-- Feb 28, 2019 (Makoto Kamada) -- n=122798: c56648(2879352710......) = 283572017603032757 * c56631(1015386756......) n=122816: c57580(2444949977......) = 1093060896651224257 * c57562(2236792099......) n=122822: c50760(9090910000......) = 4812387987171731 * c50745(1889064228......) n=122854: c56150(9349159765......) = 79240106753587841 * c56134(1179851990......) n=122884: c59389(2063058817......) = 1141446495708929 * c59374(1807407377......) n=122902: c54432(9090909090......) = 297387729848249 * c54418(3056921378......) n=122906: c52655(6129565323......) = 288637727691861157 * c52638(2123618895......) # P-1 B1=1e6 # 199738 of 300000 Phi_n(10) factorizations were cracked. -- Feb 27, 2019 (Makoto Kamada) -- n=122654: c52547(1595783537......) = 5043312131843693 * c52531(3164157790......) n=122655: c55275(8008376713......) = 227579792910601 * c55261(3518931365......) n=122698: c59341(1099999999......) = 1003985037908357 * c59326(1095633857......) n=122716: c55752(3810363692......) = 687928473025928926808941 * c55728(5538895163......) # P-1 B1=1e6 # 199736 of 300000 Phi_n(10) factorizations were cracked. -- Feb 25, 2019 (Makoto Kamada) -- n=122512: c51830(4290772702......) = 2728361027534221249 * c51812(1572655766......) n=122536: c56558(5867911222......) = 40446784134805273 * c56542(1450773244......) n=122554: c59128(1073769017......) = 6474831411136463 * c59112(1658373708......) n=122636: c55435(2691151915......) = 5097751986535529 * c55419(5279095417......) # P-1 B1=1e6 -- Feb 24, 2019 (Richard Buser) -- # via yoyo@home n=6100L: x1110(1354322894......) = 17729642323320850278883616474935850401 * c1072(7638749105......) # ECM B1=11000000, sigma=0:12691948414942556416 -- Feb 25, 2019 (Danny) -- # via yoyo@home n=6100L: c1144(9357261678......) = 69091807550221647412700483018565101 * x1110(1354322894......) # ECM B1=11000000, sigma=0:373158171685814716 -- Feb 24, 2019 (Makoto Kamada) -- n=122342: c54120(9090909091......) = 6177758042749613 * c54105(1471554733......) n=122344: c59508(2474650089......) = 417459164136929 * 164450778832357982222262617 * c59467(3604656332......) n=122356: c56161(1000000000......) = 15181175795758533890941 * c56138(6587105066......) n=122374: c52441(1099999890......) = 3507555921469831754573 * c52419(3136086536......) n=122386: c55621(1099999999......) = 392610543722717 * c55606(2801758683......) n=122398: c57961(1099999999......) = 28189178802613637 * c57944(3902206615......) n=122402: c52411(1633957722......) = 45807515241614729 * c52394(3567007977......) n=122408: c50850(9947874973......) = 515246184426689 * c50836(1930703278......) n=122426: c59681(1099999999......) = 6207375987292693 * c59665(1772085342......) n=122434: c52992(9090909090......) = 631918685618611 * c52978(1438620078......) # P-1 B1=1e6 # 199735 of 300000 Phi_n(10) factorizations were cracked. -- Feb 23, 2019 (Makoto Kamada) -- n=122192: c52309(2034303409......) = 953098292586448082934721 * c52285(2134410925......) n=122218: c59889(2002279836......) = 628443934257521 * c59874(3186091435......) n=122222: c58425(3296709191......) = 17170242659099 * c58412(1920013163......) n=122234: c52381(1099999890......) = 24308753372123042887 * c52361(4525118475......) n=122246: c57878(2739176452......) = 13260841207115809 * c57862(2065612889......) n=122264: c53760(9999000099......) = 3861553120010740484233 * c53739(2589372666......) n=122265: c51841(1001000999......) = 1060460086836151 * c51825(9439308583......) n=122318: c52406(4547406905......) = 3117255220681939 * c52391(1458785560......) n=122325: c55674(2151279023......) = 320920444526171875351 * c55653(6703465173......) # P-1 B1=1e6 # 199728 of 300000 Phi_n(10) factorizations were cracked. -- Feb 22, 2019 (Makoto Kamada) -- n=122096: c56246(1621782352......) = 265901154055656289 * c56228(6099192606......) n=122098: c59515(9009082793......) = 22003221972961 * c59502(4094437989......) n=122108: c51712(3881639351......) = 967809141047129501 * c51694(4010748800......) n=122128: c57332(4917944709......) = 28715335863377 * c57319(1712654427......) n=122132: c57800(2120151357......) = 27112768227879347141 * c57780(7819752449......) n=122162: c57459(3078901975......) = 173354995299583597 * c57442(1776067640......) n=122174: c54432(9090909090......) = 2003478523069739 * c54417(4537562537......) # P-1 B1=1e6 # 199725 of 300000 Phi_n(10) factorizations were cracked. -- Feb 22, 2019 (Makoto Kamada) -- # For 200001<=n<=300000 # 8262 prime factors were added. # Small prime factors up to 13 digit were searched. # 199724 of 300000 Phi_n(10) factorizations were cracked. -- Feb 18, 2019 (Alfred Reich) -- n=200003: x200003(1111111111......) = 402617632520700203 * x199985(2759717959......) # ECM B1=11000, sigma=4527679906989676 n=200381: x200381(1111111111......) = 14673605193564898787 * x200361(7572175320......) # ECM B1=11000, sigma=2091869554202189 n=200587: x200587(1111111111......) = 103117039411450372316483 * x200564(1077524255......) # ECM B1=11000, sigma=7457913356752279 n=200609: x200609(1111111111......) = 630186750984486757 * x200591(1763145780......) # ECM B1=11000, sigma=1498195874670333 n=200869: x200869(1111111111......) = 2107006850352484231 * x200850(5273410055......) # ECM B1=11000, sigma=7712504654752964 n=200927: x200927(1111111111......) = 68323404994565627 * x200910(1626252542......) # ECM B1=11000, sigma=3480235554064475 n=201437: x201437(1111111111......) = 5502458959874786438077 * x201415(2019299224......) # ECM B1=11000, sigma=651626598746362 n=201769: x201769(1111111111......) = 3904777029559829363 * x201750(2845517433......) # ECM B1=11000, sigma=1999845849913709 n=201781: x201781(1111111111......) = 132896006500581227 * x201763(8360756206......) # ECM B1=11000, sigma=4287926566896787 n=201809: x201809(1111111111......) = 94606227983923147 * x201792(1174458737......) # ECM B1=11000, sigma=6775591948639188 n=202121: x202121(1111111111......) = 343543816185337723 * x202103(3234263167......) # ECM B1=11000, sigma=1189646205293684 n=202127: x202127(1111111111......) = 540520707014640557 * x202109(2055630980......) # ECM B1=11000, sigma=3126867214503641 n=202441: x202441(1111111111......) = 911729543358049894399 * x202420(1218684991......) # ECM B1=11000, sigma=641300883932260 n=202679: x202679(1111111111......) = 260469904976013437 * x202661(4265794588......) # ECM B1=11000, sigma=8202508447512927 n=202733: x202733(1111111111......) = 37424896142437799 * x202716(2968909003......) # ECM B1=11000, sigma=688007263553120 n=202823: x202823(1111111111......) = 38074045769796521 * x202806(2918290107......) # ECM B1=11000, sigma=1171771534470371 n=203293: x203293(1111111111......) = 648339041257964159 * x203275(1713780970......) # ECM B1=11000, sigma=1178443079097931 n=203387: x203387(1111111111......) = 784622957248017683 * x203369(1416108336......) # ECM B1=11000, sigma=4899195301322121 n=203869: x203869(1111111111......) = 624774572092625736637 * x203848(1778419226......) # ECM B1=11000, sigma=5470603376641032 n=203977: x203977(1111111111......) = 5289190017304489717 * x203958(2100720729......) # ECM B1=11000, sigma=4640282933692644 n=203999: x203999(1111111111......) = 54477321665215180733 * x203979(2039584687......) # ECM B1=11000, sigma=3124955273858046 n=204007: x204007(1111111111......) = 96742746750255083 * x203990(1148521360......) # ECM B1=11000, sigma=7038193886919728 n=205763: x205763(1111111111......) = 1571414247535838110729 * x205741(7070771522......) # ECM B1=11000, sigma=5744781047327918 n=211933: x211933(1111111111......) = 832389963021018947 * x211915(1334844436......) # ECM B1=11000, sigma=2930446352830236 n=217319: x217319(1111111111......) = 327136068049348903751880841 * x217292(3396479996......) # ECM B1=11000, sigma=2895715347565685 n=299011: x299011(1111111111......) = 221045463366486747587120747 * x298984(5026618027......) # ECM B1=50000, sigma=4015201733820886 n=299447: x299447(1111111111......) = 5104005647061508609 * x299428(2176939423......) # ECM B1=11000, sigma=3726719826957846 n=299807: x299807(1111111111......) = 1096020580210100960507 * x299786(1013768474......) # ECM B1=11000, sigma=3958798504742561 n=299843: x299843(1111111111......) = 388263295986932803 * x299825(2861746455......) # ECM B1=11000, sigma=2597017414888041 n=299941: x299941(1111111111......) = 476143900733778479 * x299923(2333561575......) # ECM B1=11000, sigma=848901146059321 # 196255 of 300000 Phi_n(10) factorizations were cracked. # 18452 of 25997 R_prime factorizations were cracked. -- Feb 18, 2019 (Makoto Kamada) -- # Phin10.txt has been expanded up to n=300000. # Small prime factors up to 10^12 were searched. # Primality of small cofactors up to 50000 digit were checked. n=216980L: x41029(1115455115......) is (probable) prime # ----------------8<----------------8<----------------8<---------------- # $ ./pfgw64 -tc -q"3541*((10^10849+1)*((10^21698+10^10849)*(10^10849-10^5425+3)-10^5425+2)-1)/317448900341/((10^19+1)*((10^38+10^19)*(10^19+10^10+3)+10^10+2)-1)/((10^571+1)*((10^1142+10^571)*(10^571+10^286+3)+10^286+2)-1)" # PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6] # # Primality testing 3541*((10^10849+1)*((10^21698+10^10849)*(10^10849-10^5425+3)-10^5425+2)-1)/317448900341/((10^19+1)*((10^38+10^19)*(10^19+10^10+3)+10^10+2)-1)/((10^571+1)*((10^1142+10^571)*(10^571+10^286+3)+10^286+2)-1) [N-1/N+1, Brillhart-Lehmer-Selfridge] # Running N-1 test using base 3 # Running N-1 test using base 7 # Running N+1 test using discriminant 17, base 10+sqrt(17) # Calling N-1 BLS with factored part 0.04% and helper 0.00% (0.11% proof) # 3541*((10^10849+1)*((10^21698+10^10849)*(10^10849-10^5425+3)-10^5425+2)-1)/317448900341/((10^19+1)*((10^38+10^19)*(10^19+10^10+3)+10^10+2)-1)/((10^571+1)*((10^1142+10^571)*(10^571+10^286+3)+10^286+2)-1) is Fermat and Lucas PRP! (185.1254s+0.0834s) # ----------------8<----------------8<----------------8<---------------- n=288860M: x47994(4126997721......) is (probable) prime # ----------------8<----------------8<----------------8<---------------- # $ ./pfgw64 -tc -q"((10^11+1)*((10^22+10^11)*(10^11-10^6+3)-10^6+2)-1)*((10^13+1)*((10^26+10^13)*(10^13+10^7+3)+10^7+2)-1)*((10^101+1)*((10^202+10^101)*(10^101-10^51+3)-10^51+2)-1)*((10^14443+1)*((10^28886+10^14443)*(10^14443+10^7222+3)+10^7222+2)-1)/27961/((10^143+1)*((10^286+10^143)*(10^143-10^72+3)-10^72+2)-1)/((10^1111+1)*((10^2222+10^1111)*(10^1111+10^556+3)+10^556+2)-1)/((10^1313+1)*((10^2626+10^1313)*(10^1313-10^657+3)-10^657+2)-1)/866581" # PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6] # # Primality testing ((10^11+1)*((10^22+10^11)*(10^11-10^6+3)-10^6+2)-1)*((10^13+1)*((10^26+10^13)*(10^13+10^7+3)+10^7+2)-1)*((10^101+1)*((10^202+10^101)*(10^101-10^51+3)-10^51+2)-1)*((10^14443+1)*((10^28886+10^14443)*(10^14443+10^7222+3)+10^7222+2)-1)/27961/((10^143+1)*((10^286+10^143)*(10^143-10^72+3)-10^72+2)-1)/((10^1111+1)*((10^2222+10^1111)*(10^1111+10^556+3)+10^556+2)-1)/((10^1313+1)*((10^2626+10^1313)*(10^1313-10^657+3)-10^657+2)-1)/866581 [N-1/N+1, Brillhart-Lehmer-Selfridge] # Running N-1 test using base 2 # Running N+1 test using discriminant 29, base 10+sqrt(29) # Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.15% proof) # ((10^11+1)*((10^22+10^11)*(10^11-10^6+3)-10^6+2)-1)*((10^13+1)*((10^26+10^13)*(10^13+10^7+3)+10^7+2)-1)*((10^101+1)*((10^202+10^101)*(10^101-10^51+3)-10^51+2)-1)*((10^14443+1)*((10^28886+10^14443)*(10^14443+10^7222+3)+10^7222+2)-1)/27961/((10^143+1)*((10^286+10^143)*(10^143-10^72+3)-10^72+2)-1)/((10^1111+1)*((10^2222+10^1111)*(10^1111+10^556+3)+10^556+2)-1)/((10^1313+1)*((10^2626+10^1313)*(10^1313-10^657+3)-10^657+2)-1)/866581 is Fermat and Lucas PRP! (236.0476s+0.0178s) # ----------------8<----------------8<----------------8<---------------- # 1148 of 300000 Phi_n(10) factorizations were finished. # 196225 of 300000 Phi_n(10) factorizations were cracked. # 122 of 25997 R_prime factorizations were finished. # 18422 of 25997 R_prime factorizations were cracked. # 333578 (probable) prime factors were discovered. # 207638 composite factors are remaining. # 98589 factors are unidentified. -- Feb 14, 2019 (Makoto Kamada) -- n=121935: c59034(1539258888......) = 579939301640288041 * c59016(2654172399......) n=121942: c57745(1099999999......) = 61530800724647 * c57731(1787722550......) n=122012: c53352(2967008210......) = 33321706033421809910325214709 * c53323(8904130562......) n=122018: c53342(1110238227......) = 27772164483053927 * c53325(3997665461......) n=122032: c58683(8194504847......) = 34060868704307329 * c58667(2405841412......) n=122044: c56295(2368886172......) = 13759743381281 * c56282(1721606360......) n=122056: c51840(9999000099......) = 1225895669571426511417 * c51819(8156485374......) # P-1 B1=1e6 # 141057 of 200000 Phi_n(10) factorizations were cracked. -- Feb 13, 2019 (Makoto Kamada) -- n=121862: c54414(2131061194......) = 13430246386753379 * c54398(1586762545......) n=121898: c52217(4829273844......) = 93735797905197407 * c52200(5152005906......) n=121905: c54432(9999999999......) = 1238842351220671 * c54417(8072052097......) n=121912: c52059(1219851298......) = 7763743790733223204129 * c52037(1571215294......) # P-1 B1=1e6 # 141055 of 200000 Phi_n(10) factorizations were cracked. -- Feb 12, 2019 (Makoto Kamada) -- n=121702: c52153(1099999890......) = 57735941904516247 * c52136(1905225503......) n=121726: c55221(1000000000......) = 9629523225177723981521 * c55199(1038473013......) n=121737: c57601(1109999888......) = 705510577383613 * c57586(1573328486......) n=121744: c52112(1860368902......) = 49891676634010204886931361 * c52086(3728816163......) n=121748: c55314(2304395074......) = 69928862091493681 * c55297(3295341874......) n=121754: c57281(1099999999......) = 26628318978597019 * c57264(4130940450......) n=121756: c59761(1009999999......) = 369732040676701 * c59746(2731708072......) n=121784: c56161(1000099999......) = 16021477270571492718233 * c56138(6242245849......) # P-1 B1=1e6 # 141054 of 200000 Phi_n(10) factorizations were cracked. -- Feb 11, 2019 (Makoto Kamada) -- n=121628: c56106(5536002929......) = 4818261063538537912181 * c56085(1148962842......) n=121634: c59754(4521760148......) = 808136864882219 * c59739(5595290036......) n=121652: c57217(1009999999......) = 67115515499987761 * c57200(1504868125......) n=121682: c55288(2913392798......) = 13775866445943317 * c55272(2114852673......) # P-1 B1=1e6 # 141048 of 200000 Phi_n(10) factorizations were cracked. -- Feb 10, 2019 (Makoto Kamada) -- n=121485: c50666(3299965205......) = 2113080372825241 * c50651(1561684660......) n=121508: c59041(1009999999......) = 504055563052529 * c59026(2003747352......) n=121552: c59355(8226864083......) = 355626276448574993 * c59338(2313345393......) n=121568: c58221(1015399560......) = 97472713212618728449 * c58201(1041726989......) n=121582: c56153(1755207331......) = 53815536137819971 * c56136(3261525308......) # P-1 B1=1e6 # 141047 of 200000 Phi_n(10) factorizations were cracked. -- Feb 9, 2019 (Makoto Kamada) -- n=121324: c51890(1990540114......) = 3145697642939209 * 581630792235480961 * c51857(1087944063......) n=121334: c55072(3947558636......) = 12038368951111583 * c55056(3279147410......) n=121336: c58465(1000099999......) = 2048615318200533281 * c58446(4881834042......) n=121342: c55843(8241101670......) = 92180213677183321 * c55826(8940206733......) n=121348: c57987(8323101138......) = 42230559893122643501 * c57968(1970871605......) n=121354: c59334(1678590508......) = 14388455815567 * c59321(1166623111......) n=121372: c57457(1009999999......) = 24247694005132582163701 * c57434(4165344546......) n=121396: c52800(9900990099......) = 710577875080481 * c52786(1393371570......) n=121412: c59964(1549403658......) = 4702844615735926863649 * c59942(3294609507......) n=121432: c59127(4754306471......) = 2833344036664873 * c59112(1677984180......) n=121448: c52992(9999000099......) = 101078302123599193 * c52975(9892330885......) # P-1 B1=1e6 # 141046 of 200000 Phi_n(10) factorizations were cracked. -- Feb 8, 2019 (Makoto Kamada) -- n=121196: c59041(1009999999......) = 463741518416261 * 27712698804783829 * c59009(7858987037......) n=121208: c59609(4436078049......) = 44512991440165601 * c59592(9965805275......) # P-1 B1=1e6 # 141042 of 200000 Phi_n(10) factorizations were cracked. -- Feb 7, 2019 (Makoto Kamada) -- n=121132: c55032(1108041384......) = 296263916777100889 * c55014(3740048387......) n=121154: c55037(2723244978......) = 83261629371549488201 * c55017(3270708247......) n=121166: c59230(2215542200......) = 225294044339996161571 * c59209(9834002522......) # P-1 B1=1e6 -- Feb 6, 2019 (Makoto Kamada) -- n=120998: c59801(1099999999......) = 63275020330609 * c59787(1738442744......) n=121016: c51826(1050940435......) = 1416669912892376938462305409 * c51798(7418386074......) n=121024: c57601(1000000000......) = 1072399018464833 * c57585(9324887311......) n=121028: c59564(5117592521......) = 32759543883089 * c59551(1562168429......) n=121034: c59608(1276813055......) = 13314473829143 * c59594(9589662135......) n=121058: c51877(1099999890......) = 28697761780959076862477 * 562356132875827131934289 * c51830(6816056468......) n=121065: c55296(9009100000......) = 6517994928913130671 * c55278(1382188863......) n=121088: c53761(1000000000......) = 10252941014273 * c53747(9753299064......) n=121095: c57010(4063045221......) = 46018932654241 * c56996(8829073138......) # P-1 B1=1e6 # 141041 of 200000 Phi_n(10) factorizations were cracked. -- Feb 5, 2019 (Makoto Kamada) -- n=120884: c59054(1327916416......) = 2491199201129888441 * c59035(5330430485......) n=120945: c58555(1241485342......) = 48568544782538551 * c58538(2556150998......) n=120952: c55777(1000099999......) = 46680134882347201 * c55760(2142453106......) n=120958: c59977(1099999999......) = 121999396422589801729 * c59956(9016438050......) # P-1 B1=1e6 # 141036 of 200000 Phi_n(10) factorizations were cracked. -- Feb 4, 2019 (Makoto Kamada) -- n=120772: c59617(1009999999......) = 194090829161381 * c59602(5203749215......) n=120824: c54881(1000099999......) = 80593319271824142961 * c54861(1240921715......) n=120836: c56833(1009999999......) = 6004988181915986439481 * c56811(1681935033......) n=120838: c58441(1099999999......) = 29764275078136343957 * c58421(3695705664......) n=120862: c50676(3914056269......) = 468186135131702303 * c50658(8360043101......) n=120868: c52784(4594226489......) = 127729877726089 * c52770(3596829943......) n=120872: c58232(2110186672......) = 47795108301044561 * c58215(4415068294......) # P-1 B1=1e6 # 141034 of 200000 Phi_n(10) factorizations were cracked. -- Feb 3, 2019 (Makoto Kamada) -- n=120646: c59784(4992341651......) = 226238614322491 * c59770(2206670893......) n=120694: c50104(4149970849......) = 552673354490041 * 671913456824023 * c50075(1117540266......) n=120698: c58221(2599907868......) = 97601621057333 * c58207(2663795785......) n=120704: c56307(1733249879......) = 1256944032303888641 * c56289(1378939582......) n=120705: c59328(9009099100......) = 280321186822951 * c59314(3213848800......) n=120718: c55676(7875706962......) = 1096368946601891 * c55661(7183445852......) # P-1 B1=1e6 # 141030 of 200000 Phi_n(10) factorizations were cracked. -- Feb 2, 2019 (Makoto Kamada) -- n=120562: c55633(1099999999......) = 3729789604267927951973 * c55611(2949228017......) n=120568: c51639(8381230790......) = 24840842906377 * c51626(3373971979......) n=120604: c54801(1009999999......) = 5577717101376289 * c54785(1810776670......) n=120614: c55644(3658072906......) = 477839272984276321 * c55626(7655446325......) n=120615: c53749(3920769298......) = 4134954084554157081031 * c53727(9482014111......) n=120622: c58795(9119322185......) = 150895892905441 * c58781(6043452880......) n=120626: c54806(2720723899......) = 469903500365451637 * 96374324935373773927 * c54768(6007785833......) n=120632: c56705(1000099999......) = 18868950504243192641 * c56685(5300241790......) n=120638: c51661(1000000099......) = 3346684821299009 * c51645(2988031898......) # P-1 B1=1e6 # 141029 of 200000 Phi_n(10) factorizations were cracked. -- Feb 1, 2019 (Makoto Kamada) -- n=120422: c57025(1099999999......) = 38751691701889 * 148506261888251 * c56997(1911424957......) n=120454: c59728(9592559606......) = 985717943628637 * c59713(9731546096......) n=120472: c53260(1019910416......) = 19703170114268873 * 70559970408711169 * c53226(7336138643......) n=120496: c56577(1000000009......) = 14627018108120753 * 254367057298946881 * c56543(2687715770......) # P-1 B1=1e6 # 141025 of 200000 Phi_n(10) factorizations were cracked.