-- Nov 30, 2008 (Kurt Beschorner) -- n=5201: c4419(5578674800......) = 55089648550114805352943351 * c4394(1012653909......) n=5615: c4469(4171674466......) = 15864249179620029844111 * c4447(2629607250......) n=5645: c4498(4731894108......) = 4208336093111604281 * c4480(1124409743......) n=7137: c4321(1001000999......) = 1336998501562232260148437 * c4296(7486926865......) n=8115: c4316(6838696937......) = 46353260819106268043600641 * c4291(1475343226......) n=8547: c4316(1756724433......) = 76887959784937172205643 * c4293(2284784819......) n=9075: c4379(7855068107......) = 1748168644675290050401 * c4358(4493312548......) -- Nov 30, 2008 (Yousuke Koide) -- n=2461: c2296(3270448889......) = 5817983911794217594551844849 * c2268(5621275237......) n=3605: c2443(8110750990......) = 2494701692185326338954942221751 * c2413(3251190719......) -- Nov 26, 2008 (Kurt Beschorner) -- n=4697: c3601(1111110999......) = 32520794790641228634054031 * c3575(3416616989......) n=4711: c4032(9000000900......) = 540363415808464863503130467 * c4006(1665545933......) -- Nov 26, 2008 (Yousuke Koide) -- n=5115: c2392(7472675784......) = 14055293969111083264951 * c2370(5316627173......) -- Nov 24, 2008 (Kurt Beschorner) -- n=4599: c2546(6328855795......) = 839883647003733732955106161 * c2519(7535395906......) n=4693: c4076(2927559180......) = 195478954869727258881919 * c4053(1497633943......) -- Nov 23, 2008 (Torbjorn Granlund) -- n=785: c606(1062053522......) = 16663607714329041828185817458928401 * c571(6373490906......) n=1832: c892(1931309691......) = 51626338988814569262789149429131191054412260377 * c845(3740938693......) n=1354: c654(4342826963......) = 1373109878288117159960471296998025386367 * c615(3162767257......) n=1746: c499(1295162569......) = 116089721943926115626614365020206939 * c464(1115656535......) -- Nov 23, 2008 (Yousuke Koide) -- n=783: c481(6297754427......) = 87775758732852368588328089882054383747 * p443(7174821976......) n=4347: c2348(1118268759......) = 72298287811217538481899039679 * c2319(1546743074......) n=4575: c2396(2185766431......) = 55775372718378976552445769751 * c2367(3918873734......) -- Nov 20, 2008 (Kurt Beschorner) -- n=4653: c2761(1001000999......) = 2077345816528562943067 * c2739(4818653649......) n=4659: c3075(3544640224......) = 1846352526482056693 * c3057(1919806848......) n=11011: c7912(9333840882......) = 266096543200489 * c7898(3507689641......) n=11013: c7326(2779429186......) = 28328662060117 * x7312(9811367654......) n=11013: x7312(9811367654......) = 427119021934935037 * c7295(2297103886......) n=11015: c8786(6856952924......) = 1164184109766871 * c8771(5889921419......) n=11019: c7332(5582393647......) = 1632035691398227 * c7317(3420509537......) n=11023: c10795(5102937591......) = 175281514323319 * x10781(2911281095......) n=11023: x10781(2911281095......) = 1668884140334599 * c10766(1744447697......) n=11033: c9276(5035170667......) = 13826670238739557 * c9260(3641636475......) n=11039: c8832(3940697629......) = 1033261427563597 * c8817(3813843742......) n=11041: c10778(1116847380......) = 40943612460605837 * c10761(2727769519......) n=11059: c11059(1111111111......) = 4744582590814769 * c11043(2341852185......) n=11061: c7360(8292079554......) = 72095728360211893 * c7344(1150148523......) n=11063: c9496(4710829391......) = 886647150818053 * c9481(5313082421......) n=11065: c8841(1198973513......) = 3528223830742316950351 * c8819(3398235403......) n=11067: c5754(1615163681......) = 1906041761822052373 * c5735(8473915490......) n=11069: c11069(1111111111......) = 1164990118464650209 * c11050(9537515327......) n=11073: c7366(2764643627......) = 105455260582129 * c7352(2621627041......) n=11075: c8813(5944748600......) = 184237052567686351 * c8796(3226684598......) n=11077: c9354(5635274972......) = 88426322593032870601 * c9334(6372847821......) n=11081: c9474(8898281660......) = 44504430337175929 * c9458(1999414798......) n=11091: c7377(9580716347......) = 179274122431249 * c7363(5344171382......) n=11095: c7585(1111099888......) = 1893906116310058271 * c7566(5866710494......) n=11099: c10048(6198254970......) = 4870289747027 * x10036(1272666574......) n=11099: x10036(1272666574......) = 63369941968160081 * c10019(2008312672......) -- Nov 19, 2008 (Yousuke Koide) -- n=912: c261(1271438002......) = 281464188569516450327957421884016074607805300753 * p213(4517228317......) n=3933: c2326(2521672345......) = 188964344309447992433400919 * c2300(1334469926......) -- Nov 15, 2008 (Kurt Beschorner) -- n=4611: c2862(1243685551......) = 1238862954807046559239 * c2841(1003892760......) n=4617: c2897(8905982523......) = 1384761731828811064363 * c2876(6431418719......) n=5795: c4321(1111099999......) = 14966976416219585242231 * c4298(7423677094......) n=5795: c4298(7423677094......) = 460493882020632233004241 * c4275(1612111992......) n=6335: c4321(1111099888......) = 1966452643382069914961 * c4299(5650275345......) n=6335: c4299(5650275345......) = 13583236788986332498871 * c4277(4159741476......) n=6471: c4308(9990000009......) = 178391190709559934034790923 * c4282(5600052317......) n=6483: c4305(3056032538......) = 102271239639765519922759 * c4282(2988164169......) n=6543: c4347(6371051779......) = 45574356362201492401 * p4328(1397946627......) n=6609: c4392(1298331114......) = 1441662211234052189791 * c4370(9005792790......) n=7707: c4386(9232357578......) = 8741489361636322326799 * c4365(1056153842......) -- Nov 12, 2008 (Matthew Peets) -- # ***** CORRECTION ***** n=32481: c21600(9999999999......) is (probable) prime # ----------------8<----------------8<----------------8<---------------- # Primality testing 9999999999...... [N-1/N+1, Brillhart-Lehmer-Selfridge] # Running N-1 test using base 43 # Running N-1 test using base 59 # Running N+1 test using discriminant 67, base 14+sqrt(67) # Calling N-1 BLS with factored part 1.37% and helper 0.06% (4.17% proof) # 9999999999...... is Fermat and Lucas PRP! (368.6661s+0.1401s) # ----------------8<----------------8<----------------8<---------------- -- Nov 12, 2008 (Yousuke Koide) -- n=2447: c2405(3597673558......) = 1039143223290181087816293053 * c2378(3462153702......) n=3561: c2344(1654319376......) = 112789079849279160182415667 * c2318(1466737186......) -- Nov 10, 2008 (Kurt Beschorner) -- n=4579: c4283(3659515774......) = 32425003130533716962081 * c4261(1128609227......) n=4579: c4261(1128609227......) = 107439552822192838490239 * c4238(1050459721......) n=4579: c4238(1050459721......) = 138991859499995922984253 * c4214(7557706801......) -- Nov 9, 2008 (Torbjorn Granlund) -- n=1432: c619(7835079982......) = 328455338742918658426662807087083993 * p584(2385432373......) -- Nov 8, 2008 (Kurt Beschorner) -- n=4537: c4172(1102036318......) = 304651381057951306175551 * c4148(3617368529......) n=4551: c2867(8108375703......) = 16423486902182356157512963 * c2842(4937061022......) n=4565: c3266(2331751025......) = 1245377919812466190678511 * c3242(1872324045......) n=4569: c3035(4263909551......) = 16811192009562457306250083 * c3010(2536351704......) -- Nov 8, 2008 (Yousuke Koide) -- n=3059: c2369(4183677238......) = 38823407074356243222109493 * c2344(1077617229......) n=3157: c2383(9565139779......) = 59664606152342434512382360787 * c2355(1603151415......) n=3501: c2316(6990402213......) = 1875527998236278868291073399 * c2289(3727164947......) n=3513: c2313(2356366490......) = 106551591537736686403939816957 * c2284(2211479393......) -- Nov 6, 2008 (Alfred Reich) -- n=12855: c6822(1047928802......) = 574238315457511 * c6807(1824902264......) n=29060L: c5809(2824060999......) = 1407293707505141 * c5794(2006731775......) n=29100M: c3827(8976395262......) = 7164227881801 * c3815(1252946641......) n=29140M: c5506(4357610254......) = 10331706174047730541 * c5487(4217706331......) n=29420L: c5881(2824060999......) = 56358069691941911745161 * c5858(5010925702......) n=29660M: c5915(4015198676......) = 63119564106121 * c5901(6361258562......) n=29740M: c5940(9495514608......) = 7597169152506178801601 * c5919(1249875370......) n=29780L: c5940(1357338145......) = 194947091405882623121 * c5919(6962597571......) n=29980M: c5982(3068432105......) = 285589706054203062401 * c5962(1074419715......) n=34060M: c6236(1039606453......) = 6476533829741 * c6223(1605189567......) n=34220L: c6486(1846783551......) = 8661802570541 * c6473(2132100722......) n=34220M: c6497(2796100000......) = 87945112380901 * c6483(3179369409......) n=34300M: c5861(7205723231......) = 1038730078499401 * c5846(6937050713......) n=34420L: c6867(7639610378......) = 983155748209399361 * c6849(7770498613......) n=34660L: c6921(4021666630......) = 18255146071741 * c6908(2203031745......) n=34820L: c6951(9411836570......) = 12656774975084441 * c6935(7436204395......) n=34940L: c6985(2824060999......) = 347049844686121 * x6970(8137335437......) n=34940L: x6970(8137335437......) = 798676887259201 * c6956(1018851999......) n=35020L: c6528(3540999964......) = 143335199701801 * c6514(2470432923......) n=35140M: c6001(2798897498......) = 4343616043201 * c5988(6443703749......) n=35260L: c6708(5594344592......) = 33481935516859541 * c6692(1670854598......) n=35500L: c7001(1000000000......) = 288108280029001 * c6986(3470917253......) n=35500M: c6983(2459436932......) = 1960008118969501 * c6968(1254809563......) n=35620L: c6513(4859196016......) = 4920688781321 * c6500(9875032200......) n=35860L: c6475(7797323379......) = 930176875366421 * c6460(8382624408......) n=39020M: c7791(3146764769......) = 7124046727741 * c7778(4417102932......) n=39100M: c7032(8192986280......) = 9128017539401 * c7019(8975646951......) n=39220L: c7488(3541000000......) = 50097071248201 * c7474(7068277469......) n=39260L: c7200(3541003541......) = 404646046511461 * c7185(8750866520......) n=39580L: c7897(3910736895......) = 33377045316821 * c7884(1171684568......) n=39660L: c5272(8502004572......) = 186985551291001 * x5258(4546877827......) n=39660L: x5258(4546877827......) = 654647800113301 * c5243(6945532890......) n=39820M: c7196(1170314857......) = 3331011291301 * c7183(3513392046......) n=39860L: c7960(8149344499......) = 2500754408930801 * c7945(3258754426......) n=54020L: c10357(9039273003......) = 49333385509501 * c10344(1832283130......) n=54180L: c6038(9201279034......) = 131547973358341 * c6024(6994618616......) n=54220M: c10840(3576409999......) = 1437201788597215241 * c10822(2488453624......) n=54300L: c7189(2197755558......) = 9885600998101 * c7176(2223188614......) n=54300M: c7185(3495251169......) = 694658397795093888601 * c7164(5031611480......) n=54380L: c10863(6919650719......) = 79230730325393041 * c10846(8733544031......) n=54380M: c10858(2061195587......) = 3607509871421 * x10845(5713624247......) n=54380M: x10845(5713624247......) = 3456901975755824821 * x10827(1652816391......) n=54380M: x10827(1652816391......) = 8161574510331613661 * c10808(2025119526......) n=54420M: c7239(2655165474......) = 5114633986681 * c7226(5191310817......) n=54580M: c10896(1981585900......) = 3563739424601 * x10883(5560411870......) n=54580M: x10883(5560411870......) = 5665412514481 * c10870(9814663727......) n=54620L: c10920(3576409999......) = 10803709117741 * c10907(3310353842......) n=54620M: c10914(2238259121......) = 888374752812881 * c10899(2519498798......) n=54700L: c10901(1388709747......) = 13107830469001 * c10888(1059450494......) n=54700M: c10920(9900498007......) = 1676582386594301 * c10905(5905166418......) n=54740M: c8439(1501061295......) = 34213325636194321 * c8422(4387358632......) n=54780L: c6554(3797612244......) = 8814644954928121 * x6538(4308298591......) n=54780L: x6538(4308298591......) = 9714328869575881 * c6522(4434993553......) n=54780M: c6561(2555255162......) = 10037936899256616901 * c6542(2545597953......) n=54820L: c10960(3576409999......) = 934109629449660721 * c10942(3828683365......) n=54820M: c10961(2824060999......) = 6862926325441 * x10948(4114951648......) n=54820M: x10948(4114951648......) = 6965094876008861 * c10932(5907962090......) n=54860M: c10067(2032039893......) = 10029237114979681 * c10051(2026116114......) n=54940M: c10561(2796099999......) = 12253177384181 * x10548(2281938726......) n=54940M: x10548(2281938726......) = 577610990260700621 * c10530(3950649771......) n=92020L: c17793(1732015500......) = 520721303681 * x17781(3326185212......) n=92020L: x17781(3326185212......) = 88342619788065935681 * c17761(3765096870......) n=92220L: c11643(4286088960......) = 876403179121 * c11631(4890544742......) n=92260L: c15764(4783150847......) = 191137843863683641 * c15747(2502461443......) n=93060M: c11034(3739927181......) = 678909458701 * c11022(5508727464......) n=93700L: c18713(5870092150......) = 858441545201 * c18701(6838080220......) n=94060L: c18802(9505636014......) = 355076765531381 * c18788(2677065056......) n=94100L: c18800(9900498007......) = 1841349082301 * p18788(5376763212......) # ----------------8<----------------8<----------------8<---------------- # Primality testing 5376763212...... [N-1/N+1, Brillhart-Lehmer-Selfridge] # Running N-1 test using base 19 # Running N+1 test using discriminant 37, base 2+sqrt(37) # Running N+1 test using discriminant 37, base 4+sqrt(37) # Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.12% proof) # 5376763212...... is Fermat and Lucas PRP! (409.6657s+0.0417s) # ----------------8<----------------8<----------------8<---------------- n=94100M: c18801(1010050200......) = 66753134804701 * c18787(1513112760......) n=94660L: c18929(2824060999......) = 2151162611534161 * c18914(1312806844......) n=95060M: c16119(6534406896......) = 350423386887101501 * c16102(1864717693......) n=95180M: c19032(3576409999......) = 226577610915401 * c19018(1578448102......) n=95260L: c17265(7251449177......) = 675935524661 * c17254(1072801903......) n=95300L: c19034(8657300936......) = 2441497085101 * c19022(3545898534......) n=95300M: c19041(1010050200......) = 204457239450001 * c19026(4940153762......) n=95340M: c10842(9936310296......) = 58657055869861 * c10829(1693966761......) n=95500L: c18990(2853243573......) = 151815209539001 * x18976(1879418789......) n=95500L: x18976(1879418789......) = 529672375322501 * c18961(3548266583......) n=95620M: c16368(3537460769......) = 92485378370981 * c16354(3824886519......) n=95740M: c19144(3576409999......) = 79236286451761501 * x19127(4513601229......) n=95740M: x19127(4513601229......) = 1018123474388323561 * c19109(4433255241......) n=95860L: c19152(2475069005......) = 1944504454305961 * c19137(1272853348......) n=95860M: c19169(2824060999......) = 978373042201 * c19157(2886486930......) n=95900L: c16314(6882510340......) = 3666735349201 * c16302(1877013115......) n=95900M: c16314(1423287290......) = 52581668671708923601 * c16294(2706812709......) n=95980L: c19187(1961560768......) = 4710363600068521 * c19171(4164351066......) n=95980M: c19192(3576409999......) = 679524267075789066601 * c19171(5263108578......) n=96020M: c19192(2804707142......) = 73342561198953941 * c19175(3824119442......) n=96060L: c12761(5336712024......) = 36413873341249561 * c12745(1465571095......) n=96220M: c18028(1410790875......) = 9760182889081 * c18015(1445455368......) n=96860L: c18592(3540999999......) = 13351264519070321 * c18576(2652183240......) n=97020L: c10067(5922282754......) = 2563073912368444861 * c10049(2310617234......) n=97060L: c18480(3540999999......) = 4294843605376421 * c18464(8244770532......) n=97180M: c18816(3541000000......) = 63402275501041 * c18802(5584973050......) n=97540M: c19472(1881512189......) = 5818664464924144205401 * c19450(3233580834......) n=97780L: c19553(2824060999......) = 2328728382221 * c19541(1212705191......) n=97780M: c19544(7171782047......) = 2332734991739461 * c19529(3074409254......) n=97820M: c18996(2517916323......) = 1357419781215664914301 * c18975(1854928267......) n=99130: c37835(9170693324......) = 8905670679001 * c37823(1029758864......) n=99474: c32465(1097489781......) = 803345856613 * c32453(1366148555......) n=99538: x49297(1099999999......) = 6489190986877 * x49284(1695126560......) n=99720: c26482(6361483543......) = 1944230868001 * c26470(3271979499......) n=99924: c30240(9901000000......) = 432817808281 * c30229(2287567611......) -- Nov 6, 2008 (Yousuke Koide) -- n=2995: c2387(7154796448......) = 9696734379688499685077807281 * c2359(7378562894......) n=3395: c2265(4799993440......) = 1496220835847158602460486131234120721 * c2229(3208078196......) -- Nov 6, 2008 (Silverman) -- n=494: c201(3444741866......) = 438725907577156177685201819419114255533305134233669402807964649891016719989703392491612289098617653 * p102(7851694660......) -- Nov 6, 2008 (Kurt Beschorner) -- n=4509: c2976(1387311634......) = 319243959239691552628608001 * c2949(4345615927......) n=4525: c3584(1900351231......) = 672155393578343105132201 * c3560(2827249844......) n=11025: c5041(1000000000......) = 35990831571948080125201 * p5018(2778485398......) # ----------------8<----------------8<----------------8<---------------- # Primality testing 2778485398...... [N-1/N+1, Brillhart-Lehmer-Selfridge] # Running N-1 test using base 11 # Running N-1 test using base 13 # Running N-1 test using base 17 # Running N+1 test using discriminant 31, base 3+sqrt(31) # Calling N-1 BLS with factored part 0.16% and helper 0.01% (0.48% proof) # 2778485398...... is Fermat and Lucas PRP! (19.4959s+0.0936s) # ----------------8<----------------8<----------------8<---------------- -- Nov 5, 2008 (Yousuke Koide) -- n=2935: c2344(9000090000......) = 1142134362243603835908631391 * c2317(7880062362......) n=2965: c2351(2683272777......) = 6146001793715517282563681 * c2326(4365883492......) -- Nov 5, 2008 (Makoto Kamada) -- n=86221: x85477(6855658305......) = 417171686401 * x85466(1643366155......) n=88734: c28240(2442918045......) = 416121021223 * c28228(5870691267......) n=89260L: c17848(3576409999......) = 419472907001 * c17836(8525961843......) n=92473: x84229(5413951957......) = 411060054871 * x84218(1317070801......) n=93649: x92260(9000000000......) = 417320359483 * x92249(2156616564......) n=94155: x50209(1109988900......) = 415192855471 * x50197(2673429673......) n=94910: c37961(1099989000......) = 411052932161 * c37949(2676027620......) n=96022: x46795(2863919560......) = 411775367569 * x46783(6955053133......) n=97929: x58321(1000000000......) = 418159767871 * x58309(2391430445......) -- Nov 4, 2008 (Makoto Kamada) -- n=66006: c20723(1034361775......) = 402078717289 * c20711(2572535504......) n=66008: c31957(4291118790......) = 401883503249 * c31946(1067751912......) n=67376: c33671(3572101110......) = 406094758417 * c33659(8796225600......) n=67826: c30803(5396207969......) = 404037515047 * c30792(1335571022......) n=67951: x62706(7358237424......) = 407241894671 * x62695(1806846869......) n=74141: x73500(9000000000......) = 400345533827 * x73489(2248058049......) n=75925: x60720(9999900000......) = 404983342601 * x60709(2469212668......) n=76712: c37289(6208129962......) = 403982575489 * c37278(1536732111......) n=77100L: c10231(2421940821......) = 407667252301 * c10219(5940974673......) n=78474: c22401(1098901098......) = 408338988157 * c22389(2691149096......) n=80423: x68921(9325690378......) = 408394749533 * x68910(2283499087......) n=83144: c39298(6568154374......) = 401893984241 * c39287(1634300246......) n=83345: x65503(7363531187......) = 406995471391 * x65492(1809241553......) n=84197: x83616(9000000000......) = 401980053161 * x83605(2238917062......) n=84266: c33250(8660975791......) = 404208244259 * c33239(2142701420......) -- Nov 3, 2008 (Makoto Kamada) -- n=85167: x56772(9990000009......) = 406651644253 * x56761(2456648128......) n=86463: x53137(1001000999......) = 404371023031 * x53125(2475451857......) n=89934: c27633(9591698380......) = 402524168983 * c27622(2382887567......) n=92412: c28785(6041928475......) = 403750338301 * c28774(1496451619......) n=93690: c24912(9999999990......) = 407523486691 * c24901(2453846297......) n=98160: c26086(4253524032......) = 403277206561 * c26075(1054739510......) n=98461: x89473(3345398522......) = 400641944363 * x89461(8350095564......) -- Nov 2, 2008 (Yousuke Koide) -- n=623: c493(2165045687......) = 8913744173664812282361573178107163720093 * p453(2428884703......) -- Nov 1, 2008 (Kurt Beschorner) -- n=10907: c10050(1901285670......) = 130082903486453243 * c10033(1461595351......) n=10911: c7262(1480883369......) = 42754585154504161999 * c7242(3463683168......) n=10913: c9348(9000000900......) = 57188507527999 * c9335(1573742923......) n=10915: c8343(4780532077......) = 173849973240881491871 * c8323(2749803171......) n=10929: c7284(9009009009......) = 3995474745504927169 * c7266(2254803141......) n=10933: c9726(6551951342......) = 103820465109947 * x9712(6310847611......) n=10933: x9712(6310847611......) = 345886329985642880201 * x9692(1824543806......) n=10933: x9692(1824543806......) = 4562895198783259498889 * c9670(3998653764......) n=10935: c5820(6913824982......) = 327510237902401 * c5806(2111025605......) n=10941: c6241(1109999889......) = 4932411125696609689 * c6222(2250420455......) n=10943: c10548(6523998962......) = 15535114623365763161 * c10529(4199517751......) n=10945: c7921(1111099999......) = 158405891353711 * c7906(7014259321......) n=10947: c7029(8576392583......) = 63088062916446961 * x7013(1359431909......) n=10947: x7013(1359431909......) = 872689951380760483 * x6995(1557749011......) n=10947: x6995(1557749011......) = 72361330492335102973 * c6975(2152736829......) n=10951: c10672(9000000000......) = 6823195271584253 * c10657(1319030108......) n=10955: c7466(2327886845......) = 31296281554874587441 * c7446(7438221826......) n=10963: c10351(4711890064......) = 3437727110201 * x10339(1370641099......) n=10963: x10339(1370641099......) = 807150848732653 * c10324(1698122601......) n=10965: c5376(9009099100......) = 56220241415789401 * c5360(1602465388......) n=10967: c9960(9000000000......) = 12802331268095249 * c9944(7029969629......) n=10971: c6835(3084122339......) = 1440032619685879 * c6820(2141703109......) n=10975: c8755(9111443175......) = 7149170248151 * x8743(1274475618......) n=10975: x8743(1274475618......) = 18770665354151 * c8729(6789719995......) n=10987: c10979(5544386665......) = 20862312113483 * c10966(2657608914......) n=10989: c6474(2096775852......) = 111107807088894991 * c6457(1887154384......) n=10991: c10584(9000000000......) = 978680330137957 * c10569(9196056897......) n=10997: c9420(9000000900......) = 9501069094534388071 * c9401(9472619144......)