)

n=29460L: c3873(2031929421......) = 39802953149870190361 * c3853(5104971518......)

n=47780M: c9528(1655006060......) = 31505396031616061 * c9511(5253087624......)

n=48980L: c9330(3007526771......) = 35724710474639761 * c9313(8418617622......)

n=61780M: c12336(6578877445......) = 50855505677381 * c12323(1293641142......)

n=63020M: c11962(3466285074......) = 3598398781703261 * c11946(9632854181......)

n=75980L: c14527(3384665847......) = 178693741753055341 * c14510(1894115492......)

n=89220L: c11859(3770975989......) = 52451554410443761 * c11842(7189445636......)

July 26, 2011 2011 年 7 月 26 日 (Kurt Beschorner)

n=10873: c10621(1485834349......) = 8554088320060524015547 * c10599(1736987384......)

n=12227: c12218(1245116292......) = 442952564029693 * c12203(2810947252......)

July 25, 2011 2011 年 7 月 25 日 (Alfred Reich)

n=73540M: c14698(2315816260......) = 89426992072840901 * c14681(2589616632......)

n=76540L: c14771(4163989586......) = 3774187130629180621 * c14753(1103281168......)

n=78340L: c15642(6735630748......) = 168786658238898640824092821 * c15616(3990617989......)

n=79300M: c14390(5247858412......) = 12668231542519543901 * c14371(4142534334......)

n=79700L: c15911(1015037710......) = 3098811824746901 * c15895(3275570662......)

n=81140M: c16225(2824060999......) = 1294286054047781 * c16210(2181945011......)

n=81260L: c15228(1146972088......) = 170212628002317945481 * c15207(6738466483......)

n=81700L: c15095(3355938197......) = 3276078938108847301 * c15077(1024376475......)

n=83780M: c16232(3924369236......) = 89744615377172521 * c16215(4372818603......)

n=84380M: c16859(3879567255......) = 652479594731941 * c16844(5945882884......)

n=84860L: c16969(2824060999......) = 283270364382229841 * c16951(9969489769......)

n=85180M: c17027(2550308351......) = 716453539738296781 * c17009(3559628377......)

n=85780M: c17152(3576409999......) = 150041075117074541 * c17135(2383620616......)

n=86980M: c17387(2497531264......) = 4654608992645219281 * c17368(5365716580......)

n=88300M: c17623(5816797664......) = 12518093378154101 * c17607(4646712153......)

n=90140L: c18012(9098570585......) = 1336932181726209721 * c17994(6805558808......)

n=90460M: c18074(8647386672......) = 526344673024361 * c18060(1642913306......)

n=90580L: c15498(5579054333......) = 28400857048484341 * c15482(1964396470......)

n=91580M: c17280(3540999996......) = 21157349266181 * c17267(1673650111......)

n=95140M: c18481(2796099999......) = 2187553883644495741 * c18463(1278185657......)

n=96020L: c19182(1238236235......) = 22945562813508421 * c19165(5396408207......)

n=96620M: c19302(1290185476......) = 122450859746329441 * c19285(1053635293......)

n=99740M: c19924(3757938374......) = 29255282942098720541 * c19905(1284533252......)

n=33580L: c6298(9194007407......) = 4636968003171530561 * c6280(1982762745......)

n=76620L: c10208(3913542626......) = 17739503026025320005421 * c10186(2206117398......)

n=77460M: c10278(8295901808......) = 11909933538488710801 * c10259(6965531572......)

n=77580L: c10305(3674094833......) = 1382825916419814901 * c10287(2656946756......)

n=78220M: c15640(3576409999......) = 151872950321861 * x15626(2354869640......)

n=78220M: x15626(2354869640......) = 229187815702421 * c15612(1027484656......)

n=78300L: c10070(8155266553......) = 121883657703921901 * c10053(6691025447......)

n=79180L: c15258(3726736837......) = 83433269158929941 * c15241(4466727571......)

n=85700M: c17113(2786260756......) = 14687730882355120501 * c17094(1896998779......)

n=87260M: c17433(9404092348......) = 176052564769434581 * c17416(5341638936......)

n=88580M: c17136(3541000000......) = 13831059947973661 * c17120(2560179778......)

n=70940L: c14176(9351456058......) = 532459059009639761 * c14159(1756277013......)

n=84740M: c15961(3436735257......) = 3326852718038133181 * c15943(1033028976......)

n=91060M: c17460(1040208923......) = 26138088410921 * c17446(3979667171......)

July 21, 2011 2011 年 7 月 21 日 (Alfred Reich)

n=60700L: c12083(2084421225......) = 2564166307599323364601 * c12061(8129040691......)

n=72260L: c14437(1564308612......) = 202111516908463661 * c14419(7739829164......)

July 20, 2011 2011 年 7 月 20 日 (Alfred Reich)

n=98700L: c11034(1650570210......) = 4202497626608265601 * c11015(3927593439......)

n=26700M: c3490(2270395865......) = 5303969792707801 * c3474(4280559569......)

n=44420L: c8868(4508798293......) = 10586919884067152261 * c8849(4258838588......)

n=64060M: c12782(1160439781......) = 1999541481953710241 * c12763(5803529417......)

n=65020L: c12989(9584114706......) = 410729051205102041 * c12972(2333439691......)

n=72100M: c12224(2625903835......) = 6807276702900101 * c12208(3857495369......)

n=74700M: c9806(1164259806......) = 2038140366422357689201 * c9784(5712363219......)

July 20, 2011 2011 年 7 月 20 日 (Joppe Bos and Thorsten Kleinjung)

n=688: c262(4397219662......) = 12964211609561579909063446696451764692875452342031494097 * p207(3391814169......)

# Phi_688(10) is the 1036th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

July 18, 2011 2011 年 7 月 18 日 (Alfred Reich)

n=32540M: c6490(1507169610......) = 234957909189288821 * c6472(6414636628......)

n=45580L: c8719(1265962655......) = 28598247891916445853941 * c8696(4426714044......)

n=46140L: c6126(1000522088......) = 279179461843141 * c6111(3583795462......)

n=66460L: c13253(3059367903......) = 333465317216441 * c13238(9174471064......)

n=34740L: c4596(1796218586......) = 2105314855530301 * c4580(8531828776......)

n=47020M: c9364(7314695994......) = 446746452318831461861 * c9344(1637326039......)

n=70220M: c14008(6589680340......) = 195158960760768761 * c13991(3376570727......)

n=96620L: c19321(2824060999......) = 4313337908879561 * c19305(6547275125......)

July 14, 2011 2011 年 7 月 14 日 (Bruce Dodson)

n=680: c244(9335511757......) = 3706128023114119218916379460291345996769984434163189932241 * p187(2518939361......)

# Phi_680(10) is the 1035th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

July 14, 2011 2011 年 7 月 14 日 (Kurt Beschorner)

n=12289: c12289(1111111111......) = 4495122884000467878157 * c12267(2471814764......)

# R_12289 is the 7256th cracked repunit of prime number length less than 100000.

n=12301: c12301(1111111111......) = 74525769271434437623384231 * c12275(1490908610......)

# R_12301 is the 7257th cracked repunit of prime number length less than 100000.

n=13980M: c1806(1931791971......) = 21166873440679239162423181074773929272724025103001 * c1756(9126487089......)

# 21166873440679239162423181074773929272724025103001 is the largest known factor that appears after n=5100L.

Largest known factors that appear after the previous one
  1  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
  2  n=1060M: 22534789481525070481066146802824209631029690388674663333618185041786620876200193924826168812981 (Raman / Sep 22, 2010)
  3  n=1220M: 27186363592392725942593454290345801336551729326489701011779461 (Shaopu Lin / Sep 7, 2007)
  4  n=1500L: 36605832263463437733314604426708004731796978480010361966001 (Polybius / Nov 3, 2010)
  5  n=1860L: 1891014345342089253412148254805092014919223493735583702021 (Yousuke Koide / Aug 14, 2010)
  6  n=5100L: 185898550709887865845976723509058449254706894935901 (Frank Boerner / Jun 28, 2010)
  7  n=13980M: 21166873440679239162423181074773929272724025103001 (Kurt Beschorner / Jul 14, 2011)
  8  n=82700L: 7732652742988151960568776872507813340801 (Alfred Reich / Dec 12, 2010)
  9  n=96769: 232405044211150158012128920618163 (Serge Batalov / Jun 2, 2011)
  10  n=98345: 31476775338259256593745673622081 (Serge Batalov / Jun 2, 2011)
  11  n=99220L: 30847430620382008736997413844941 (Alfred Reich / Dec 19, 2010)
  12  n=99380M: 6592290434322258947071767721 (Alfred Reich / Apr 26, 2010)
  13  n=99874: 20466106492496275108462693 (Alfred Reich / Mar 29, 2010)
  14  n=100000: 10667937242260969298800001 (Serge Batalov / May 15, 2011)

July 14, 2011 2011 年 7 月 14 日 (Alfred Reich)

n=83500L: c16581(1201620698......) = 36703845957153406501 * c16561(3273827762......)

July 12, 2011 2011 年 7 月 12 日 (Kurt Beschorner)

n=11609: c9937(1111111111......) = 632476112581549778959 * c9916(1756763755......)

n=12269: c12269(1111111111......) = 1254524101378908188237 * c12247(8856833518......)

# 2337 of 9592 R_prime factorizations are still blank.

n=13980L: c1818(3051014108......) = 30425975154161597574776941 * c1793(1002766252......)

July 11, 2011 2011 年 7 月 11 日 (Joppe Bos and Thorsten Kleinjung)

n=598: c192(4472393023......) = 1281657376897297354090423403366881099978010686253604381263 * p135(3489538705......)

# Phi_598(10) is the 1034th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

July 8, 2011 2011 年 7 月 8 日 (Kurt Beschorner)

n=5325: c2784(6551147233......) = 1881829796107057951909351 * c2760(3481264483......)

n=10859: c10844(3571103412......) = 424035269368353718039 * c10823(8421713168......)

n=11113: c11113(1111111111......) = 1431484465523262922201 * c11091(7761950184......)

# 2338 of 9592 R_prime factorizations are still blank.

July 6, 2011 2011 年 7 月 6 日 (Alfred Reich)

n=40380M: c5357(2925126287......) = 883889743913313171540601 * c5333(3309379147......)

July 7, 2011 2011 年 7 月 7 日 (Joppe Bos and Thorsten Kleinjung)

n=598: c254(3385206625......) = 75691170432105638169937308505913924514228814615635050477687293 * c192(4472393023......)

July 6, 2011 2011 年 7 月 6 日 (Kurt Beschorner)

n=10813: c9791(1239749317......) = 313624340155303427013272323 * c9764(3952975451......)

n=10843: c9270(2919292796......) = 63802808773094913204610481 * c9244(4575492604......)

n=13940M: c2536(6955658522......) = 10505679958301633722820919787717001 * c2502(6620855147......)

July 6, 2011 2011 年 7 月 6 日 (Serge Batalov)

n=65792: c32766(3891050583......) = 815894265584129 * x32751(4769062301......)

n=65792: x32751(4769062301......) = 310662839389893377 * c32734(1535124802......)

July 5, 2011 2011 年 7 月 5 日 (Alfred Reich)

n=18446: c8773(4923628635......) = 1258644545122399207 * c8755(3911849977......)

n=34114: c16534(3215532130......) = 592130723053893295575847 * c16510(5430442984......)

n=81120: c19962(6848559850......) = 13767053015041 * c19949(4974601204......)

July 4, 2011 2011 年 7 月 4 日 (Alfred Reich)

n=18402: c6106(8008687159......) = 4912677270247255698964807 * c6082(1630208279......)

n=18914: c8059(1652212725......) = 84720952286064133103 * c8039(1950181957......)

n=56738: c25762(2037437739......) = 3476163526128807361 * c25743(5861167705......)

n=56818: c28397(1224664729......) = 118076691029515961 * c28380(1037177379......)

n=56938: c24099(1029638938......) = 178890119803917677 * x24081(5755706011......)

n=56938: x24081(5755706011......) = 84678718761059088247 * c24061(6797110414......)

n=56978: c27533(2925105518......) = 129717493439689 * c27519(2254981530......)

n=57098: c28536(9958722561......) = 3990468613294477 * c28521(2495627337......)

n=57218: c23708(6772222940......) = 2188916019551171 * c23693(3093870609......)

n=91522: c45003(1515422591......) = 5210030908207268917 * c44984(2908663342......)

July 2, 2011 2011 年 7 月 2 日 (Serge Batalov)

n=33852: c8602(5233013809......) = 13849559842120395121 * c8583(3778469402......)

# ECM B1=250000, sigma=1359304330

n=33870: c9017(6064943835......) = 17808928734887076931 * c8998(3405563538......)

# ECM B1=250000, sigma=416375491

n=20910: c5080(6965583818......) = 44732551046170914961 * c5061(1557162213......)

# ECM B1=250000, sigma=499540829

n=33858: c9713(1052195117......) = 51239451389540437 * c9696(2053486305......)

# ECM B1=250000, sigma=4258145806

n=20958: c5954(5430876878......) = 70985386453642323045977413 * c5928(7650697065......)

# ECM B1=250000, sigma=2456758928

July 1, 2011 2011 年 7 月 1 日 (Kurt Beschorner)

n=10763: c10477(1975187707......) = 181801387586205221568467 * c10454(1086453592......)

n=10775: c8577(1538250426......) = 103482067809514301028551 * c8554(1486489841......)

n=10793: c10452(1738589790......) = 57562150753477280927158855081 * c10423(3020369753......)

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