# via Kurt Beschorner
n=2258: c1114(4641147783......) = 52874014350801951051108908233818746760979 * c1073(8777748088......)
# ECM
n=8542: c4235(2207612955......) = 17931120838017673840027504869107406677 * c4198(1231162834......)
# ECM
n=9194: c4580(2042132469......) = 1667300272156337810113084656668394139 * c4544(1224813852......)
# ECM
n=10786: c5348(7793454050......) = 729914506072054827065390364470411767 * c5313(1067721491......)
# ECM
n=12226: c6020(1689809652......) = 2580548816983922435815679475699119371 * c5983(6548256872......)
# ECM
n=12434: c6212(1462242700......) = 10644871877697887832917616752925689 * c6178(1373659276......)
# ECM
n=1916: c899(1571178986......) = 10226546821709282341572622484214465901185349 * c856(1536372945......)
n=1398: c421(3733501901......) = 97829644721777630795842442531391034522052011 * c377(3816329816......)
# ECM B1=3e6, sigma=2651071350
n=1706: c844(1951636045......) = 273616243605203095321334459213437522758336721927 * c796(7132749209......)
# ECM B1=20e6, sigma=3:637627561
n=5584: c2715(7985835769......) = 33032585669354748100507532307619217 * c2681(2417563023......)
# ECM B1=1e6, sigma=0:8727546104645156
n=6217: c6195(1426666053......) = 91732344502157195313784261059592121 * c6160(1555248654......)
# ECM B1=1e6, sigma=5453357092045402
n=10036: c4589(1661018374......) = 35412413276700529015461294244357049 * c4554(4690497542......)
# ECM B1=1e6, sigma=8297072652981896
# via factordb.com
n=3238: c1551(1650720259......) = 88376853595525515029074288804105939891 * c1513(1867819674......)
n=3986: c1967(1110095215......) = 25555944415936379078066369218667934588173 * c1926(4343784748......)
# via Kurt Beschorner
n=1695: c846(3271171232......) = 3589492355981051731952052034695940490303247751 * c800(9113186234......)
# ECM B1/2=3e6/1e10, sigma=1:4277327597
n=2222: c938(2208722365......) = 2918644992157154213086063524625094205307903 * c895(7567629400......)
# ECM B1/2=3e6/1e10, sigma=1:2987761698
n=2262: c650(1400032384......) = 16087663360588803253849167238238929939 * c612(8702521635......)
# ECM B1/2=3e6/1e10, sigma=1:697874091
n=2590: c830(1138660404......) = 1587566981848255160768964580712527697515091 * c787(7172361336......)
# ECM B1/2=3e6/1e10, sigma=1:3594502645
n=3015: c1467(2535819604......) = 145561727061614082264058665770390854831 * c1429(1742092276......)
# ECM B1/2=2e6/1e10, sigma=0:9283897034382382548
n=3495: c1813(4749434783......) = 387453933028530938632676729870153370630391 * c1772(1225806316......)
# ECM B1/2=2e6/1e10, sigma=0:16005981700032064947
n=7740L: c943(6431629651......) = 36821525146880395030522367502885042322081 * c903(1746703762......)
# ECM B1/2=3e6/1e10, sigma=1:525306835
n=23220M: c2998(4457166297......) = 1753801360355145706859984612168517841 * p2962(2541431656......)
# ECM B1/2=2e6/1e10, sigma=0:5078811757710992863
$ ./pfgw64 -tc -q"((10^1161+1)*((10^2322+10^1161)*(10^1161+10^581+3)+10^581+2)-1)/393479005148507464343902335924102063323422304111075933686636668525699060382185781561669007081931020440654581463144851912827525752166401/((10^387+1)*((10^774+10^387)*(10^387+10^194+3)+10^194+2)-1)" PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] Primality testing ((10^1161+1)*((10^2322+10^1161)*(10^1161+10^581+3)+10^581+2)-1)/393479005148507464343902335924102063323422304111075933686636668525699060382185781561669007081931020440654581463144851912827525752166401/((10^387+1)*((10^774+10^387)*(10^387+10^194+3)+10^194+2)-1) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 13, base 8+sqrt(13) Calling N-1 BLS with factored part 0.25% and helper 0.15% (0.94% proof) ((10^1161+1)*((10^2322+10^1161)*(10^1161+10^581+3)+10^581+2)-1)/393479005148507464343902335924102063323422304111075933686636668525699060382185781561669007081931020440654581463144851912827525752166401/((10^387+1)*((10^774+10^387)*(10^387+10^194+3)+10^194+2)-1) is Fermat and Lucas PRP! (0.3297s+0.0111s)
n=1278: c398(4911851953......) = 158720442461371770292217981455847347981577942503 * c351(3094656162......)
# ECM B1=11e6, sigma=3746762614
n=1554: c389(1855820022......) = 116462699941346570110788260883522270500646769 * c345(1593488750......)
# ECM B1=11e6, sigma=1916824559
n=1734: c424(5771480751......) = 81377921661876815257762625738857311135506265389843731 * p371(7092194828......)
# ECM B1=11e6, sigma=1492419122
n=1784: c846(8012243918......) = 1506299242872513223456886300848222812688553 * c804(5319158166......)
# ECM B1=3e6, sigma=3:1325250992
n=8262: c2579(2544996603......) = 47834304614166196220391418206434330161 * c2541(5320442357......)
# ECM B1=1e6, sigma=0:582667912455680
n=9945: c4570(1671629783......) = 3771493051636833160947409738692384129946962271 * c4524(4432275919......)
# ECM B1=1e6, sigma=8483609740963473
n=2737: c2070(1971804258......) = 323561112669360093053960758986830954689 * x2031(6094070581......)
# ECM B1=6e6, sigma=3:1034679873
n=2737: x2031(6094070581......) = 2329335556062616465955090470284053489 * c1995(2616227003......)
# ECM B1=6e6, sigma=3:1034680092
n=4132: c2007(1167676473......) = 216429619541732561630783629448941813493521 * p1965(5395178698......)
# ECM B1=6e6, sigma=3:1097376947
$ ./pfgw64 -tc -q"(10^2066+1)/185350672497337263431611976959882442624285591134547859225033369288906071409290314478880595324026435149" PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] Primality testing (10^2066+1)/185350672497337263431611976959882442624285591134547859225033369288906071409290314478880595324026435149 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.32% and helper 0.26% (1.26% proof) (10^2066+1)/185350672497337263431611976959882442624285591134547859225033369288906071409290314478880595324026435149 is Fermat and Lucas PRP! (0.1542s+0.0026s)
n=5528: c2731(1872759341......) = 451186401343223171107045654150718718457 * c2692(4150744205......)
# ECM B1=1e6, sigma=2263027098662890
n=100658: c50309(8716307578......) = 1475471431340247807924769 * c50285(5907472956......)
# P-1 B1=60e6
# via Kurt Beschorner
n=1941: c1235(8322544868......) = 18324102196986246938793220693979072780479 * c1195(4541856828......)
# ECM B1/2=2e6/1e10, sigma=0:7468102543256745624
n=2299: c1980(9999999999......) = 19105127944897718190086548183045306170227 * c1940(5234196823......)
# ECM B1/2=2e6/1e10, sigma=0:3279931155824969364
n=2501: c2356(4228525981......) = 532671658113886260212473422727898747 * c2320(7938334839......)
# ECM B1/2=2e6/1e10, sigma=0:147276043833136226
n=2515: c1981(9952745050......) = 263595080192736026475317249565311401 * c1946(3775770413......)
# ECM B1/2=2e6/1e10, sigma=0:6883472396746942790
n=2529: c1627(7955633255......) = 127219007062638077428906168365635325319 * c1589(6253494221......)
# ECM B1/2=2e6/1e10, sigma=0:11412115806074526478
n=2609: c2563(2737807394......) = 277754527334147030597898460232281117 * c2527(9856931662......)
# ECM B1/2=2e6/1e10, sigma=0:13117153927448746996
n=2634: c877(1098901098......) = 64120497550578280872882092218394447992627303 * c833(1713806256......)
# ECM B1/2=2e6/1e10, sigma=1:3414020500
n=2754: c838(2901274861......) = 1070573021045188175955629702678917835979037 * c796(2710020526......)
# ECM B1/2=2e6/1e10, sigma=1:3789776932
n=2905: c1969(1111099888......) = 77232347813946503213768066560793045431 * c1931(1438645749......)
# ECM B1/2=2e6/1e10, sigma=0:1144948186446810884
n=2906: c1444(1055208486......) = 1282595439643508256615285638105070370531 * c1404(8227134248......)
# ECM B1/2=2e6/1e10, sigma=0:15512752377311098215
n=2941: c2703(8910147452......) = 4730412442713592348500757280176674959 * c2667(1883587860......)
# ECM B1/2=2e6/1e10, sigma=0:13714635867003721288
n=3038: c1239(3194783992......) = 13738284126212945085230983501010742373 * c1202(2325460707......)
# ECM B1/2=2e6/1e10, sigma=0:544105926907405447
n=3106: c1546(5180326921......) = 27153601113610968310227740816836137241 * c1509(1907786337......)
# ECM B1/2=2e6/1e10, sigma=0:7205582932242741153
n=3134: c1553(2052721482......) = 220904983261414113425123770729713126253 * c1514(9292327645......)
# ECM B1/2=2e6/1e10, sigma=0:5254817483696869123
n=3143: c2647(1290238099......) = 6363169036007123426660812216597533517 * c2610(2027665919......)
# ECM B1/2=2e6/1e10, sigma=0:11924672347211046095
n=3240: c831(7375921026......) = 51568786797481312749777492089812443769921 * c791(1430307262......)
# ECM B1/2=2e6/1e10, sigma=1:2331525317
n=3278: c1426(3892835483......) = 17755640483959884120539570514840731 * c1392(2192450048......)
# ECM B1/2=2e6/1e10, sigma=0:5357041020037774198
n=3288: c1052(6387100731......) = 777058547419946709306622094508543214393 * p1013(8219587510......)
# ECM B1/2=2e6/1e10, sigma=0:6285167283484008294
$ ./pfgw64 -tc -q"(10^1096-10^548+1)/121660606285465795549520731803413338484151574232341824637049313554009510862833014537" PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] Primality testing (10^1096-10^548+1)/121660606285465795549520731803413338484151574232341824637049313554009510862833014537 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 6+sqrt(13) Calling N+1 BLS with factored part 0.54% and helper 0.45% (2.08% proof) (10^1096-10^548+1)/121660606285465795549520731803413338484151574232341824637049313554009510862833014537 is Fermat and Lucas PRP! (0.0567s+0.0004s)
n=3423: c1920(7604430632......) = 1144226731506033672190976008207066090933 * c1881(6645912408......)
# ECM B1/2=2e6/1e10, sigma=0:12532628322984785219
n=3475: c2754(3330634382......) = 62748931924597058869804224298540379782751 * c2713(5307874222......)
# ECM B1/2=2e6/1e10, sigma=0:7049605378945519835
n=3550: c1359(1204630504......) = 70419611464033010410132410420235801 * c1324(1710646337......)
# ECM B1/2=2e6/1e10, sigma=0:10970266613014061893
n=3656: c1763(2517531325......) = 105014349820837827448113787173636073 * c1728(2397321251......)
# ECM B1/2=2e6/1e10, sigma=0:17887679712477353355
n=3759: c2081(1795719331......) = 10327348071198268614035070731437877311 * c2044(1738800047......)
# ECM B1/2=2e6/1e10, sigma=0:3539741285481088433
n=3894: c1151(2956199109......) = 13260827060071926678250146533712008317 * c1114(2229272047......)
# ECM B1/2=2e6/1e10, sigma=0:3965792511863434232
n=4000: c1562(8033307043......) = 431208300727476872730730418825856001 * c1527(1862975974......)
# ECM B1/2=2e6/1e10, sigma=0:16591244462271258547
n=4146: c1376(5300762620......) = 106849963662552664223405606288976466477 * c1338(4960940031......)
# ECM B1/2=2e6/1e10, sigma=0:9396526448657271941
n=4406: c2122(3342932280......) = 1071324633510414739083765749592126851 * c2086(3120372832......)
# ECM B1/2=2e6/1e10, sigma=0:2816116091175757641
n=4436: c2119(1358320520......) = 1261089691387822202605227321473564089 * c2083(1077100645......)
# ECM B1/2=2e6/1e10, sigma=0:11754549913371875997
n=4509: c2913(1766341542......) = 1184214232188511528770779091912013627 * c2877(1491572634......)
# ECM B1/2=2e6/1e10, sigma=0:9855240741001512686
n=4530: c1170(1614297466......) = 4833105202991763724410365536299494658103651 * c1127(3340083442......)
# ECM B1/2=2e6/1e10, sigma=0:8805604252382697202
n=4786: c2367(4601890454......) = 73826850772785509838139153011838927 * c2332(6233356030......)
# ECM B1/2=2e6/1e10, sigma=0:13633838615548872606
n=4872: c1315(1151703278......) = 27318745527311727819945109054958161 * c1280(4215798554......)
# ECM B1/2=2e6/1e10, sigma=0:5506612397258730679
n=4890: c1289(1375228552......) = 61520492294787443392030024940131 * c1257(2235399134......)
# ECM B1/2=2e6/1e10, sigma=0:15911322850500161954
n=4964: c2218(1912247652......) = 20923796916369387192791205169351481 * c2183(9139104437......)
# ECM B1/2=2e6/1e10, sigma=0:2803036211503127557
n=5178: c1694(6534873397......) = 35537869080356130336157108560442539373 * c1657(1838847844......)
# ECM B1/2=2e6/1e10, sigma=0:9580092485660964118
n=5230: c2057(1301376464......) = 913715366384021444166496647038109361 * c2021(1424268992......)
# ECM B1/2=2e6/1e10, sigma=0:771331845369412953
n=5235: c2731(1530721592......) = 10028232741957259837543150522085514121 * c2694(1526412112......)
# ECM B1/2=2e6/1e10, sigma=0:16463553687904428697
n=5308: c2616(8940540772......) = 405422528576191204049464657373849 * c2584(2205240247......)
# ECM B1/2=2e6/1e10, sigma=0:4154012416662622810
n=5316: c1746(1858508349......) = 560423341854478230067939871606964709 * c1710(3316257926......)
# ECM B1/2=2e6/1e10, sigma=0:16478966460039119882
n=5330: c1914(8883473182......) = 14560622194640776900404672373438993691 * p1877(6101025810......)
# ECM B1/2=2e6/1e10, sigma=0:16916451267224957947
$ ./pfgw64 -tc -q"9091*(10^13+1)*(10^41+1)*(10^2665+1)/14900772889729780089575025924754902022615451/(10^65+1)/(10^205+1)/(10^533+1)" PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] Primality testing 9091*(10^13+1)*(10^41+1)*(10^2665+1)/14900772889729780089575025924754902022615451/(10^65+1)/(10^205+1)/(10^533+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 11, base 7+sqrt(11) Calling N+1 BLS with factored part 0.48% and helper 0.45% (1.94% proof) 9091*(10^13+1)*(10^41+1)*(10^2665+1)/14900772889729780089575025924754902022615451/(10^65+1)/(10^205+1)/(10^533+1) is Fermat and Lucas PRP! (0.1489s+0.0005s)
n=5388: c1765(1561871622......) = 21656572209677916741002017772043949 * c1730(7211998312......)
# ECM B1/2=2e6/1e10, sigma=0:5719176353965550791
n=5622: c1836(4309912407......) = 341081075879744338226461559626068859 * c1801(1263603498......)
# ECM B1/2=2e6/1e10, sigma=0:15687442952726193675
n=5868: c1911(2658972621......) = 249411959185579871748145934199205969 * c1876(1066096682......)
# ECM B1/2=2e6/1e10, sigma=0:2459702306581111855
n=5890: c2150(5973627551......) = 16935951972289968452376690210403796291 * c2113(3527187347......)
# ECM B1/2=2e6/1e10, sigma=0:390719063034802979
n=6170: c2366(1386171442......) = 2853558046418662190707429941067051691 * c2329(4857694920......)
# ECM B1/2=2e6/1e10, sigma=0:3703652619764946765
n=6182: c2801(1099999999......) = 861496550506872179749984508575822237 * c2765(1276847828......)
# ECM B1/2=2e6/1e10, sigma=0:717745911794574277
n=6405: c2827(3773412660......) = 559442291539908392262507732453840724831 * c2788(6744954247......)
# ECM B1/2=2e6/1e10, sigma=0:7284976652874111983
n=6530: c2563(6992359281......) = 2926107539440275683794349973830631007081 * c2524(2389645352......)
# ECM B1/2=2e6/1e10, sigma=0:4708019548394877062
n=6546: c2148(8739806510......) = 50307524775512934941398395832874762172859 * c2108(1737276192......)
# ECM B1/2=2e6/1e10, sigma=0:10141722170644269264
n=6692: c2849(5135300160......) = 208071485014255604030387220484316221 * c2814(2468046094......)
# ECM B1/2=2e6/1e10, sigma=0:16465480567995558808
n=6770: c2692(5407041327......) = 1040714678805099503565514029401569361 * c2656(5195507892......)
# ECM B1/2=2e6/1e10, sigma=0:17573951911627414303
n=6864: c1905(1143498680......) = 346106500337352643358162709980222689 * c1869(3303892529......)
# ECM B1/2=2e6/1e10, sigma=0:2249601743126028204
n=7030: c2565(6579809959......) = 171960618591011490717176252193335075737891 * c2524(3826346993......)
# ECM B1/2=2e6/1e10, sigma=0:18392358690554521141
n=7236: c2371(2879114614......) = 400288859420739294212152112413380781 * c2335(7192592416......)
# ECM B1/2=2e6/1e10, sigma=0:12356903377649969917
n=7410: c1665(2177526315......) = 1633286398863103905950712556611395383441 * c1626(1333217687......)
# ECM B1/2=2e6/1e10, sigma=0:17670493216894934013
n=8060L: c1378(8025919910......) = 386338641439776181619664471909647893561 * c1340(2077431312......)
# ECM B1/2=2e6/1e10, sigma=0:6311439625869618970
n=8082: c2643(4200581672......) = 20194304465331386932841152087225309921 * c2606(2080082371......)
# ECM B1/2=2e6/1e10, sigma=0:3102672091120149002
n=8380M: c1615(3007996844......) = 792156824106885237618863734084839941 * c1579(3797223924......)
# ECM B1/2=2e6/1e10, sigma=0:10820090694979692954
n=8586: c2751(1619423470......) = 8537084702259015572963832941561033893 * c2714(1896927964......)
# ECM B1/2=2e6/1e10, sigma=0:10901450953734906347
n=9870: c2168(1010916456......) = 86826123740937613587552553154967653881 * c2130(1164299881......)
# ECM B1/2=2e6/1e10, sigma=0:6548336698675500456
n=9996: c2578(6976929622......) = 111483444357097578875486923992489149401 * c2540(6258265218......)
# ECM B1/2=2e6/1e10, sigma=0:12921914954328391707
n=10060M: c1995(1945777007......) = 14246454484575018741314919379810621 * p1961(1365797370......)
# ECM B1/2=2e6/1e10, sigma=0:12480918535794735290
$ ./pfgw64 -tc -q"((10^503+1)*((10^1006+10^503)*(10^503+10^252+3)+10^252+2)-1)/7321730307647437739022664528548464873597918238666121" PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8] Primality testing ((10^503+1)*((10^1006+10^503)*(10^503+10^252+3)+10^252+2)-1)/7321730307647437739022664528548464873597918238666121 [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 13 Running N+1 test using discriminant 67, base 1+sqrt(67) Calling N-1 BLS with factored part 0.32% and helper 0.05% (1.04% proof) ((10^503+1)*((10^1006+10^503)*(10^503+10^252+3)+10^252+2)-1)/7321730307647437739022664528548464873597918238666121 is Fermat and Lucas PRP! (0.2243s+0.0005s)
n=10122: c2803(1691587763......) = 106202679188864885351768778431861641 * c2768(1592791986......)
# ECM B1/2=2e6/1e10, sigma=0:16301053652210695925
n=10542: c2983(3245716181......) = 15926368861211790854013583970087766571 * c2946(2037951155......)
# ECM B1/2=2e6/1e10, sigma=0:1984221174329883152
n=11060L: c1822(1502907556......) = 1306386752415034616582029039902606041 * c1786(1150430799......)
# ECM B1/2=2e6/1e10, sigma=0:13740617811951633182
n=13060M: c2608(3576409999......) = 3435607759751666834283061237370911741 * c2572(1040983211......)
# ECM B1/2=2e6/1e10, sigma=0:9804163578888007668
n=15060M: c1994(5413813098......) = 531926477151291349837112885170943687795161 * c1953(1017774698......)
# ECM B1/2=2e6/1e10, sigma=0:10210524568510546119
n=15300L: c1881(1471340317......) = 999786224815367576155466884562939401 * c1845(1471654920......)
# ECM B1/2=2e6/1e10, sigma=0:13242376715890128600
n=16260M: c2161(2529932837......) = 390303076274243657098402096393505345281 * c2122(6481970014......)
# ECM B1/2=2e6/1e10, sigma=0:602491869415975576
n=19500L: c2323(1504479935......) = 4308766264946517744668657682808098880501 * c2283(3491672194......)
# ECM B1/2=2e6/1e10, sigma=0:10835374908913931446
n=20580L: c2353(1000000000......) = 31457113222307445802735328546790121 * c2318(3178931241......)
# ECM B1/2=2e6/1e10, sigma=0:3552031685095845501
n=22620M: c2648(1112286061......) = 8988880162931117783301843876885301 * c2614(1237402258......)
# ECM B1/2=2e6/1e10, sigma=0:874322887550625721
n=24780L: c2751(3331970320......) = 1170087313865534265656105558330641 * x2718(2847625370......)
# ECM B1/2=2e6/1e10, sigma=0:10507601487646200759
n=24780L: x2718(2847625370......) = 137626664115004896703002373026744466081 * c2680(2069094232......)
# ECM B1/2=2e6/1e10, sigma=0:14262530245873970156
# via Kurt Beschorner
n=30161: c30161(1111111111......) = 393873747961389636907917681425843 * c30128(2820982908......)
# ECM B1=1e6, sigma=2891847040901991
n=51563: c51563(1111111111......) = 475153622502302533783645711 * c51536(2338425002......)
# ECM B1=1e6, sigma=3844687670739452
# 217088 of 300000 Φn(10) factorizations were cracked. 300000 個中 217088 個の Φn(10) の素因数が見つかりました。
# 20112 of 25997 Rprime factorizations were cracked. 25997 個中 20112 個の Rprime の素因数が見つかりました。
n=7140L: c731(1659050888......) = 850887009985028048281840574127405664310675881 * c686(1949789888......)
# ECM B1=20e6, sigma=3:840203700
n=9720: c2575(1044943731......) = 69298762819407285039147739725468732721 * c2537(1507882231......)
# ECM B1=1e6, sigma=0:8168440396961977
n=33551: c28736(1505085440......) = 1344801398186149725603816707 * c28709(1119187891......)
# P-1 B1=26e6
n=101477: c101477(1111111111......) = 6911312173017829164982119329 * c101449(1607670270......)
# P-1 B1=100e6