-- Nov 29, 2024 (Torbjorn Granlund) -- # via Kurt Beschorner n=3028: c1493(5702780114......) = 350811664667433614608602654291207889 * c1458(1625595921......) # ECM B1=3e6 n=4174: c2064(5826788376......) = 108918422903303886126910580318696251 * c2029(5349681184......) # ECM B1=3e6 n=4972: c2208(3969406518......) = 577837704901733035210523216577847049549 * c2169(6869414171......) # ECM B1=3e6 n=5398: c2698(9090909090......) = 3279708514581454577251383230741819 * c2665(2771864954......) # ECM B1=3e6 n=5478: c1566(3306727606......) = 68607233373205142171625494377086752971 * c1528(4819794421......) # ECM B1=3e6 n=5496: c1788(3031648595......) = 16720796591104964964012274961761 * c1757(1813100577......) # ECM B1=3e6 n=6738: c2235(2051073712......) = 51245455168258282841893513998267997 * c2200(4002449984......) # ECM B1=3e6 n=11180L: c1950(2017447970......) = 28211252517426651484369691411498741 * c1915(7151217299......) # ECM B1=1e6 n=11390: c4196(5299876253......) = 241089081105899896676693655121 * c4167(2198306214......) # ECM B1=1e6 n=12718: c6337(3816009818......) = 1622472125404964255486174113693 * c6307(2351972498......) # ECM B1=1e6 n=12898: c6444(7047762687......) = 196349392321387598699516016347797 * c6412(3589398777......) # ECM B1=3e6 n=14354: c7146(5579905307......) = 811272527195511473736461822117911962841 * c7107(6877966552......) # ECM B1=1e6 n=14754: c4870(1576530302......) = 4313006097050418055872643089194023 * c4836(3655293469......) # ECM B1=1e6 n=15382: c7686(5909711428......) = 3175391604742537135819667361565371653 * c7650(1861096886......) # ECM B1=1e6 n=16118: c8026(5435402175......) = 129949302924329134475319109727 * c7997(4182709759......) # ECM B1=1e6 n=17812: c8641(1009999999......) = 175676229085567924131541957505849 * c8608(5749212658......) # ECM B1=3e6 -- Nov 27, 2024 (Alfred Eichhorn) -- # via Kurt Beschorner n=16487: c16487(1111111111......) = 85855843852342041551190326949071 * c16455(1294158977......) # ECM B1=1e6, sigma=3540680568445972 n=17011: c17011(1111111111......) = 371269994862869743297843049482351 * c16978(2992730698......) # ECM B1=1e6, sigma=3467295196514019 n=25771: c25771(1111111111......) = 1618919654638410532966695689809 * c25740(6863287550......) # ECM B1=1e6, sigma=0:8929280927174938 n=26107: c26107(1111111111......) = 749172713584380613761044507 * c26080(1483117432......) # ECM B1=1e6, sigma=7689781701333303 -- Nov 27, 2024 (Kurt Beschorner) -- n=1505: c945(6223710974......) = 62115703652442437970564849055491434518411781791 * c899(1001954515......) # ECM B1=43e6, sigma=3:3612922203 n=1507: c1343(1206932669......) = 205639315737380899003691742110287041179812977689 * c1295(5869172755......) # ECM B1=43e6, sigma=3:3793980079 n=1533: c848(1954727074......) = 213522434186075863894759359560240658151 * c809(9154668371......) # P-1 B1=5e9 n=2459: c2400(5652559723......) = 646583676742128689455152852799720600889 * c2361(8742193666......) # ECM B1=3e6, sigma=3:2720534563 -- Nov 27, 2024 (Torbjorn Granlund) -- # via Kurt Beschorner n=18660L: c2463(7714422472......) = 280810859436055742441906429115682141 * c2428(2747195207......) # ECM B1=1e6 n=16494: c5456(1409289493......) = 96430542755514493448598981025129 * c5424(1461455523......) # ECM B1=3e6 n=19554: c6476(7011653342......) = 23151524580580099975005537223 * c6448(3028592487......) # ECM B1=1e6 n=17982: c5825(1224915551......) = 134863768349399846909652035340487213 * c5789(9082614007......) # ECM B1=3e6 n=11572: c5225(1107354125......) = 240366513598327598232574876974329 * c5192(4606940081......) # ECM B1=1e6 n=19850: c7889(1195956042......) = 719094391284743442614635765229882651 * c7853(1663141942......) # ECM B1=1e6 n=13736: c6368(3084719749......) = 81636676076256779577902555701248518369 * c6330(3778595476......) # ECM B1=3e6 n=13940L: c2531(3151418229......) = 63590216313243802118407932917711441 * c2496(4955822471......) # ECM B1=1e6 n=16020L: c2104(9382968970......) = 46051351274930993358718249052727481 * c2070(2037501335......) # ECM B1=1e6 n=16646: c6686(1126150672......) = 882603787036186239195049938701028731 * c6650(1275941355......) # ECM B1=3e6 n=8432: c3816(2520626534......) = 4160555408329388877269057170438527953 * c3779(6058389533......) # ECM B1=3e6 n=9492: c2681(7325062077......) = 165957148309580907134016699617855329 * c2646(4413827395......) # ECM B1=1e6 n=18484: c9232(1073407719......) = 26786665988236101934497919349 * c9203(4007246439......) # ECM B1=1e6 n=11244: c3720(7603846104......) = 1037919397567674352091169149521 * c3690(7326046822......) # ECM B1=1e6 n=7836: c2566(8512852219......) = 32023331502072669887932498701092929 * c2532(2658328106......) # ECM B1=1e6 n=5050: c1934(5169130785......) = 2858645341697598342769128549063601 * c1901(1808244873......) # ECM B1=1e6 n=14622: c4838(1022674687......) = 126702984205340775076852610183187601 * p4802(8071433312......) # ECM B1=3e6 # ----------------8<----------------8<----------------8<---------------- # $ ./pfgw64 -tc -q"(10^4874-10^2437+1)/1238937325340127610488425471233981493598328763421614271059727825618837103" # PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] # # Primality testing (10^4874-10^2437+1)/1238937325340127610488425471233981493598328763421614271059727825618837103 [N-1/N+1, Brillhart-Lehmer-Selfridge] # # Running N-1 test using base 3 # Running N+1 test using discriminant 7, base 6+sqrt(7) # # Calling N-1 BLS with factored part 0.20% and helper 0.03% (0.64% proof) # (10^4874-10^2437+1)/1238937325340127610488425471233981493598328763421614271059727825618837103 is Fermat and Lucas PRP! (0.7634s+0.0269s) # ----------------8<----------------8<----------------8<---------------- n=4758: c1440(9100000000......) = 597843259303729297849229332466764327 * c1405(1522138095......) # ECM B1=1e6 n=18238: c8254(2409181924......) = 93318215426166207055121421888263 * c8222(2581684522......) # ECM B1=3e6 n=15212: c7575(3315207720......) = 613215826748498466338715936749 * c7545(5406265748......) # ECM B1=1e6 n=11126: c5549(2869595114......) = 653130462612717769801874495375011 * c5516(4393601705......) # ECM B1=3e6 -- Nov 24, 2024 (Torbjorn Granlund) -- # via Kurt Beschorner n=4398: c1455(1247177094......) = 2250655759461579907658456158341378523393459 * c1412(5541394276......) # ECM B1=1e6 n=5876: c2635(1182876272......) = 122881028931838072024623429521 * c2605(9626191142......) # ECM B1=1e6 n=9486: c2871(4292400930......) = 60517505137742238213182649655345933 * c2836(7092825325......) # ECM B1=1e6 n=11022: c3304(1240262015......) = 13492101419840095990357182938407 * c3272(9192504388......) # ECM B1=1e6 n=11112: c3692(2249994375......) = 1119796977199941669609379841122801 * c3659(2009287773......) # ECM B1=1e6 n=11736: c3835(9636905442......) = 470600578956966664935199936226689 * c3803(2047788692......) # ECM B1=1e6 n=12576: c4145(2526892012......) = 6062905159404990134935177885249 * c4114(4167790764......) # ECM B1=1e6 n=13638: c4501(2743034729......) = 1595592606471382368015524884129 * c4471(1719132263......) # ECM B1=1e6 n=18020L: c3322(2955551749......) = 1162109319238402957122414931013024101 * c3286(2543264820......) # ECM B1=1e6 n=10022: c5002(1706349318......) = 250943251882275453879549409410077912971 * c4963(6799741797......) # ECM B1=3e6 n=18582: c5823(1098046910......) = 2254438383557621906725366187851 * c5792(4870600669......) # ECM B1=1e6 n=19398: c6233(2764410805......) = 53368281288604331981616356387059 * c6201(5179876020......) # ECM B1=1e6 n=19820M: c3931(1870023402......) = 485934143371278336976535377992521 * c3898(3848306253......) # ECM B1=1e6 n=18286: c8859(1217934169......) = 72525096985342433957750796787969 * c8827(1679327874......) # P-1 B1=1e8 n=18334: c8960(3426224301......) = 20598739132682122829209932331 * c8932(1663317487......) # P-1 B1=1e8 n=19456: c9212(5139538469......) = 3041954552273693420412238735872001 * c9179(1689551366......) # P-1 B1=1e8 n=18976: c9448(4047221336......) = 1458761088353707777088761432321 * c9418(2774423700......) # P-1 B1=1e8 n=18982: c9482(9686946006......) = 154958614462087209921940257943 * c9453(6251311707......) # P-1 B1=1e8 -- Nov 23, 2024 (Kurt Beschorner) -- n=1513: c1363(4061339734......) = 4073058989811163061967384961255100449 * c1326(9971227386......) # ECM B1=11e6, sigma=3:1710696692 n=2996: c1273(1009999999......) = 10070868837525352428796400989776525941 * x1236(1002892616......) # ECM B1=11e6, sigma=3:1184495260 n=2996: x1236(1002892616......) = 2569164908474306407837982546400715548833401 * c1193(3903574322......) # ECM B1=11e6, sigma=3:2623389524 n=5522: c2438(2710261695......) = 228175830687389378268569034706114933 * c2403(1187795257......) # ECM B1=3e6, sigma=3:310935704 n=10384: c4641(1000000009......) = 99627958818782147774783267894286635387087681 * c4597(1003734315......) # ECM B1=1e6, sigma=0:1429027484175333 n=10490: c4166(1347817173......) = 3404715218879286112653170559931 * c4135(3958678146......) # P-1 B1=1e9 n=14133: c8040(7048505411......) = 3390061178096991195841 * c8019(2079167614......) # P-1 B1=180e6 n=14137: c13846(2351124900......) = 84758687585502487473359 * c13823(2773904324......) # P-1 B1=150e6 n=14363: c14031(1109955856......) = 13765349940537143422113359 * c14005(8063404574......) # P-1 B1=26e6 n=20113: c20087(3979713420......) = 196700194240250118970483 * c20064(2023238175......) # P-1 B1=26e6 n=33515: c26776(7173034193......) = 5949278585630719634724161 * x26752(1205698151......) # P-1 B1=26e6 n=33515: x26752(1205698151......) = 1714004804552864730734075201 * c26724(7034391901......) # P-1 B1=26e6 n=100535: c80413(5094463905......) = 2526448671711960287521 * c80392(2016452565......) # P-1 B1=26e6 n=100538: c47297(1099999999......) = 240472609350127589116607 * c47273(4574325545......) # P-1 B1=55e6 n=100543: c97029(1023500854......) = 6298531939174331317 * c97010(1624983192......) # P-1 B1=26e6 n=100546: c50272(9090909090......) = 6482347212241646693060952407 * c50245(1402410082......) # P-1 B1=55e6 n=100558: c49777(1099999999......) = 1367806470521025574997 * c49755(8042073375......) # P-1 B1=55e6 n=100562: c39097(6950743739......) = 460020248685831655897866108011 * c39068(1510964736......) # P-1 B1=55e6 n=100563: c67035(2239637494......) = 95363442016382434729 * c67015(2348528373......) # P-1 B1=26e6 n=100570: c39424(9091000000......) = 20354394369217378890302717166091 * c39393(4466357404......) # P-1 B1=55e6 n=100574: c50260(1636469877......) = 841314902037959111785409 * c50236(1945133591......) # P-1 B1=55e6 n=172127: c172113(3956104227......) = 1219673247598548763 * c172095(3243577110......) # gr-mfaktc -- Nov 22, 2024 (Torbjorn Granlund) -- # via Kurt Beschorner n=3320: c1281(1676912197......) = 209855077384496402528794210924081 * c1248(7990810697......) # ECM B1=1e6 n=4264: c1885(4636716352......) = 7830904558151282394453258027420068448313 * c1845(5921048224......) # ECM B1=1e6 n=4634: c1951(3528093691......) = 133497367767000665131131678430301773 * c1916(2642818918......) # ECM B1=3e6 n=5310: c1364(4273625525......) = 38072168879843482870802927929991371 * c1330(1122506453......) # ECM B1=1e6 n=5854: c2884(2557884369......) = 23382325431546395261196228437659 * c2853(1093939256......) # ECM B1=1e6 n=5904: c1889(1139627394......) = 1869537495549965870641867493011201 * c1855(6095771800......) # ECM B1=1e6 n=8166: c2707(4843566583......) = 123422355630783710434507634464892127931 * c2669(3924383519......) # ECM B1=1e6 n=8174: c3938(1365606052......) = 426606414881654882020447697779817923778449 * c3896(3201091229......) # ECM B1=1e6 n=8370: c2120(3285444197......) = 712453221758660496775090393681 * c2090(4611452509......) # ECM B1=1e6 n=8492: c3835(1043292507......) = 3719668025351558497787621075044901 * c3801(2804800052......) # ECM B1=1e6 n=10350: c2626(1525517945......) = 777528354247066024351829083575001 * c2593(1962009407......) # ECM B1=1e6 n=11626: c5787(6421508431......) = 3662442622632712655098853009 * c5760(1753340350......) # ECM B1=1e6 n=13042: c6494(3500733375......) = 6618448990102777708230288089 * c6466(5289356132......) # ECM B1=1e6 n=14248: c6529(1000099999......) = 110038620618729917903338883737 * c6499(9088627196......) # ECM B1=1e6 n=14370: c3749(8034718450......) = 11616138821969139121723043000521 * c3718(6916858152......) # ECM B1=1e6 n=14380M: c2863(1372215686......) = 154471537280653399451928917390806964581 * c2824(8883291452......) # ECM B1=1e6 n=14910: c3361(1098890000......) = 680200055480364010929968817691 * c3331(1615539415......) # ECM B1=1e6 n=15144: c5002(5268784940......) = 123493751144798553672423177510553 * c4970(4266438497......) # ECM B1=1e6 n=15432: c5107(3818950095......) = 126772018625252090476333716073 * c5078(3012455064......) # ECM B1=1e6 n=15516: c5112(2214164736......) = 15662937123666521974558553298049 * c5081(1413633163......) # ECM B1=1e6 n=15680: c5364(6518123212......) = 22655473916191773174317040641 * c5336(2877063281......) # ECM B1=1e6 n=15848: c6769(1000099999......) = 115806814146026246525146363409 * c6739(8635933967......) # ECM B1=1e6 n=16134: c5317(9722553800......) = 2595661175357965328882122630414123129 * c5281(3745694504......) # ECM B1=1e6 n=17368: c7955(3112118143......) = 402732350235867873516535246754642790481 * c7916(7727509701......) # ECM B1=1e6 n=17420M: c3169(2796097203......) = 67737935728841701410303869871661 * p3137(4127815785......) # ECM B1=1e6 # ----------------8<----------------8<----------------8<---------------- # $ ./pfgw64 -tc -q"((10^871+1)*((10^1742+10^871)*(10^871+10^436+3)+10^436+2)-1)/24225887295451271139593466940975365564882861763174939416814215108126431780711701/((10^67+1)*((10^134+10^67)*(10^67+10^34+3)+10^34+2)-1)" # PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] # # Primality testing ((10^871+1)*((10^1742+10^871)*(10^871+10^436+3)+10^436+2)-1)/24225887295451271139593466940975365564882861763174939416814215108126431780711701/((10^67+1)*((10^134+10^67)*(10^67+10^34+3)+10^34+2)-1) [N-1/N+1, Brillhart-Lehmer-Selfridge] # Running N-1 test using base 2 # Running N-1 test using base 17 # Running N-1 test using base 19 # Running N+1 test using discriminant 29, base 16+sqrt(29) # # Calling N-1 BLS with factored part 0.23% and helper 0.11% (0.82% proof) # ((10^871+1)*((10^1742+10^871)*(10^871+10^436+3)+10^436+2)-1)/24225887295451271139593466940975365564882861763174939416814215108126431780711701/((10^67+1)*((10^134+10^67)*(10^67+10^34+3)+10^34+2)-1) is Fermat and Lucas PRP! (0.4966s+0.0005s) # ----------------8<----------------8<----------------8<---------------- n=17736: c5895(4541570320......) = 129544664562140547265456563409 * c5866(3505794959......) # ECM B1=1e6 n=17750: c6990(2014077880......) = 12904244867890415385714718903195001 * c6956(1560787090......) # ECM B1=1e6 n=17938: c8913(4005189504......) = 1381988647388392386045478881481 * c8883(2898134881......) # ECM B1=1e6 n=18070: c6570(2058342947......) = 1755924560430390901867470711752521 * c6537(1172227437......) # ECM B1=1e6 n=18490: c7212(1383877030......) = 773592060142970046680286931091441 * c7179(1788897665......) # ECM B1=1e6 n=18996: c6262(5945098255......) = 119605123684705889520287885416681 * c6230(4970604997......) # ECM B1=1e6 n=19628: c8361(6914770872......) = 10769352505741295714306444836409 * c8330(6420786086......) # ECM B1=1e6 n=19672: c9764(6425021251......) = 36529171118425857022042396289 * c9736(1758874087......) # ECM B1=1e6 n=19782: c5591(6380156071......) = 741143489923205859402689063047489 * c5558(8608530140......) # ECM B1=1e6 n=14698: c7344(6184712627......) = 2347654209857259248783821628575634401 * c7308(2634422310......) # P-1 B1=1e8 n=14818: c7123(6938680835......) = 1637485139034609598162047343 * c7096(4237400798......) # P-1 B1=1e8 n=14908: c7427(1088255693......) = 37253476624085787593410949116909 * c7395(2921219150......) # P-1 B1=1e8 n=15352: c7178(2912059298......) = 1757324406290874041814576343116300807569 * c7139(1657098307......) # P-1 B1=1e8 n=15452: c7715(4176249840......) = 1126613563272465257067147493643221 * c7682(3706905346......) # P-1 B1=1e8 n=15524: c7760(9900990099......) = 314332212901582730925189258815801 * c7728(3149849010......) # P-1 B1=1e8 n=16388: c7637(7254376276......) = 1239052552006641587808012658390968721 * c7601(5854776913......) # P-1 B1=1e8 n=16576: c6892(1357209155......) = 483653178803446515441471666245761 * c6859(2806161966......) # P-1 B1=1e8 n=16682: c7885(1099999999......) = 140317884197941008513757925312934823 * c7849(7839342834......) # P-1 B1=1e8 n=17854: c8709(1258466533......) = 10644741565602130380564188903557 * c8678(1182242448......) # P-1 B1=1e8 n=17950: c7101(1494552112......) = 6547524750392708564395830928001 * c7070(2282621555......) # P-1 B1=1e8 n=18370: c6623(1069230309......) = 28437868215125373269850499008161 * c6591(3759882074......) # P-1 B1=1e8 n=19118: c8544(1690897832......) = 3120623069126251566095923748891 * c8513(5418462258......) # P-1 B1=1e8 n=19270: c7333(2504227825......) = 290694874772740871608588982542835202641 * c7294(8614626684......) # P-1 B1=1e8 n=19280: c7676(2593293768......) = 246916406995489455549633165127046148961 * c7638(1050271952......) # P-1 B1=1e8 n=19884: c6612(6836839190......) = 750773332364679943571213455473980401 * c6576(9106395893......) # P-1 B1=1e8 -- Nov 22, 2024 (-) -- # via factordb.com n=5842 p2714(2606283565......) is proven n=9930 p2558(1317124600......) is proven -- Nov 21, 2024 ([CSF] Christian Carquillat) -- # via yoyo@home n=565: c399(5468945355......) = 28530703974361421653060495976660829753238063969572240893311 * p341(1916863096......) # ECM B1=850000000, sigma=0:15932297432089603866 # 1284 of 300000 Phi_n(10) factorizations were finished. -- Nov 18, 2024 (Torbjorn Granlund) -- # via Kurt Beschorner n=2388: c695(1106311477......) = 30839997133023404987314306863618048001 * c657(3587261933......) # P-1 B1=1e9 n=2442: c663(2561186003......) = 49456490287679221045707935346512906387197 * c622(5178665103......) # P-1 B1=1e9 n=2738: c1316(6819591153......) = 961583576338166687686823020221823 * c1283(7092042045......) # P-1 B1=1e9 n=2770: c1100(1890957693......) = 1269913878336593802382585415846565761 * c1064(1489044041......) # P-1 B1=1e9 n=2896: c1345(2173894884......) = 46186243200327796436048713490806993 * c1310(4706801710......) # P-1 B1=1e9 n=3164: c1329(4250882811......) = 34453877927677573724583746662925863572929 * c1289(1233789363......) # P-1 B1=1e9 n=4032: c1101(8311176875......) = 1149577083859947625594601713224390529 * c1065(7229769097......) # P-1 B1=1e9 n=4154: c1954(1324323887......) = 24885676845841029876280206797458941379223 * c1913(5321630976......) # P-1 B1=1e9 n=4336: c2145(9223772266......) = 120503097025934614225984117089275131153 * c2107(7654386064......) # P-1 B1=1e8 n=4746: c1256(2384347040......) = 566256935791593456102477071486505601 * c1220(4210715824......) # P-1 B1=1e9 n=4748: c2342(3467824539......) = 11008452797970068679277520033958689 * c2308(3150147076......) # P-1 B1=1e8 n=5242: c2587(1831543024......) = 643083186967699780266670713918928931 * c2551(2848065477......) # P-1 B1=1e8 n=5278: c1997(1143300339......) = 10557304966503810141196212383472343369213 * c1957(1082947156......) # P-1 B1=1e9 n=5476: c2640(4068154736......) = 39704605233301365544142402346649 * c2609(1024605259......) # P-1 B1=1e8 n=5612: c2613(1129157680......) = 5200572835917560280870095774827921 * c2579(2171217895......) # P-1 B1=1e8 n=5676: c1640(2266229893......) = 60010660555308299243971058378689609 * c1605(3776378851......) # P-1 B1=1e9 n=5746: c2482(4948135946......) = 28742894780382677995250968097648752463 * c2445(1721516216......) # P-1 B1=1e8 n=5842: c2753(1593114544......) = 611259099144640384957656663318759207463 * p2714(2606283565......) # P-1 B1=1e6 # ----------------8<----------------8<----------------8<---------------- # $ ./pfgw64 -tc -q"11*(10^2921+1)/42205691447586263349158483268522510530112813321529721550317/(10^23+1)/(10^127+1)" # PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] # # Primality testing 11*(10^2921+1)/42205691447586263349158483268522510530112813321529721550317/(10^23+1)/(10^127+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] # # Running N-1 test using base 5 # Running N+1 test using discriminant 11, base 2+sqrt(11) # # Calling N+1 BLS with factored part 0.17% and helper 0.13% (0.67% proof) # 11*(10^2921+1)/42205691447586263349158483268522510530112813321529721550317/(10^23+1)/(10^127+1) is Fermat and Lucas PRP! (0.2833s+0.0004s) # ----------------8<----------------8<----------------8<---------------- n=5888: c2810(4717691011......) = 5190431816856039227338578055761409 * c2776(9089207174......) # P-1 B1=1e8 n=5910: c1540(1416532900......) = 37578013293914885440756732730401 * c1508(3769579007......) # P-1 B1=1e9 n=5934: c1848(9100000000......) = 246889735346482803823124949695587412078539 * c1807(3685855949......) # P-1 B1=1e9 n=5970: c1554(2764690769......) = 111645105744695543769378129533591929201 * c1516(2476320615......) # P-1 B1=1e9 n=6006: c1384(8383420744......) = 1127405843603847671204058787760709019 * c1348(7436027400......) # P-1 B1=1e9 n=6048: c1675(6180206335......) = 27463289803537363527885340451375058863041 * c1635(2250351789......) # P-1 B1=1e9 n=6176: c3067(1005695252......) = 2593760010604408630401448600207562593 * c3030(3877364320......) # P-1 B1=1e8 n=6390: c1630(5004627231......) = 9896646236002933822798196874660931 * c1596(5056892115......) # P-1 B1=1e9 n=6456: c2128(5534702999......) = 197390459653772512675213065371018917260960721 * c2084(2803936425......) # P-1 B1=1e8 n=6486: c1982(9871528924......) = 4759976125582735881156140675266005188887 * c1943(2073861016......) # P-1 B1=1e9 n=7052: c3335(1407178520......) = 4608158402387156248919515491038699029 * c3298(3053667859......) # P-1 B1=1e8 n=7232: c3563(4834013690......) = 8114613370481922230652951941118288294977 * c3523(5957170687......) # P-1 B1=1e8 n=7308: c1993(4627616657......) = 4452278235642219158759369430433189 * c1960(1039381730......) # P-1 B1=1e9 n=7698: c2517(1409712421......) = 680967535797761329479818305375688058373 * c2478(2070160979......) # P-1 B1=1e8 n=8246: c3218(1409438178......) = 24749806404758076780332504664299816455649 * c3177(5694744254......) # P-1 B1=1e8 n=8302: c3544(1021574246......) = 24847902339257338205683745064387481 * c3509(4111309812......) # P-1 B1=1e8 n=8370: c2156(2389429162......) = 727277354166367703302208465230580401 * c2120(3285444197......) # P-1 B1=1e7 n=8498: c3615(3899590303......) = 658795774320753696940038361251296983 * c3579(5919270365......) # P-1 B1=1e8 n=8610: c1921(1098890000......) = 5004844858427955006137433437029141894459256983171 * c1872(2195652475......) # P-1 B1=1e9 n=8828: c4383(6969639402......) = 908048334163502127235157462720849 * c4350(7675405747......) # P-1 B1=1e8 n=8886: c2910(3272514660......) = 4610799943809342524332325125122139 * c2876(7097498698......) # P-1 B1=1e8 n=9278: c4625(7846911005......) = 178967609457260723734945736769930758491 * c4587(4384542560......) # P-1 B1=1e8 n=9500M: c1740(1675522818......) = 1389276995921038490276012693684170501 * c1704(1206039416......) # P-1 B1=1e9 n=9602: c4796(3155798622......) = 15207616059867348952985702076478757 * c4762(2075143539......) # P-1 B1=1e7 n=9656: c4466(3037225147......) = 315444077393162364745161425645089 * c4433(9628410756......) # P-1 B1=1e8 n=9666: c3182(2753776060......) = 12855978003019647537974939713465431265165477 * c3139(2142019891......) # P-1 B1=1e7 n=9930: c2601(8122869272......) = 61671228916866667209759217595104005501763171 * p2558(1317124600......) # P-1 B1=1e8 # ----------------8<----------------8<----------------8<---------------- # $ ./pfgw64 -tc -q"91*(10^331+1)*(10^3310-10^1655+1)/690898947570333872987985756751184674247861873575495003493834629864278481996018870175506708531/(10^993+1)" # PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] # # Primality testing 91*(10^331+1)*(10^3310-10^1655+1)/690898947570333872987985756751184674247861873575495003493834629864278481996018870175506708531/(10^993+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] # Running N-1 test using base 7 # Running N-1 test using base 11 # Running N-1 test using base 19 # Running N-1 test using base 31 # Running N+1 test using discriminant 41, base 12+sqrt(41) # # Calling N-1 BLS with factored part 0.35% and helper 0.15% (1.21% proof) # 91*(10^331+1)*(10^3310-10^1655+1)/690898947570333872987985756751184674247861873575495003493834629864278481996018870175506708531/(10^993+1) is Fermat and Lucas PRP! (0.4537s+0.0004s) # ----------------8<----------------8<----------------8<---------------- n=9942: c3288(5075592784......) = 43467985151114679005547700224343 * c3257(1167662307......) # P-1 B1=1e8 n=10488: c3168(9999000100......) = 287374954797570518269388577100751017 * c3133(3479426419......) # P-1 B1=1e8 n=10658: c5235(1153969529......) = 20691076470793661181542957533 * c5206(5577136264......) # P-1 B1=1e8 n=10814: c5394(3095444933......) = 4024882991335789017910299401112406279032157 * c5351(7690769991......) # P-1 B1=1e8 n=11214: c3152(2712004211......) = 1627099537708421295488917956882995216738329 * c3110(1666772160......) # P-1 B1=1e8 n=11630: c4636(1053115308......) = 174128888010298790779720344400493016890949851 * c4591(6047906927......) # P-1 B1=1e8 n=11682: c3464(3270528100......) = 42819917640216465507294153124177263691957 * c3423(7637866395......) # P-1 B1=1e8 n=11702: c5835(7796329309......) = 35659510626055479151905581947019 * c5804(2186325379......) # P-1 B1=1e8 n=11798: c5537(1099999999......) = 771444069344282691412094893770299087 * c5501(1425897279......) # P-1 B1=1e8 n=11810: c4714(3462470069......) = 3374803948069233657246676428211 * c4684(1025976656......) # P-1 B1=1e8 n=12690: c3279(2594332866......) = 137575581863383286618080444161841 * c3247(1885750967......) # P-1 B1=1e7 n=13464: c3840(9999999999......) = 3269715600000850288606774756873 * c3810(3058369969......) # P-1 B1=1e7 n=13740L: c1790(3433044691......) = 1548452449774981487124114738255451081759501 * c1748(2217081119......) # P-1 B1=1e9 n=14234: c6438(1638816068......) = 2151794470154731199911566897889901567 * c6401(7616043686......) # P-1 B1=1e8 n=14402: c6800(2545883768......) = 3395246939013047559825870109666696331 * c6763(7498375860......) # P-1 B1=1e7 n=14712: c4875(2816095694......) = 189406563350567423601791210549970073 * c4840(1486799424......) # P-1 B1=1e8 n=14744: c6891(4283911168......) = 14277904858100191941756199650929 * c6860(3000378004......) # P-1 B1=1e6 n=14892: c4587(6054987374......) = 2079392210786906583659785328450330461 * c4551(2911902498......) # P-1 B1=1e8 n=15238: c7192(3460592087......) = 5731595372087037824234893121 * c7164(6037746670......) # P-1 B1=1e7 n=15318: c4736(4108920011......) = 1229012880303385954419155875783 * c4706(3343268469......) # P-1 B1=1e7 n=15370: c5790(4639839461......) = 1667014347124004912178088065636721 * c5757(2783323052......) # P-1 B1=1e7 n=15392: c6913(1000000000......) = 239415107968342305240235441409 * c6883(4176845849......) # P-1 B1=1e7 n=15562: c7416(2241010661......) = 4826088623169168098832958142188637 * c7382(4643534002......) # P-1 B1=1e6 n=15804: c5227(2769060033......) = 1898300805512526704694359881 * c5200(1458704556......) # P-1 B1=1e7 n=15862: c6120(9090910000......) = 36530183445954827944549810076117 * c6089(2488602339......) # P-1 B1=1e7 n=15888: c5267(2453679101......) = 45502340134172462287114845715057 * c5235(5392423982......) # P-1 B1=1e8 n=15924: c5250(5179682471......) = 560073201418766239105754045955002716009 * c5211(9248224086......) # P-1 B1=1e8 n=16028: c7989(3351611928......) = 53469438971172405641464482200929 * c7957(6268275847......) # P-1 B1=1e6 n=16038: c4819(4055544679......) = 1376526137506499047899570858595400419 * c4783(2946216979......) # P-1 B1=1e8 n=16488: c5440(2786951107......) = 14410637565324152730789889 * c5415(1933954063......) # P-1 B1=1e7 n=16560: c4176(4961448978......) = 159287226231413970347326561 * c4150(3114781452......) # P-1 B1=1e7 n=16722: c5530(4614839527......) = 4394595902339685132940987171 * c5503(1050116923......) # P-1 B1=1e7 n=16822: c7707(3141551307......) = 9740166824765577309862169 * c7682(3225356776......) # P-1 B1=1e7 n=16828: c7191(1698282898......) = 10477431663972441052746002292649 * c7160(1620896182......) # P-1 B1=1e7 n=17010: c3861(1157656789......) = 50621935015761465614958084132091 * c3829(2286867915......) # P-1 B1=1e7 n=17022: c5632(1921477233......) = 37644083708680825738427567701369 * c5600(5104327278......) # P-1 B1=1e8 n=17050: c6000(9999900000......) = 8078109936717326780557734001 * c5973(1237900954......) # P-1 B1=1e7 n=17098: c8336(2339640781......) = 16463155407829534621460504529887 * c8305(1421137518......) # P-1 B1=1e6 n=17208: c5713(1000000000......) = 6533031042598722528390472477334385527580001 * c5670(1530683068......) # P-1 B1=1e8 n=17248: c6709(5304824921......) = 525228098136988412500970239410509473 * c6674(1010004022......) # P-1 B1=1e6 n=17302: c8378(2875862011......) = 2273909772621090032319456103 * c8351(1264721250......) # P-1 B1=1e7 n=17328: c5446(1737081935......) = 6931065797831945307392334049 * c5418(2506226294......) # P-1 B1=1e7 n=17526: c5485(1074261060......) = 779639506416144466327250239406401 * c5452(1377894593......) # P-1 B1=1e8 n=17588: c8779(1833561548......) = 14855343049146052775095167601 * c8751(1234277486......) # P-1 B1=1e7 n=17628: c5371(1369908502......) = 1687037625132951509072929 * c5346(8120201243......) # P-1 B1=1e7 n=17712: c5731(2608821758......) = 5203915699038722059111489 * c5706(5013189892......) # P-1 B1=1e7 n=17768: c8847(2152004804......) = 5226487155193245474030477521 * c8819(4117497547......) # P-1 B1=1e7 n=17842: c8077(7980772656......) = 29501729355362438190395567 * c8052(2705188079......) # P-1 B1=1e7 n=18040: c6378(7468138990......) = 1819661811025550271298810671855079441 * c6342(4104135694......) # P-1 B1=1e8 n=18090: c4695(6295051634......) = 96375212967008103876091 * c4672(6531816056......) # P-1 B1=1e6 n=18224: c8403(4576800897......) = 24349529357003116699932975521 * c8375(1879626020......) # P-1 B1=1e6 n=18448: c9199(1244080063......) = 1301304643418538210621368512129 * c9168(9560252241......) # P-1 B1=1e7 n=18456: c6106(1194656209......) = 9886770903035092853593001371393030769919121 * c6063(1208338112......) # P-1 B1=1e8 n=18530: c6883(1828906916......) = 6313775540419270536811811 * c6858(2896692961......) # P-1 B1=1e6 n=18744: c5591(1185788582......) = 21436091543942058367910400073 * c5562(5531738749......) # P-1 B1=1e6 n=18950: c7500(1158658229......) = 530844533904549991939648601 * c7473(2182669605......) # P-1 B1=1e7 n=19082: c7728(9090910000......) = 2360879607556819530149067517810283641 * c7692(3850645314......) # P-1 B1=1e6 n=19086: c6361(1098901098......) = 417348818736070836256064980080164983 * c6325(2633051897......) # P-1 B1=1e8 n=19322: c9644(6255799800......) = 61083757027408257997360971533 * c9616(1024134746......) # P-1 B1=1e7 n=19332: c6394(5982974922......) = 1728427915141191848623821949 * c6367(3461512551......) # P-1 B1=1e7 n=19336: c9664(9999000099......) = 1085564316404443310310485998777 * c9634(9210877650......) # P-1 B1=1e7 n=19440: c5176(5768146324......) = 91764153360544926880194996535201 * c5144(6285838329......) # P-1 B1=1e7 n=19476: c6438(4258830566......) = 476746985409136101272620112643001 * c6405(8933104343......) # P-1 B1=1e8 n=19600: c6700(1641803578......) = 936733721876058671317016174401 * c6670(1752689734......) # P-1 B1=1e7 n=19642: c7870(8913146140......) = 37677953735792038920592727 * c7845(2365613112......) # P-1 B1=1e7 # 1283 of 300000 Phi_n(10) factorizations were finished. # 213393 of 300000 Phi_n(10) factorizations were cracked. # 130 of 25997 R_prime factorizations were finished. # 20081 of 25997 R_prime factorizations were cracked. # ----------------8<----------------8<----------------8<---------------- # Largest known factors that appear after the previous one # 1 n=604: 188981422179250214477885038956646476812007525220846625175628245017547495717341304519447280552146559165713534073382085460954497219653965265520569 (NFS@Home / Mar 16, 2017) # 2 n=730: 209567419815575088893039502374017044565180465719504614143239653652312239618655809712098924957353042723741728874079596356118568603287093812371 (NFS@Home / Jul 26, 2024) # 3 n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009) # 4 n=816: 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881 (Yousuke Koide / Apr 5, 2020) # 5 n=1420L: 247950328172294050136754481538951409190364075674960071233394038784474817867352415168199452660754962688866321901 (NFS@Home / Mar 17, 2024) # 6 n=1420M: 150068993718936038588227244574366404285884513639444374982663085901463237698274075317154251769989823397761 (NFS@Home / Mar 13, 2024) # 7 n=1540M: 647799461893729229242068652342456021003805852058736425973158141325454469108253161834095467738437014341 (NFS@Home / Sep 18, 2013) # 8 n=1740M: 38500497070688096027556817882565728990416892548263819672284096593431517949011701136219584563960572421 (Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner / Jun 27, 2021) # 9 n=2340L: 54416219768345058780693800256182138078138198676424989328564702046179663087831396313663972761 (Bo Chen, Wenjie Fang, Maksym Voznyy and Kurt Beschorner / Feb 15, 2016) # 10 n=2700M: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201 (Bo Chen, Maksym Voznyy, Wenjie Fang, Alfred Eichhorn and Kurt Beschorner / May 7, 2017) # 11 n=2940M: 1044845694645532615440579579338650347038975456315052342814839763722781 (George Bradshaw / Feb 19, 2023) # 12 n=5900M: 593243597135622945022444401922545308692618865123732027101 (pi / Sep 17, 2018) # 13 n=13980M: 21166873440679239162423181074773929272724025103001 (Kurt Beschorner / Jul 14, 2011) # 14 n=14316: 57346926970351862773268747899315323798217129 (Kurt Beschorner / Aug 5, 2024) # 15 n=18456: 9886770903035092853593001371393030769919121 (Torbjorn Granlund / Nov 18, 2024) # 16 n=103748: 1941549624124837091592820526305327246593529 (Makoto Kamada / Jun 18, 2018) # 17 n=112666: 356334694333381082120764457775238849699 (Makoto Kamada / Oct 17, 2018) # 18 n=120833: 79670409416595961896605938971188364397 (Maksym Voznyy / Nov 27, 2015) # 19 n=135070: 9855589830288396166509564150666175361 (Makoto Kamada / Dec 6, 2017) # 20 n=253620L: 1221015147166230558535777472152845661 (Alfred Reich / Oct 23, 2023) # 21 n=268140L: 60348364918187687874129722715181 (Alfred Reich / Oct 23, 2023) # 22 n=283706: 526153303629299051259344033783 (Alfred Reich / Oct 23, 2023) # 23 n=295980M: 98690902056965040529354491601 (Alfred Reich / Oct 23, 2023) # 24 n=298740L: 66173162995033300571567659861 (Alfred Reich / Oct 23, 2023) # 25 n=299420L: 33569847171752615806052144021 (Alfred Reich / Oct 23, 2023) # 26 n=299996: 38693214591429090355181 (Alfred Reich / Oct 23, 2023) # 27 n=299999: 246755644878443 (Makoto Kamada / Oct 23, 2021) # 28 n=300000: 47847600001 (Makoto Kamada / Feb 15, 2019) # ----------------8<----------------8<----------------8<---------------- -- Nov 16, 2024 (Torbjorn Granlund) -- # via Kurt Beschorner n=2604: c686(2638579025......) = 24448546850113917037786674257956049252521 * c646(1079237568......) # ECM B1=1e6 n=2916: c892(2511437049......) = 4195814654151937120330327975639201 * c858(5985576715......) # ECM B1=1e6 n=2970: c689(7432459902......) = 690282702009816065768196407742211 * c657(1076726952......) # ECM B1=1e6 n=3162: c948(3221988899......) = 134910124895643680784194263388480883007609 * c907(2388248399......) # ECM B1=1e6 n=3570: c745(1594362456......) = 25865722661111109914481075964342795441 * c707(6163997340......) # ECM B1=1e6 n=2192: c1065(3834784083......) = 22697864788706004146519819933242976609 * c1028(1689491112......) # ECM B1=1e6 n=2342: c1093(3562802167......) = 49299730037908119786764739353618327 * c1058(7226818817......) # ECM B1=1e6 n=3110: c1208(7485617892......) = 28035951049347859956384327321687704851 * c1171(2670006763......) # ECM B1=1e6 n=3496: c1520(5235745689......) = 2432060640329428482194730414131113 * c1487(2152802279......) # ECM B1=2.5e5 n=3706: c1729(1099999999......) = 88735662850196739797693338555620259 * c1694(1239636877......) # ECM B1=5e5 n=4114: c1701(3732753848......) = 52609226627306010745333111068274343 * c1666(7095245620......) # ECM B1=5e5 n=4268: c1911(2704555255......) = 280154685995581059221433954462109 * c1878(9653792673......) # ECM B1=1e6 n=4458: c1370(3834532536......) = 318843739793503408108159272791503 * c1338(1202636921......) # ECM B1=1e6 n=4488: c1280(9999000100......) = 354638747142779622617897664545205355417 * c1242(2819488896......) # ECM B1=1e6 n=4620M: c402(1879597399......) = 391165830331081935356094833268262692283321 * c360(4805116535......) # ECM B1=3e6 n=4712: c2155(1583917872......) = 148171581742857600717643876024801 * c2123(1068975476......) # ECM B1=1e6 n=4756: c2148(9765147514......) = 95352041920513968713795611265741 * c2117(1024115196......) # ECM B1=1e6 n=5028: c1571(2436519602......) = 93687467337623351797267989687273857859361 * c1530(2600688940......) # ECM B1=2.5e5 n=5104: c2227(2890777745......) = 6375049854966150323090311653281 * c2196(4534517864......) # ECM B1=1e6 n=5562: c1829(4534462394......) = 1675166469754979318318966655391573062632681050411 * c1781(2706872705......) # ECM B1=5e5 n=5584: c2746(2787793515......) = 3490922673200692730234939992961 * c2715(7985835769......) # ECM B1=1e6 n=5718: c1883(8741238093......) = 1546465965707343370500722733355870823023 * c1844(5652396035......) # ECM B1=5e5 n=5726: c2441(3980649734......) = 270439634555423977654733043208901161 * c2406(1471918027......) # ECM B1=5e5 n=5792: c2799(8460365523......) = 2481725917682043318986617115873 * c2769(3409065224......) # ECM B1=5e5 n=5852: c2139(4144278843......) = 44850747452221536403435503888089 * c2107(9240155580......) # ECM B1=1e6 n=6278: c2989(7315421701......) = 6740793551471253406606942970921183 * c2956(1085246365......) # ECM B1=2.5e5 n=6438: c1996(3292149774......) = 1286086381532881761631010370196549201 * c1960(2559820103......) # ECM B1=2.5e5 n=6536: c2966(3246614303......) = 1775209233038246078828291007421337 * c2933(1828862898......) # ECM B1=1e6 n=6670: c2430(2075524650......) = 4963082191798150637820060861662561 * c2396(4181926814......) # ECM B1=1e6 n=7090: c2823(3463958498......) = 568771060529228349938490987697721 * c2790(6090250961......) # ECM B1=5e5 n=7312: c3619(4033721086......) = 10119007661569323615826076623009 * c3588(3986281285......) # ECM B1=5e5 n=7342: c3655(8899876998......) = 3059346759646825975141748361824956517 * c3619(2909077557......) # ECM B1=1e5 n=7422: c2449(1238530148......) = 14776241343822319590361898631133 * c2417(8381902538......) # ECM B1=1e5 n=7874: c3768(7677190544......) = 6607467708901962419025297081737761249601 * c3729(1161896036......) # ECM B1=5e5 n=7918: c3805(1170577562......) = 29466805352305404977974596605386651 * c3770(3972529592......) # ECM B1=5e5 n=8176: c3427(2519730109......) = 2931483180150892088295038024449 * c3396(8595410428......) # ECM B1=2.5e5 n=8226: c2720(3065620513......) = 198195508972868055641231971076246099449 * c2682(1546765882......) # ECM B1=5e5 n=8272: c3649(1327911929......) = 26860356253353129182987114159855489 * c3614(4943761418......) # ECM B1=5e5 n=8296: c3831(3632388514......) = 13952265865824379919786738885136937 * c3797(2603439863......) # ECM B1=1e6 n=8410: c3241(5630021662......) = 1666185659584144442885553966342654061809451 * c3199(3378988187......) # ECM B1=1e6 n=8504: c4202(2254805194......) = 26644578023188204357380507022124180965433 * c4161(8462529195......) # ECM B1=5e5 n=8656: c4303(4713943187......) = 865588623131698184950812116593 * c4273(5445939400......) # ECM B1=5e5 n=8734: c3955(8396241536......) = 4623381423183970412975545037921 * c3925(1816039121......) # ECM B1=1e5 n=8736: c2295(4651504100......) = 52866958603164277225413781258884193 * c2260(8798508981......) # ECM B1=1e6 n=8764: c3740(1152428657......) = 4515114965644660959626141751170021 * c3706(2552379433......) # ECM B1=5e5 n=8866: c3593(2946458508......) = 2177860289102579516374524848693 * c3563(1352914382......) # ECM B1=5e5 n=8910: c2134(2553016584......) = 296612839453782466705709405330136451 * c2098(8607235578......) # ECM B1=5e5 n=9016: c3680(9540690439......) = 42256126489094363510123459600153 * c3649(2257824186......) # ECM B1=5e5 n=9028: c4293(3852684134......) = 1464758504041686136002192290225809 * c4260(2630252102......) # ECM B1=5e5 n=9042: c2692(4525563738......) = 86778193639335707300180875246597 * c2660(5215093272......) # ECM B1=1e6 n=9290: c3697(7338323582......) = 100408285641455848359633351464742841 * c3662(7308484091......) # ECM B1=5e5 n=9384: c2784(6778743997......) = 22817517429241759831682085255337 * c2753(2970850802......) # ECM B1=1e5 n=9416: c4225(4477399260......) = 335040615412148390577192870137 * c4196(1336375070......) # ECM B1=5e5 n=9476: c4476(3915506690......) = 111032467520745186412085016022501001 * c4441(3526452017......) # ECM B1=2.5e5 n=9642: c3196(1979592565......) = 31574122623080342748374740637533447 * c3161(6269667694......) # ECM B1=1e6 n=9678: c3218(1356586460......) = 1965882483203529879660380424472459 * c3184(6900648804......) # ECM B1=5e5 n=9758: c3840(9090910000......) = 21444211120295385972789535602419 * c3809(4239330581......) # ECM B1=5e5 n=9772: c4110(1274181094......) = 74915436117173227002352013241469 * c4078(1700825838......) # ECM B1=5e5 n=9938: c4951(1207654896......) = 12885729436820377182691483828182623 * c4916(9372033631......) # ECM B1=1e6 n=10024: c4225(2795216143......) = 73824261337791943727420399969977 * c4193(3786311021......) # ECM B1=5e5 n=10136: c4291(5237321719......) = 1250563890967936376520370627523257 * c4258(4187968129......) # ECM B1=2.5e5 n=10138: c4875(2687803279......) = 25608258703071667568105205956809147133 * c4838(1049584554......) # ECM B1=1e5 n=10320: c2589(9190728533......) = 29768847245696641373030027581441 * c2558(3087364605......) # ECM B1=1e6 n=10402: c4410(2406427290......) = 36206121470408003902670552797 * c4381(6646465273......) # ECM B1=5e5 n=10406: c4573(1472726921......) = 36681078089170920840417698299 * c4544(4014949937......) # ECM n=10440: c2681(2169054314......) = 199596062698660731812098984778161 * c2649(1086721995......) # ECM B1=1e6 n=10472: c3811(1070288366......) = 282670477292048196738936635804873 * c3778(3786346479......) # ECM B1=1e6 n=10480: c4161(1000000009......) = 2802810330363381786539817366881 * x4130(3567847596......) # ECM B1=2.5e5 n=10480: x4130(3567847596......) = 6629779694691625657435026103453921 * c4096(5381547744......) # ECM B1=2.5e5 n=10506: c3255(4859035739......) = 67820437322889292482243257383 * c3226(7164559727......) # ECM B1=2.5e5 n=10536: c3472(1923752315......) = 444414420704301489917273627599489 * c3439(4328735131......) # ECM B1=1e5 n=10578: c3360(9100000000......) = 13996471563941380413696864629042527 * c3326(6501638615......) # ECM B1=5e5 n=10650: c2775(1808553896......) = 3053503133839300328295837015091801 * c2741(5922882071......) # ECM B1=5e5 n=10718: c5036(2640426437......) = 119670649951726278420161541533253173 * c5001(2206411044......) # ECM B1=1e6 n=10798: c5353(8104926186......) = 669674476616131953456956036303 * c5324(1210278496......) # ECM B1=5e5 n=10818: c3580(7533042523......) = 1434404523925979355327831397 * c3553(5251686255......) # ECM B1=5e5 n=10842: c3297(9144457929......) = 13729128856658695075888233397 * c3269(6660625029......) # ECM B1=5e5 n=10936: c5460(9142360885......) = 27711473863192880106060060189378553 * c5426(3299124734......) # ECM B1=2.5e5 n=11016: c3450(7091952123......) = 1109026080822830514639500391019201 * c3417(6394756846......) # ECM B1=2.5e5 n=11024: c4950(6991898060......) = 332579999513366769784850650577 * c4921(2102320666......) # ECM B1=1e6 n=11040: c2740(1130928778......) = 9006198100013090328398440321 * x2712(1255722743......) # ECM B1=5e5 n=11040: x2712(1255722743......) = 20847280586087471498290675201 * c2683(6023436670......) # ECM B1=2.5e5 n=11202: c3711(1033425189......) = 21907187823972771337194302757607 * c3679(4717288215......) # ECM B1=1e6 n=11390: c4224(9091000000......) = 17153230689231584649837649841 * c4196(5299876253......) # ECM B1=2.5e5 n=11488: c5675(1282881620......) = 133128234562132983277422982690212289 * c5639(9636435309......) # ECM B1=5e5 n=11496: c3805(4614534360......) = 214667979267639381575151369409 * c3776(2149614663......) # ECM B1=1e6 n=11528: c5158(7019210540......) = 42080380078316924098145628073 * c5130(1668048275......) # ECM B1=2.5e5 n=11542: c5524(5657157727......) = 43839848215897989300615748597 * p5496(1290414533......) # ECM B1=2.5e5 # ----------------8<----------------8<----------------8<---------------- # $ ./pfgw64 -tc -q"11*(10^5771+1)/8524392522983226175490943651896140989001183787573/(10^29+1)/(10^199+1)" # PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] # # Primality testing 11*(10^5771+1)/8524392522983226175490943651896140989001183787573/(10^29+1)/(10^199+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] # # Running N-1 test using base 5 # Running N+1 test using discriminant 13, base 1+sqrt(13) # # Calling N+1 BLS with factored part 0.10% and helper 0.07% (0.37% proof) # 11*(10^5771+1)/8524392522983226175490943651896140989001183787573/(10^29+1)/(10^199+1) is Fermat and Lucas PRP! (1.0720s+0.0004s) # ----------------8<----------------8<----------------8<---------------- n=11544: c3447(1352409595......) = 154543556543181065980759137858553 * c3414(8750993092......) # ECM B1=1e6 n=11564: c4859(1527363038......) = 5984418359912710034809254001 * c4831(2552233060......) # ECM n=11632: c5768(3902849271......) = 851720552623604512729686194287009 * c5735(4582311956......) # ECM B1=2.5e5 n=11662: c4705(1000000000......) = 42418529436229745362507033787453 * c4673(2357460320......) # ECM B1=5e5 n=11690: c3959(5074611296......) = 7904462718373304246181590624081 * c3928(6419931977......) # ECM B1=1e5 n=11730: c2783(1031816816......) = 390981032853677597062360545691 * c2753(2639045707......) # ECM B1=2.5e5 n=11738: c5830(3752683862......) = 2019331313420157569012277087539 * c5800(1858379473......) # ECM B1=5e5 n=11774: c4864(1513631716......) = 314845215303602953133267485366601 * c4831(4807542382......) # ECM B1=2.5e5 n=11776: c5620(5453850386......) = 130565509284503661354753782273 * c5591(4177098849......) # ECM B1=5e5 n=11786: c5713(2093849338......) = 31787967714422217319600477 * c5687(6586924202......) # ECM B1=1e5 n=11914: c4727(1984301655......) = 706203981344402422660622425993237 * c4694(2809813747......) # ECM B1=2.5e5 n=11928: c3349(1130587560......) = 972115965253491672413654066689 * c3319(1163017171......) # ECM B1=5e5 n=12018: c3996(6018029101......) = 24048873394995562522191060997 * c3968(2502416226......) # ECM n=12034: c5433(6337374004......) = 67642725084977763442937627551481 * c5401(9368892214......) # ECM B1=1e6 n=12080: c4801(1000000009......) = 225705841967550450973642605281 * c4771(4430545533......) # ECM B1=5e5 n=12124: c5154(4721689455......) = 1248642798157518166292531877996601 * c5121(3781457325......) # ECM B1=2.5e5 n=12194: c4705(4148235063......) = 2878875581137649191245362032091 * c4675(1440921966......) # ECM B1=5e5 n=12234: c4042(9829243833......) = 692282787828675733331172926430967 * c4010(1419830740......) # ECM B1=1e6 n=12610: c4541(2622632523......) = 538234799606924316896497112291 * c4511(4872655067......) # ECM B1=5e5 n=12636: c3889(1000000000......) = 269056522286959441805146114129 * c3859(3716691167......) # ECM B1=2.5e5 n=12722: c6345(2903162639......) = 18433098563529181172365303197691 * c6314(1574972666......) # ECM B1=5e5 n=12748: c6342(8043363198......) = 3311832982798520008911409821589 * c6312(2428674163......) # ECM B1=5e4 n=12768: c3402(4567197678......) = 4551383393875377064140138685249 * c3372(1003474610......) # ECM B1=1e6 n=12782: c4870(3416955788......) = 326347601544518914374612227376209 * c4838(1047029539......) # ECM B1=1e6 n=12788: c6052(3452424748......) = 1435709494292762635483332775841 * c6022(2404681979......) # ECM B1=1e6 n=12842: c6384(3398220690......) = 9006669323727909767286426197 * c6356(3773004835......) # ECM B1=2.5e5 n=12880: c4204(1261601332......) = 27952092506826619737096937601 * x4175(4513441461......) # ECM B1=2.5e5 n=12880: x4175(4513441461......) = 84537643288109619097286339932481 * c4143(5338972421......) # ECM n=12894: c3648(1408173318......) = 234727238099089060112103037 * c3621(5999190081......) # ECM B1=2.5e5 n=12896: c5737(1269428750......) = 5005818621047576360540553669909682337 * c5700(2535906405......) # ECM B1=1e6 n=12930: c3435(1082762826......) = 51620027637650204736344569947157441 * c3400(2097563437......) # ECM B1=2.5e5 n=12958: c5359(2409896809......) = 30493145644837246434700876349969 * c5327(7903077096......) # ECM B1=5e5 n=12996: c4039(1489763100......) = 101344338278189772667549201 * c4013(1470001310......) # ECM B1=5e5 n=13024: c5752(1169929858......) = 241019581721193052208099329 * c5725(4854086337......) # ECM B1=5e4 n=13160: c4407(1443333369......) = 10399560941239009589202858696551281 * c4373(1387879140......) # ECM B1=2.5e5 n=13266: c3870(4182837571......) = 8400723629806519924849958093995693 * c3836(4979139602......) # ECM B1=1e5 n=13310: c4796(7179713961......) = 13404997029935255925004241479921 * c4765(5355998173......) # ECM B1=1e5 n=13320: c3452(3753612852......) = 66361568276849539952469235681 * c3423(5656305222......) # ECM B1=2.5e5 n=13392: c4297(9925752956......) = 26232818720187931375631356397835217 * c4263(3783715757......) # ECM B1=1e6 n=13426: c5713(1000000099......) = 20541281909723984638470049269049 * c5681(4868245830......) # ECM B1=5e5 n=13454: c5572(8902543649......) = 3032523894813796341541882541929 * c5542(2935687882......) # ECM B1=5e5 n=13492: c6744(9900990099......) = 853895375502126821508240245161 * c6715(1159508574......) # ECM B1=5e5 n=13496: c5735(2106182900......) = 770094742824181876075570185521 * c5705(2734965950......) # ECM B1=1e5 n=13786: c6691(1065662623......) = 105165018454783366906467915089 * c6662(1013324239......) # ECM B1=2.5e5 n=13842: c4568(1417268558......) = 124627418621257081726371384412601527 * c4533(1137204456......) # ECM B1=1e6 n=13938: c4327(4591069139......) = 4427113289495605428225554948023 * c4297(1037034482......) # ECM B1=5e5 n=14056: c5996(7114604823......) = 431255299688076877105081009251235201 * c5961(1649743163......) # ECM B1=1e6 n=14064: c4653(2812269791......) = 21245882682636993989106780433 * c4625(1323677549......) # ECM B1=2.5e5 n=14124: c4213(1033810331......) = 1297277772932505851539328095119169 * c4179(7969074571......) # ECM B1=5e5 n=14152: c6656(1117560758......) = 3361952297019359757554116873 * c6628(3324142225......) # ECM B1=5e5 n=14170: c5146(5903957481......) = 2511591657546754721042285332841 * c5116(2350683664......) # ECM B1=2.5e5 n=14176: c7026(6621163623......) = 1516059613366139561595263956481 * c6996(4367350442......) # ECM B1=2.5e5 n=14198: c6817(3872281026......) = 1913059137030898792636503157 * c6790(2024130332......) # ECM B1=1e5 n=14224: c6023(2942721216......) = 828717425209303089487305401645761 * c5990(3550934404......) # ECM B1=5e5 n=14240: c5627(8778012833......) = 404002712055519493954443521 * c5601(2172760868......) # ECM B1=2.5e5 n=14366: c6487(2025073448......) = 11740030300229508820141845617779 * c6456(1724930342......) # ECM B1=1e6 n=14370: c3780(1106913753......) = 1377663399126809063549171681131 * c3749(8034718450......) # ECM B1=5e5 n=14376: c4785(1000099999......) = 3004772510257772818187427201217921 * c4751(3328371770......) # ECM B1=1e6 n=14394: c4733(3204033486......) = 229267027003298432379891714329533 * c4701(1397511682......) # ECM B1=1e6 n=14400: c3830(1772956697......) = 34452548147600267070268801 * c3804(5146082924......) # ECM B1=2.5e5 n=14436: c4775(9854868195......) = 1566885269716288671740953637269 * c4745(6289463807......) # ECM B1=2.5e5 n=14446: c6929(2517966553......) = 1464507953996332757755951247 * x6902(1719325966......) # ECM B1=5e5 n=14446: x6902(1719325966......) = 3865571383335063860376937301783 * c6871(4447792566......) # ECM B1=2.5e5 n=14452: c7192(1023028190......) = 26838459182879846059864897808501 * c7160(3811799268......) # ECM B1=1e5 n=14456: c6593(8917804242......) = 1767619128995256227118639017 * c6566(5045093762......) # ECM B1=5e5 n=14554: c6877(1099999999......) = 135336386823049038099304642480757 * c6844(8127895430......) # ECM B1=2.5e5 n=14670: c3888(9990010000......) = 104640352044654413219714960446531 * c3856(9546995785......) # ECM B1=2.5e5 n=14720: c5614(3546291926......) = 251180046864709520196696779361281 * c5582(1411852561......) # ECM B1=5e5 n=14758: c7163(4133302747......) = 211563917185306057204172594413 * c7134(1953689836......) # ECM B1=2.5e5 n=14778: c4905(4256966502......) = 704793176185448510948224583492504811841 * c4866(6040022301......) # ECM B1=2.5e5 n=14804: c7400(9900990099......) = 136668773910075171760938072041341 * c7368(7244515199......) # ECM B1=5e5 n=14814: c4885(9767577844......) = 4200414975085449674046138444703 * c4855(2325384016......) # ECM B1=2.5e5 n=14840: c4955(5403841383......) = 92489237599328406977461441 * c4929(5842670481......) # ECM B1=1e5 n=14988: c4932(1579636517......) = 4554051187384079436518092294261 * c4901(3468640232......) # ECM B1=2.5e5 n=15036: c4217(1968300711......) = 1718261553014792273409364122984361 * c4184(1145518682......) # ECM B1=5e5 n=15044: c7460(3234821963......) = 1589311786347105358080229081 * c7433(2035360205......) # ECM B1=5e5 n=15048: c4245(2576385233......) = 20976332822310082894904905921 * c4217(1228234341......) # ECM B1=1e5 n=15110: c5990(1016688436......) = 646490920735696141052743321051 * c5960(1572626009......) # ECM B1=5e5 n=15114: c4463(3499750634......) = 12833935819657299441456979130269801 * c4429(2726950394......) # ECM B1=5e5 n=15274: c6489(1188727545......) = 21602917490324077152062234920007 * c6457(5502625031......) # ECM B1=5e5 n=15320: c6049(6251621589......) = 72694853200189837533769625180274001 * c6014(8599813211......) # ECM B1=2.5e5 n=15330: c3457(1098890000......) = 119074877094181756818017595481 * c3427(9228562959......) # ECM B1=2.5e5 n=15358: c6509(3841756918......) = 13310088572337389634342801863 * c6481(2886349627......) # ECM B1=2.5e5 n=15432: c5137(1000099999......) = 261878258438022137952239306929 * c5107(3818950095......) # ECM B1=5e5 n=15496: c7036(1311188124......) = 285426910637479686587379193 * x7009(4593778916......) # ECM B1=2.5e5 n=15496: x7009(4593778916......) = 13306099079477488146909217894897201 * c6975(3452385923......) # ECM B1=5e5 n=15550: c6176(1224623275......) = 61281151495471694491664186251 * c6147(1998368577......) # ECM B1=5e5 n=15618: c4885(8736446239......) = 702203650243936676542601302453 * c4856(1244147084......) # ECM B1=1e6 n=15632: c7785(1148458704......) = 4838223656632224191848904449 * c7757(2373719749......) # ECM B1=1e6 n=15690: c4169(8936717965......) = 551883358395935280956995365683161 * c4137(1619312818......) # ECM B1=5e5 n=15694: c6233(5168213917......) = 111896991941250243042183358940171 * c6201(4618724621......) # ECM B1=1e6 n=15714: c5137(3178897866......) = 1868407445370434596095957562879327 * c5104(1701394347......) # ECM B1=1e6 n=15718: c7537(8573450374......) = 58386544606416584478687517 * c7512(1468394889......) # ECM n=15744: c4979(1683999210......) = 16662312225239949817689139969 * c4951(1010663578......) # ECM B1=5e5 n=15784: c7835(3770686930......) = 97326341848135596112877411177 * c7806(3874271711......) # ECM B1=2.5e5 n=15790: c6313(1099989000......) = 478471676195244910731603502531 * c6283(2298963668......) # ECM B1=2.5e5 n=15830: c6324(2316205175......) = 181735940122423942397354442691 * c6295(1274489335......) # ECM B1=5e5 n=15858: c5235(1349899013......) = 799695139888605420639138928357 * x5205(1688017027......) # ECM B1=5e5 n=15858: x5205(1688017027......) = 10624365242220737879424805222438579 * c5171(1588816827......) # ECM B1=1e6 n=15906: c4780(3119185105......) = 1072877406722537242064474261166769 * c4747(2907308035......) # ECM B1=1e6 n=15968: c7938(1208098279......) = 198256482506676882829296139502113 * c7905(6093613002......) # ECM B1=5e5 n=15972: c4841(1000000000......) = 176604931709427632153361400321 * c4811(5662356030......) # ECM B1=1e6 n=15996: c4997(1106181294......) = 1919794695678255545841984829 * c4969(5761977030......) # ECM B1=1e0 n=16098: c5298(8488708252......) = 59051891945598167859824731 * c5273(1437499794......) # ECM B1=2.5e5 n=16226: c6467(2694104355......) = 437822287350745706486873039808753407 * c6431(6153419854......) # ECM B1=1e6 n=16258: c7366(3564780505......) = 24358569084536808645026202437 * c7338(1463460555......) # ECM B1=1e5 n=16274: c7925(8971747878......) = 23824821207333348486876449303 * c7897(3765714672......) # ECM B1=1e6 n=16296: c4603(8765439762......) = 86426983626665652269725227649 * c4575(1014201745......) # ECM B1=1e5 n=16304: c8118(1032136064......) = 201272912888734212524452579713678475313 * c8079(5128042565......) # ECM B1=2.5e5 n=16364: c8163(4565719440......) = 72494882841718026134545350512221 * c8131(6297988577......) # ECM B1=2.5e5 n=16452: c5473(1000000999......) = 37919027182322759686834353708601 * c5441(2637201094......) # ECM B1=1e6 n=16456: c7032(3309809841......) = 2689448060768801465894964457 * c7005(1230665090......) # ECM B1=1e5 n=16494: c5485(1225739932......) = 86975737610796985673904235051 * c5456(1409289493......) # ECM B1=2.5e5 n=16498: c8056(1808766435......) = 16711386254924846704216980361 * c8028(1082355711......) # ECM B1=1e5 n=16516: c8244(3491752910......) = 103077292025391318037126649 * c8218(3387509355......) # ECM B1=2.5e5 n=16518: c5470(1548360891......) = 68101842761457413108021611 * x5444(2273596174......) # ECM B1=1e5 n=16518: x5444(2273596174......) = 1482081102658796106776479827379 * c5414(1534056517......) # ECM B1=5e5 n=16524: c5159(8332276576......) = 57335082222680413300052573860618669 * c5125(1453259723......) # ECM B1=1e6 n=16558: c7724(9851790025......) = 15429532319091493805830664263 * c7696(6385021802......) # ECM B1=5e5 n=16566: c4929(7628092411......) = 86579194832347439851096124164663 * c4897(8810537481......) # ECM B1=1e6 n=16608: c5487(5428754213......) = 1073501220012024038088343393 * c5460(5057054535......) # ECM B1=5e5 n=16646: c6715(9102105589......) = 808249358593054391816451815797 * c6686(1126150672......) # ECM B1=2.5e5 n=16692: c5067(1715567693......) = 36268974756953313149238120229 * c5038(4730124590......) # ECM B1=5e5 n=16698: c4804(1623122137......) = 3627696187353241323286768891 * c4776(4474250470......) # ECM B1=2.5e5 n=16722: c5560(1470864918......) = 318725041257190396222497947863 * c5530(4614839527......) # ECM B1=5e5 n=16742: c7601(1099999999......) = 7213425056141600565452740130663 * c7570(1524934398......) # ECM B1=2.5e5 n=16758: c4531(2983640698......) = 20630943706468996500242146183 * c4503(1446196907......) # ECM B1=2.5e5 n=16808: c7601(1000099999......) = 9330732845794712417079998781337 * c7570(1071834352......) # ECM B1=2.5e5 n=16832: c8375(1410874285......) = 104118466588381985227072247301589121 * c8340(1355066331......) # ECM B1=2.5e5 n=16898: c6670(2702027273......) = 2421843816564599707908254677891 * p6640(1115690142......) # ECM B1=2.5e5 # ----------------8<----------------8<----------------8<---------------- # $ ./pfgw64 -tc -q"909091*(10^17+1)*(10^71+1)*(10^8449+1)/814823906115239146435608781127077031373697040944185947532896577230713013096247491/(10^119+1)/(10^497+1)/(10^1207+1)" # PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] # # Primality testing 909091*(10^17+1)*(10^71+1)*(10^8449+1)/814823906115239146435608781127077031373697040944185947532896577230713013096247491/(10^119+1)/(10^497+1)/(10^1207+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] # Running N-1 test using base 3 # Running N+1 test using discriminant 11, base 10+sqrt(11) # # Calling N-1 BLS with factored part 0.25% and helper 0.04% (0.79% proof) # 909091*(10^17+1)*(10^71+1)*(10^8449+1)/814823906115239146435608781127077031373697040944185947532896577230713013096247491/(10^119+1)/(10^497+1)/(10^1207+1) is Fermat and Lucas PRP! (1.6364s+0.0005s) # ----------------8<----------------8<----------------8<---------------- n=16914: c5637(1098901098......) = 1787085587992110191220245930983 * c5606(6149124061......) # ECM B1=5e5 n=16930: c6695(1882363859......) = 64964129440349720611230721 * c6669(2897543421......) # ECM n=16954: c7200(2128499390......) = 19317754362871679533741980121 * p7172(1101835829......) # ECM B1=2.5e5 # ----------------8<----------------8<----------------8<---------------- # $ ./pfgw64 -tc -q"(10^7+1)*(10^8477+1)/90757631330376326863295767995211184299160077091998013/(10^49+1)/(10^1211+1)" # PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] # # Primality testing (10^7+1)*(10^8477+1)/90757631330376326863295767995211184299160077091998013/(10^49+1)/(10^1211+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] # # Running N-1 test using base 2 # Running N+1 test using discriminant 5, base 5+sqrt(5) # # Calling N-1 BLS with factored part 0.08% and helper 0.03% (0.29% proof) # (10^7+1)*(10^8477+1)/90757631330376326863295767995211184299160077091998013/(10^49+1)/(10^1211+1) is Fermat and Lucas PRP! (1.8502s+0.0004s) # ----------------8<----------------8<----------------8<---------------- n=17040: c4460(1102759048......) = 392601064906199226580223783382721 * c4427(2808853941......) # ECM B1=5e5 n=17072: c7631(4174842976......) = 11070083461703539430116485836113 * c7600(3771284101......) # ECM B1=5e5 n=17122: c7311(5111904648......) = 679734091059746608092706279333535767 * c7275(7520447651......) # ECM B1=1e6 n=17266: c8434(1290852294......) = 18736042748728415076807450769 * c8405(6889674151......) # ECM B1=1e6 n=17312: c8627(2212783432......) = 127617578991569984606766136769 * c8598(1733917419......) # ECM B1=5e5 n=17320: c6893(8139446056......) = 38415068557774647821480472001 * c6865(2118815965......) # ECM B1=5e5 n=17338: c8632(2545868845......) = 11169444483984971330840130331 * c8604(2279315546......) # ECM B1=5e5 n=17342: c7367(7288394368......) = 44000949292536455286208051 * c7342(1656417528......) # ECM B1=1e5 n=17358: c5240(9100000000......) = 35578014550565996806639717 * c5215(2557759367......) # ECM B1=2.5e5 n=17366: c8133(3894941816......) = 115198670490331891663813237 * c8107(3381064902......) # ECM B1=1e6 n=17374: c6832(5064203729......) = 5605722320153116654998214459 * c6804(9033989626......) # ECM B1=2.5e5 n=17430: c3931(4203043783......) = 1366261029014564184194320768697761 * c3898(3076310963......) # ECM B1=5e5 n=17448: c5777(6607787662......) = 28286597769083247455970457 * c5752(2336013583......) # ECM B1=1e5 n=17452: c8695(4662907987......) = 159256185746954218183974851641241 * c8663(2927928962......) # ECM B1=1e6 n=17496: c5810(5437809792......) = 6870978376243388122154693917249 * c5779(7914171017......) # ECM B1=5e5 n=17534: c7961(1099999999......) = 64900862121584159555289263 * c7935(1694892739......) # ECM B1=2.5e5 n=17546: c8454(1402513278......) = 3646263333245800669367047324556108437 * c8417(3846439903......) # ECM B1=1e6 n=17548: c8467(5047607522......) = 8580782286087959767195156478209 * c8436(5882456114......) # ECM B1=2.5e5 n=17570: c5987(7621328092......) = 71266542079023826681277451041 * c5959(1069411798......) # ECM B1=2.5e5 n=17608: c8392(3218566677......) = 15569394173922408466932549113 * c8364(2067239509......) # ECM B1=2.5e5 n=17632: c8058(1407321477......) = 118632382421034512471137 * c8035(1186287798......) # ECM B1=5e4 n=17680: c6144(9999999900......) = 220703955874848692869733204641 * c6115(4530956348......) # ECM B1=5e5 n=17682: c5011(3854334087......) = 8590328505584670240853568771437 * c4980(4486829677......) # ECM B1=1e6 n=17692: c8828(2826112393......) = 16402439019146061322694101 * c8803(1722983021......) # ECM B1=2.5e5 n=17708: c8330(3968857371......) = 1319087518458946826469949 * c8306(3008790027......) # ECM B1=2.5e5 n=17712: c5756(5645571049......) = 21640309583248110802137121 * c5731(2608821758......) # ECM B1=1e5 n=17716: c8557(1125179990......) = 2784409934462866088585729561 * x8529(4040999769......) # ECM B1=5e5 n=17716: x8529(4040999769......) = 19344730976907279767604053281 * c8501(2088940794......) # ECM B1=2.5e5 n=17758: c8185(1099999999......) = 95284647325766442427651 * x8162(1154435715......) # ECM n=17758: x8162(1154435715......) = 1970078714426350513553647 * c8137(5859845634......) # ECM B1=1e5 n=17770: c7090(6363352453......) = 21764072680422736103368531 * c7065(2923787540......) # ECM B1=2.5e5 n=17792: c8783(1599900826......) = 4675931842161310583507968890881 * c8752(3421565754......) # ECM B1=1e6 n=17798: c8069(8764663160......) = 71894272242556060911493411247 * c8041(1219104510......) # ECM B1=5e5 n=17808: c4986(7292791658......) = 4627886814120273252034417 * c4962(1575836218......) # ECM B1=2.5e5 n=17810: c6507(3280465853......) = 57946038874313992007718364331 * x6478(5661242627......) # ECM B1=1e5 n=17810: x6478(5661242627......) = 32955251835755850457644813561251 * c6447(1717857492......) # ECM B1=5e5 n=17822: c7112(5229079846......) = 1049892931362591697783081 * c7088(4980583915......) # ECM B1=2.5e5 n=17826: c5941(1098901098......) = 146894199175295127536263813 * x5914(7480901935......) # ECM B1=5e5 n=17826: x5914(7480901935......) = 1411559946422946524755879813291 * c5884(5299740867......) # ECM B1=5e5 n=17844: c5902(2636595588......) = 2599259209671117723583110286921 * c5872(1014364238......) # ECM B1=1e6 n=17852: c8924(9900990099......) = 2213033880064722350076939971069 * c8894(4473944203......) # ECM B1=5e5 n=17862: c5404(1182284480......) = 61529649778472766631838527 * x5378(1921487421......) # ECM B1=5e5 n=17862: x5378(1921487421......) = 137322298748367731674668033729267529 * c5343(1399253754......) # ECM B1=2.5e5 n=17886: c5383(1722148749......) = 89896282650822418495991718738383197 * c5348(1915706299......) # ECM B1=2.5e5 n=17898: c5567(1402859550......) = 129678866052222581631967 * c5544(1081795047......) # ECM B1=1e5 n=17906: c7643(1727162874......) = 348961416349166613602595259 * c7616(4949437941......) # ECM B1=1e5 n=17910: c4739(7654177467......) = 1198814424640560542051371 * c4715(6384789263......) # ECM B1=2.5e5 n=17950: c7131(1658732994......) = 1109852898748975398424645263401 * c7101(1494552112......) # ECM B1=2.5e5 n=18018: c4293(6224366493......) = 561767227566460201690463069011 * c4264(1107997438......) # ECM B1=1e6 n=18078: c5679(4555760299......) = 9643632563529047358967233798001 * c5648(4724112277......) # ECM B1=2.5e5 n=18098: c9012(5701271822......) = 336944375164833446945685391889 * c8983(1692051342......) # ECM B1=5e5 n=18130: c6033(4675051602......) = 1673037346547595498440370588161 * c6003(2794349816......) # ECM B1=5e5 n=18136: c9034(3340595926......) = 6836442794539781036510288822561 * c9003(4886453418......) # ECM B1=1e5 n=18188: c9028(7973166846......) = 58698220113855288132253654789 * c9000(1358331961......) # ECM B1=5e5 n=18202: c8583(5213254592......) = 420235190982534739773397853 * c8557(1240556408......) # ECM B1=2.5e5 n=18224: c8436(9035613899......) = 1974220444064801429068929251940641 * c8403(4576800897......) # ECM B1=2.5e5 n=18244: c9110(1250367892......) = 70624642945024825618684845809 * c9081(1770441365......) # ECM B1=1e6 n=18246: c6071(7991051803......) = 664744518532140608367533851 * c6045(1202123760......) # ECM B1=5e5 n=18248: c9113(6327372183......) = 79491952270041047010879041 * c9087(7959764483......) # ECM B1=2.5e5 n=18262: c8699(1592371183......) = 73636894424276705006056499 * c8673(2162463796......) # ECM B1=2.5e5 n=18274: c9104(9184523960......) = 79260031146329006765733467845201 * c9073(1158783793......) # ECM B1=5e5 n=18276: c6065(9830348109......) = 245423580243775276257082768749109 * c6033(4005461944......) # ECM B1=2.5e5 n=18282: c5505(2260568042......) = 4957670380267197331208251 * c5480(4559738484......) # ECM B1=2.5e5 n=18284: c7816(4550210334......) = 970466858172329580815962656471221 * c7783(4688681840......) # ECM B1=5e5 n=18288: c6026(2465983118......) = 21187903633717358030385457 * c6001(1163863665......) # ECM B1=1e5 n=18292: c8547(6626765818......) = 2129127948810677054006815849 * c8520(3112431933......) # ECM n=18306: c6014(2154907128......) = 5722334055069204813504284107825704772037641 * c5971(3765783520......) # ECM B1=5e5 n=18310: c7283(1157829742......) = 91147034316458883390201731 * c7257(1270287893......) # ECM B1=1e6 n=18326: c6667(2334636008......) = 22986891679238342738229441557 * c6639(1015637973......) # ECM B1=2.5e5 n=18328: c8727(2617249977......) = 737601128404023660018762697 * c8700(3548326970......) # ECM B1=2.5e5 n=18330: c4411(4611546848......) = 17100550347922712270530321 * c4386(2696724230......) # ECM B1=2.5e5 n=18338: c8926(8325935307......) = 114367468002868344413010713237 * c8897(7279985692......) # ECM B1=1e6 n=18342: c6090(1572079646......) = 12088795286888908042392086167 * c6062(1300443600......) # ECM B1=2.5e5 n=18354: c4713(5789562829......) = 3219501798419182858462118659 * c4686(1798279110......) # ECM B1=5e5 n=18416: c9179(7969947514......) = 402212070455004903763567649 * c9153(1981528675......) # ECM B1=5e4 n=18422: c9001(1099999999......) = 113389814179412997698348293 * c8974(9701047734......) # ECM B1=2.5e5 n=18426: c5892(3325388310......) = 6356067262460248555527859642237 * c5861(5231833102......) # ECM B1=5e5 n=18440: c7346(7765283875......) = 4087216638704228718491757841 * c7319(1899895347......) # ECM B1=5e5 n=18510: c4928(9100090999......) = 33536004775219266377896224811 * c4900(2713528657......) # ECM B1=1e5 n=18512: c8449(1000000009......) = 9137374150100906303425110241 * c8421(1094406328......) # ECM B1=1e6 n=18528: c6114(4659880195......) = 1169044202530351992033313 * x6090(3986059881......) # ECM B1=1e5 n=18528: x6090(3986059881......) = 26856215310490234191404080417 * c6062(1484222492......) # ECM B1=1e5 n=18538: c7899(1708655362......) = 8704334980210684513811161501453 * c7868(1962993573......) # ECM B1=1e6 n=18542: c9073(1099999999......) = 272185903883276105584550788637 * c9043(4041355501......) # ECM B1=2.5e5 n=18548: c9245(3247186898......) = 27269257810662925488871481 * x9220(1190786680......) # ECM B1=2.5e5 n=18548: x9220(1190786680......) = 27623423032111861107813356341 * c9191(4310786100......) # ECM B1=2.5e5 n=18584: c8801(1000099999......) = 1516378750803331257697681 * c8776(6595317953......) # ECM n=18618: c5908(1534960996......) = 11512067897421281653697887 * c5883(1333349499......) # ECM B1=2.5e5 n=18634: c7181(6048406182......) = 2017497989727596908657280059213 * c7151(2997973833......) # ECM B1=2.5e5 n=18704: c7959(4763875654......) = 3794297644379391470290033 * x7935(1255535569......) # ECM B1=2.5e5 n=18704: x7935(1255535569......) = 208559444579947227867521 * c7911(6020036983......) # ECM B1=5e4 n=18716: c9325(4539458599......) = 5631445778382473644315352191835029 * c9291(8060911492......) # ECM B1=2.5e5 n=18760: c6336(9999000099......) = 265298704010638921240003121 * x6310(3768959270......) # ECM B1=1e5 n=18760: x6310(3768959270......) = 4931194017897773965475458561 * c6282(7643096696......) # ECM n=18762: c6022(2464667578......) = 26101211653801232901493 * c5999(9442732434......) # ECM B1=1e5 n=18770: c7483(2208452085......) = 13548340109398914903379623521 * c7455(1630053620......) # ECM B1=5e5 n=18782: c9353(1166859065......) = 739907396358719715520774404379 * c9323(1577033925......) # ECM B1=5e5 n=18836: c8800(1342239927......) = 5023097998097721732412889 * c8775(2672135657......) # ECM B1=2.5e5 n=18930: c5009(3674642967......) = 2952383010305612924902615921 * c4982(1244636266......) # ECM B1=2.5e5 n=18950: c7561(1000009999......) = 412072599910852552751064240852851 * x7528(2426781106......) # ECM B1=2.5e5 n=18950: x7528(2426781106......) = 20944753549248446423309641801 * c7500(1158658229......) # ECM B1=5e5 n=18958: c9454(4255315800......) = 11096112000374002481632511813 * c9426(3834961110......) # ECM B1=2.5e5 n=18996: c6292(4709119478......) = 792101202706203043786760269249 * c6262(5945098255......) # ECM B1=5e5 n=19000: c7174(3330734518......) = 7268905938936362591099030392001 * c7143(4582167586......) # ECM B1=1e6 n=19062: c6321(8515345800......) = 39878207066402943176831131 * c6296(2135338177......) # ECM B1=2.5e5 n=19068: c5419(2472598138......) = 113327027279205174877705369 * c5393(2181825640......) # ECM B1=5e5 n=19154: c9354(2234601008......) = 58262481085303324179207703 * c9328(3835403105......) # ECM B1=2.5e5 n=19160: c7529(6651270072......) = 365692840223281292418610961 * c7503(1818813315......) # ECM B1=2.5e5 n=19178: c9290(3964617864......) = 151402889440440486941741983 * c9264(2618587980......) # ECM B1=5e4 n=19182: c6054(1350509002......) = 42799482626798894925771469327 * c6025(3155433008......) # ECM n=19208: c8232(9999999999......) = 7399618793424734906373520790393689729 * c8196(1351420968......) # ECM B1=5e5 n=19222: c8170(2020492341......) = 342648688895364322077376024613 * c8140(5896687794......) # ECM B1=5e5 n=19290: c5111(5979806274......) = 2457739215194282820655692093931 * c5081(2433051577......) # ECM B1=2.5e5 n=19292: c7454(3404740995......) = 97015358758155216276716372009 * c7425(3509486579......) # ECM B1=5e5 n=19302: c6405(6197422759......) = 412297201109023264989400005997 * c6376(1503144513......) # ECM B1=5e4 n=19306: c8215(7781755309......) = 43656025981803124718332924519807 * c8184(1782515731......) # ECM B1=5e5 n=19310: c7702(1698080770......) = 9219696970796774258549891 * p7677(1841796726......) # ECM B1=1e5 # ----------------8<----------------8<----------------8<---------------- # $ ./pfgw64 -tc -q"(10^9655+1)/542948081886669914746500880036351407378149370371/(10^1931+1)" # PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] # # Primality testing (10^9655+1)/542948081886669914746500880036351407378149370371/(10^1931+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] # # Running N-1 test using base 2 # Running N+1 test using discriminant 7, base 2+sqrt(7) # # Calling N-1 BLS with factored part 0.11% and helper 0.09% (0.44% proof) # (10^9655+1)/542948081886669914746500880036351407378149370371/(10^1931+1) is Fermat and Lucas PRP! (1.9792s+0.0004s) # ----------------8<----------------8<----------------8<---------------- n=19314: c6044(1724109901......) = 271646749249028437547781289 * c6017(6346882139......) # ECM B1=2.5e5 n=19330: c7716(3197532993......) = 8668678235162318516907261691 * c7688(3688605006......) # ECM B1=2.5e5 n=19378: c9662(2300809403......) = 6877644199791394382938162688339 * c9631(3345345203......) # ECM B1=5e5 n=19384: c9688(9999000099......) = 3938019285748798482726649257318449 * c9655(2539093735......) # ECM B1=1e6 n=19392: c6381(4315253116......) = 260291657223921864829105784715649 * c6349(1657853026......) # ECM B1=5e5 n=19396: c8929(1009999999......) = 1676028712711900231893709489 * c8901(6026149745......) # ECM B1=2.5e5 n=19416: c6460(5150641190......) = 1463999310188709611599330075009 * c6430(3518199192......) # ECM B1=5e5 n=19428: c6456(2407782820......) = 14371162305701180042487673969 * c6428(1675426642......) # ECM B1=5e5 n=19432: c8287(9595309595......) = 1882986798530979318026412879728777 * c8254(5095792282......) # ECM B1=5e5 n=19446: c5515(1017328902......) = 1719597542449275224486215816010437 * c5481(5916087210......) # ECM B1=5e5 n=19492: c8808(1976653429......) = 478974309826268620316223904469 * c8778(4126846447......) # ECM B1=5e5 n=19494: c6109(1235014693......) = 50004694676289453980869664209 * c6080(2469797489......) # ECM B1=5e5 n=19518: c6482(6527472515......) = 235459138494755104848585847 * c6456(2772231546......) # ECM n=19544: c8284(1753253700......) = 85884311800644096574196243695969 * c8252(2041413226......) # ECM B1=1e6 n=19644: c6502(3554281157......) = 36954787534838503023144251341 * c6473(9617917987......) # ECM B1=5e5 n=19656: c5184(9999999999......) = 5160540506200863523681033 * c5160(1937781514......) # ECM B1=5e5 n=19712: c7664(1381227280......) = 2289529535987506275146923009 * c7636(6032799574......) # ECM B1=2.5e5 n=19720: c7134(1153435904......) = 1859583231963069265096481 * c7109(6202658125......) # ECM B1=1e5 n=19722: c6183(2290223653......) = 49448819845523984010326227757491 * c6151(4631503158......) # ECM B1=2.5e5 n=19734: c5251(5462469736......) = 125061565350184147751833835641 * c5222(4367824536......) # ECM B1=5e5 n=19746: c6540(2800415735......) = 3776420413083983795790931 * c6515(7415529600......) # ECM B1=1e5 n=19816: c9879(2680756786......) = 39428074988864044610430680478267913 * c9844(6799106441......) # ECM B1=1e6 n=19950: c4259(9598387681......) = 650736548221532423486343751413451 * c4227(1475003625......) # ECM B1=2.5e5 n=19970: c7958(2321664979......) = 28661588680355154688524810148931 * c7926(8100266197......) # ECM B1=5e5 n=19978: c8542(3860380492......) = 1114877885115904326741125717413 * c8512(3462603881......) # ECM B1=1e5 n=19940L: c3966(6752706662......) = 156271046319575398183239500556123497773481 * c3925(4321150220......) # ECM B1=5e5 # 1281 of 300000 Phi_n(10) factorizations were finished. # 213381 of 300000 Phi_n(10) factorizations were cracked. # 130 of 25997 R_prime factorizations were finished. # 20081 of 25997 R_prime factorizations were cracked. # ----------------8<----------------8<----------------8<---------------- # Largest known factors that appear after the previous one # 1 n=604: 188981422179250214477885038956646476812007525220846625175628245017547495717341304519447280552146559165713534073382085460954497219653965265520569 (NFS@Home / Mar 16, 2017) # 2 n=730: 209567419815575088893039502374017044565180465719504614143239653652312239618655809712098924957353042723741728874079596356118568603287093812371 (NFS@Home / Jul 26, 2024) # 3 n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009) # 4 n=816: 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881 (Yousuke Koide / Apr 5, 2020) # 5 n=1420L: 247950328172294050136754481538951409190364075674960071233394038784474817867352415168199452660754962688866321901 (NFS@Home / Mar 17, 2024) # 6 n=1420M: 150068993718936038588227244574366404285884513639444374982663085901463237698274075317154251769989823397761 (NFS@Home / Mar 13, 2024) # 7 n=1540M: 647799461893729229242068652342456021003805852058736425973158141325454469108253161834095467738437014341 (NFS@Home / Sep 18, 2013) # 8 n=1740M: 38500497070688096027556817882565728990416892548263819672284096593431517949011701136219584563960572421 (Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner / Jun 27, 2021) # 9 n=2340L: 54416219768345058780693800256182138078138198676424989328564702046179663087831396313663972761 (Bo Chen, Wenjie Fang, Maksym Voznyy and Kurt Beschorner / Feb 15, 2016) # 10 n=2700M: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201 (Bo Chen, Maksym Voznyy, Wenjie Fang, Alfred Eichhorn and Kurt Beschorner / May 7, 2017) # 11 n=2940M: 1044845694645532615440579579338650347038975456315052342814839763722781 (George Bradshaw / Feb 19, 2023) # 12 n=5900M: 593243597135622945022444401922545308692618865123732027101 (pi / Sep 17, 2018) # 13 n=13980M: 21166873440679239162423181074773929272724025103001 (Kurt Beschorner / Jul 14, 2011) # 14 n=14316: 57346926970351862773268747899315323798217129 (Kurt Beschorner / Aug 5, 2024) # 15 n=18306: 5722334055069204813504284107825704772037641 (Torbjorn Granlund / Nov 16, 2024) # 16 n=103748: 1941549624124837091592820526305327246593529 (Makoto Kamada / Jun 18, 2018) # 17 n=112666: 356334694333381082120764457775238849699 (Makoto Kamada / Oct 17, 2018) # 18 n=120833: 79670409416595961896605938971188364397 (Maksym Voznyy / Nov 27, 2015) # 19 n=135070: 9855589830288396166509564150666175361 (Makoto Kamada / Dec 6, 2017) # 20 n=253620L: 1221015147166230558535777472152845661 (Alfred Reich / Oct 23, 2023) # 21 n=268140L: 60348364918187687874129722715181 (Alfred Reich / Oct 23, 2023) # 22 n=283706: 526153303629299051259344033783 (Alfred Reich / Oct 23, 2023) # 23 n=295980M: 98690902056965040529354491601 (Alfred Reich / Oct 23, 2023) # 24 n=298740L: 66173162995033300571567659861 (Alfred Reich / Oct 23, 2023) # 25 n=299420L: 33569847171752615806052144021 (Alfred Reich / Oct 23, 2023) # 26 n=299996: 38693214591429090355181 (Alfred Reich / Oct 23, 2023) # 27 n=299999: 246755644878443 (Makoto Kamada / Oct 23, 2021) # 28 n=300000: 47847600001 (Makoto Kamada / Feb 15, 2019) # ----------------8<----------------8<----------------8<---------------- -- Nov 17, 2024 (-) -- # via factordb.com n=2453 p2163(1754612408......) is proven n=2921 p2738(6643381158......) is proven n=12611 p12581(7329415337......) is proven n=13917 p9225(6418845379......) is proven n=17003 p14500(4642216475......) is proven n=45340M p9034(8192636567......) is proven -- Nov 15, 2024 (Torbjorn Granlund) -- # via Kurt Beschorner n=1683: c924(3854343395......) = 7094269136760977218014836948723305450933 * c884(5433038021......) n=1731: c1112(3283823477......) = 21481225216685350678161515038389787 * c1078(1528694683......) n=2187: c1379(5547864394......) = 21308633677099951037311635962017389361 * c1342(2603575845......) n=2289: c1271(8760993305......) = 19306123439772405301786737066921362521 * c1234(4537934988......) n=2349: c1474(8598619043......) = 1450728419450614246387071597126321883351 * c1435(5927104569......) n=2439: c1620(9990000009......) = 1750951613605088127239925104483031647431 * c1581(5705468918......) n=2711: c2711(1111111111......) = 2429177830781265239696373889891451437603 * c2671(4574021288......) n=2947: c2497(5519534286......) = 1111254447528443572188121925013179399474723363 * c2452(4966940108......) n=3375: c1740(2020648766......) = 5636920616578062840761562879001 * c1709(3584667771......) n=3395: c2229(3208078196......) = 1047259165586024962957754415606196751 * c2193(3063308779......) n=3763: c3602(1767854317......) = 261631815901886754901630209830896414999 * c3563(6757031100......) n=3783: c2260(2412975616......) = 2050156379068493102584809457787886092923 * c2221(1176971493......) n=3865: c3025(5329513960......) = 12715708181685060600558310150912985641 * c2988(4191283634......) n=4001: c4001(1111111111......) = 785668012864498594153755090667981081 * c3965(1414224701......) n=4123: c3203(6977443626......) = 3615006019244589866307965298512979191 * c3167(1930133335......) n=5291: c4277(6053192674......) = 46572831190351972867499154106274351597 * c4240(1299726153......) n=5295: c2805(6120890581......) = 8569153920827778069491014006637714616026551 * c2762(7142934574......) n=5509: c4686(4574602943......) = 245655366636481904294387728335220853 * c4651(1862203543......) n=5551: c4321(1111110999......) = 2994317007589622287680380348501561156477 * c4281(3710732688......) n=5597: c5367(8576297302......) = 3841078687097124869407100790777529 * c5334(2232783548......) n=5717: c5717(1111111111......) = 12747258772040276660632435799376009307 * c5679(8716470976......) n=5729: c5320(8048663073......) = 18860988209785924086716853780111143627 * c5283(4267360216......) n=5761: c4932(9000000900......) = 43990530197708684383325546514137021161 * c4895(2045895073......) n=5885: c4183(1258520670......) = 844450056620074126938596588698793372581001 * c4141(1490343521......) n=5997: c3996(9009009009......) = 42003117580999868437768661876437 * c3965(2144842937......) n=6011: c5964(1788300214......) = 5925206112374253156818936638869529 * c5930(3018123219......) n=6223: c5264(6213076471......) = 1545303686192035046953668811992769 * c5231(4020618424......) n=6415: c5128(9000090000......) = 9175104058281655753339473156391 * c5097(9809251147......) n=6519: c4147(2228113243......) = 8318214534161460105630870205573 * c4116(2678595550......) n=6527: c6350(1874325034......) = 768232679725546485130495224797 * c6320(2439788210......) n=6529: c6517(3103248990......) = 3155681180270721374056974637173625027 * c6480(9833848266......) n=6535: c5217(9893773812......) = 323945983881118599812279882508165647507231 * c5176(3054143068......) n=6539: c6024(9000000000......) = 33805533821179999361542638159881 * c5993(2662286017......) n=6601: c5250(2101785888......) = 3403226914877674366263719982773 * c5219(6175861736......) n=6795: c3601(1001000999......) = 71318086372916239886625581556376591 * c3566(1403572432......) n=6803: c6795(6481215373......) = 2167561857840026739852602279591 * c6765(2990094769......) n=6823: c6800(1441376914......) = 4032610279007793201227302922034311773 * c6763(3574302535......) n=6969: c4360(5903162464......) = 17284863696672036215929959110331284917 * c4323(3415220720......) n=6975: c3569(1745143837......) = 283685716992988738279636629628152151 * c3533(6151680301......) n=7003: c6651(3195719953......) = 1034885622798742700218772650666152755600801 * c6609(3087993381......) n=7083: c4694(1143420173......) = 765085263684007765631988055037138839 * c4658(1494500322......) n=7093: c6797(7634981519......) = 16386969842132484127375116377292439 * c6763(4659178355......) n=7227: c4303(8549326793......) = 927315974687849547564996700237243 * c4270(9219432239......) n=7471: c7140(3475260461......) = 5623173146639554770850636699184323 * c7106(6180248004......) n=7473: c4769(3182949236......) = 7754432367783782127690087312836359 * c4735(4104683728......) n=7701: c4759(1395995176......) = 5823687850949224270769389820151199 * c4725(2397098216......) n=7819: c6692(2877514115......) = 90296000163190254168920720349030323 * c6657(3186757010......) n=7901: c7879(2825146455......) = 14107041510778662073368754306929281 * c7845(2002649849......) n=7929: c5280(9990000009......) = 9774230640445511234063175519001 * c5250(1022075330......) n=7961: c7494(2789003841......) = 13629218040032503695263790183056171911 * c7457(2046341788......) n=8195: c5893(2528390311......) = 273524796752500296358251688669379591 * c5857(9243733442......) n=8253: c4660(1063307988......) = 47829062731517382751976640941655830569 * c4622(2223142013......) n=8261: c7472(2509971762......) = 3164534367938109650289010885319835740161 * c7432(7931567400......) n=8301: c5521(5511569730......) = 450385768288539083956297050438758857243 * c5483(1223744202......) n=8335: c6646(1852375856......) = 1448902497362749961768537685911711 * c6613(1278468261......) n=8411: c7743(8832835384......) = 34556671521668258064024578047376557 * c7709(2556043448......) n=8475: c4400(8651698344......) = 824732370149634210114393712167055801 * c4365(1049031013......) n=8523: c5676(9990000009......) = 133352804218021396519406310387613 * c5644(7491406025......) n=8617: c7352(4719731832......) = 773008187701896989389487349175434820573 * c7313(6105668617......) n=8751: c5824(2806049310......) = 250757533321745462773227135763987 * c5792(1119028917......) n=8995: c6079(4929226720......) = 2642890492661890777326121144043315351 * c6043(1865089277......) n=9179: c8963(7319446284......) = 41407118535863836328231199438831683 * c8929(1767678250......) n=9373: c7336(4481468151......) = 16965568701949010634245850663569 * c7305(2641507767......) n=9663: c6389(4571504838......) = 332615451808491919488183612731787973 * c6354(1374411445......) n=9935: c7862(1742273156......) = 40972083250831015509382919165858664610349401 * c7818(4252342128......) n=9991: c9770(1280461404......) = 128170195863151014481182999902603 * c9737(9990321041......) -- Oct 23, 2024 (Bo Chen) -- n=11933: c11893(4867831159......) = 414925980131129258619162561359861129 * c11858(1173180613......) # ECM B1=1000000, sigma=0:2535354785099330417 -- Nov 12, 2024 (Richard G.) -- n=6620L: p1239(8766924399......) is proven -- Nov 12, 2024 (Kurt Beschorner) -- n=2588: c1263(2993786427......) = 358707685867464791644043614080398407699364549 * c1218(8346033679......) # ECM B1=11e6, sigma=3:520840551 n=6620L: c1280(1065922849......) = 12158458323280420106135772848381096322161 * p1239(8766924399......) # ECM B1=11e6, sigma=3:2600717268 n=6620M: c1312(1235469654......) = 642287726920966940956750396648795252481 * c1273(1923545480......) # ECM B1=11e6, sigma=3:1012836728 n=10020M: c1316(5091300117......) = 777584027810159345125925179689199834434421 * c1274(6547588345......) # ECM B1=11e6, sigma=3:2384873688 n=10534: c4954(1365183994......) = 226205881193915161320009774462839717 * c4918(6035139258......) # ECM B1=1e6, sigma=0:3438171638309662 n=10552: c5268(2368926082......) = 177396567174208802425121364413353 * c5236(1335384398......) # ECM B1=1e6, sigma=0:3957437626118494 n=20106: c6667(3973370413......) = 18683064958877822776369923274751573259529 * c6627(2126723009......) # P-1 B1=56e6 n=100530: c26784(9990010000......) = 8880823511451062371 * c26766(1124896805......) # P-1 B1=56e6 n=100531: c99854(8046578604......) = 13602355372259569 * c99838(5915577401......) # P-1 B1=26e6 -- Nov 12, 2024 (-) -- # via factordb.com n=177147: c118076(1731996431......) = 17975564821722439 * c118059(9635282385......) -- Nov 6, 2024 (Kurt Beschorner) -- n=8942: c4151(7159668544......) = 1464836520301341417091423101371315459 * c4115(4887691182......) # P-1 B1=1e9 n=10424: c5152(3731625899......) = 57942252239189441677496005862320636721 * c5114(6440249999......) # ECM B1=1e6, sigma=0:59832573212747 n=14094: c4490(2930506857......) = 12480093421238519381361994578001 * c4459(2348144968......) # P-1 B1=500e6 n=14107: c14100(5321828816......) = 1956842749478358759504522649 * c14073(2719599629......) # P-1 B1=150e6 n=14108: c7006(1847438350......) = 216582055761926451208752488813449 * c6973(8529969597......) # P-1 B1=200e6 n=33505: c26795(4476966239......) = 1045822484578566791 * c26777(4280808937......) # P-1 B1=26e6 n=100513: c84625(1111110999......) = 4406172854153813 * c84609(2521714505......) # P-1 B1=26e6 n=100515: c53562(8697039474......) = 940445147333643232441 * c53541(9247790261......) # P-1 B1=26e6 n=100525: c80393(8289728235......) = 5732011026124335751 * c80375(1446216379......) # P-1 B1=26e6 n=170537: c170526(4833501601......) = 2652533123498678267 * c170508(1822221015......) n=170579: c170564(1772735094......) = 2383885374440306441 * c170545(7436326903......) n=171167: c171161(1081896655......) = 2082228604826256881 * c171142(5195859154......) n=171341: c171329(5449415990......) = 13001283521808877717 * c171310(4191444623......) n=171449: c171438(1824575353......) = 9777801130672250089 * c171419(1866038518......) n=171539: c171516(2037600020......) = 1443611262079414159 * c171498(1411460324......) # gr-mfaktc -- Nov 1, 2024 (Alfred Eichhorn) -- # via Kurt Beschorner n=15991: c15991(1111111111......) = 172162941266993330396729039 * c15964(6453834390......) # ECM B1=1e6, sigma=4867608413414300 n=16069: c16069(1111111111......) = 133668399424837027337344405603231 * c16036(8312444196......) # ECM B1=1e6, sigma=4413080158643041 n=25031: c25031(1111111111......) = 609471758670332641184098358947 * x25001(1823072349......) # ECM B1=1e6, sigma=5196294818478462 n=25031: x25001(1823072349......) = 51200151616835849440828708535231 * c24969(3560677638......) # ECM B1=1e6, sigma=1742695876983339 # 213327 of 300000 Phi_n(10) factorizations were cracked. # 20078 of 25997 R_prime factorizations were cracked. -- Nov 1, 2024 (Kurt Beschorner) -- n=8332: c4130(5901343496......) = 680445408889792780179826779807875306556149 * c4088(8672765544......) # P-1 B1=1e9 n=10448: c5184(5729023481......) = 20669254225975294991344335110737 * c5153(2771761099......) # ECM B1=1e6, sigma=0:606849483862269 n=10456: c5195(6209495142......) = 34803087160489599423500860348073 * c5164(1784179407......) # ECM B1=1e6, sigma=0:927816581658530