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September 16, 2024 2024 年 9 月 16 日 (Kurt Beschorner)

n=7714: c3016(9520883276......) = 674756255553554784010629810684186001 * c2981(1411010746......)

# P-1 B1=55e6

n=13959: c8225(1438565069......) = 10908706960626889587131773 * c8200(1318731060......)

# P-1 B1=200e6

n=13967: c13959(7576437216......) = 1546739122898324683549717612079311 * c13926(4898329074......)

# P-1 B1=150e6

n=14329: c11608(2381975029......) = 183712653538982131518024939751 * c11579(1296576465......)

# P-1 B1=26e6

n=20059: c18498(1438065169......) = 80375529458480386963639 * c18475(1789182826......)

# P-1 B1=26e6

n=33428: c16293(3839001903......) = 598073364853609567951344661 * c16266(6418948123......)

# P-1 B1=55e6

n=33430: c13348(1488332194......) = 1940207172302679533640091 * c13323(7670996249......)

# P-1 B1=55e6

n=33431: c32976(9298196351......) = 2986536836872837600454184202658521 * c32943(3113370723......)

# P-1 B1=26e6

n=33433: c32846(1613302257......) = 40818089630691856577333 * c32823(3952419802......)

# P-1 B1=26e6

n=33435: c17797(6218233396......) = 105983936158364548054452631 * c17771(5867147061......)

# P-1 B1=26e6

n=100281: c66852(9009009009......) = 1815632202447883 * c66837(4961912989......)

# P-1 B1=26e6

n=100283: c94112(9999999999......) = 42379862892338239 * c94096(2359611220......)

# P-1 B1=26e6

n=100302: c32826(1564241239......) = 163812185449385920151179 * c32802(9548991942......)

# P-1 B1=55e6

n=100307: c97560(9000000000......) = 821138291293898067154050639683 * c97531(1096039497......)

# P-1 B1=26e6

n=161503: c161497(1719951628......) = 446701045025113763 * c161479(3850341626......)

n=161831: c161799(2144367799......) = 3150992875204990759 * c161780(6805371779......)

n=161923: c161899(1521245029......) = 265409454752698439 * c161881(5731691173......)

n=161983: c161975(7621588787......) = 3102607059593915561 * c161957(2456511134......)

n=162053: c162031(3117380273......) = 455764003592207053 * c162013(6839900144......)

n=162263: c162247(1858883693......) = 16573976462383659653 * c162228(1121567716......)

n=162709: c162700(6163198449......) = 6151846505317453609 * c162682(1001845290......)

n=162821: c162815(3412052803......) = 533085113807320037 * c162797(6400577909......)

n=163147: c163131(5702797603......) = 226382336474367907 * c163114(2519100073......)

n=163243: c163227(5791027631......) = 450452936170769321 * x163210(1285601039......)

n=163243: x163210(1285601039......) = 1158816080244718243 * c163192(1109409044......)

n=163351: c163333(1621694346......) = 655996977828896117 * c163315(2472106429......)

# gr-mfaktc

September 15, 2024 2024 年 9 月 15 日 (Torbjörn Granlund)

# via Kurt Beschorner

n=1213: c1169(7642013827......) = 3802200856589814744657128636563499435894999 * c1127(2009892195......)

# ECM B1=1e6, sigma=0:14488647671416981951

n=1815: c877(2754062241......) = 4098441872200433015045042676505414155509641 * c834(6719778705......)

# ECM B1=1e6, sigma=0:11990104957816418499

n=2285: c1803(3795280466......) = 2051498341294060742933143147274846947443401 * c1761(1850004160......)

# P-1 B1=1e9, B2=6084866733918

n=2391: c1547(3044508346......) = 103182654083788921684537334713499683 * c1512(2950600925......)

# ECM B1=1e6, sigma=0:12020620644682256341

n=2449: c2315(2926565858......) = 600858453913730403856532541976772589443 * c2276(4870641062......)

# P-1 B1=1e9, B2=6084866733918

n=2527: c2011(2076778741......) = 647353766385319691857417203558887401 * c1975(3208104824......)

# ECM B1=1e6, sigma=0:3621277789841061197

n=2535: c1219(3635690525......) = 156754634687052062764416759087670471 * c1184(2319351216......)

# ECM B1=1e6, sigma=1:3393956487

n=2543: c2525(1890946834......) = 753304164049013002621804486735652843 * c2489(2510203613......)

# ECM B1=1e6, sigma=1:1466944611

n=2705: c2136(1391017077......) = 109195685007337483022299748369716146161 * c2098(1273875498......)

# ECM B1=1e6, sigma=0:8906779298094550009

n=2745: c1424(3270025958......) = 28485167471844891801410276138004175081 * c1387(1147974980......)

# ECM B1=1e6, sigma=0:8604497436349318999

n=2829: c1756(2179761600......) = 16410236115549830906505363137937169 * c1722(1328293868......)

# ECM B1=1e6, sigma=0:1951234959635419041

n=2937: c1705(3571617425......) = 18896097703630454952291685509584942533 * c1668(1890134927......)

# ECM B1=1e6, sigma=1:759148817

n=3021: c1834(4557057975......) = 27330873097344696912154806989332483 * c1800(1667366409......)

# ECM B1=1e6, sigma=0:3201172410425856953

n=3569: c3428(2183376647......) = 11400139053302182410990498057327124417267 * c3388(1915219312......)

# ECM B1=3e6, sigma=0:10865405958817156427

n=3585: c1863(7826086355......) = 58085336248307618498777162746561 * c1832(1347342868......)

# ECM B1=1e6, sigma=0:15009441137241804824

n=3667: c3416(3536073635......) = 2080475367504865290478276992253031 * c3383(1699646960......)

# ECM B1=1e6, sigma=0:12437885057015613011

n=3757: c3242(1474080211......) = 33694379761057967269754016089273036507 * c3204(4374854863......)

# ECM B1=1e6, sigma=1:273908683

n=3787: c3208(1025566888......) = 7055345299224159172828355011806649 * c3174(1453602686......)

# ECM B1=1e6, sigma=0:2830813724368277207

n=4055: c3209(2813674769......) = 1948787780852220980547111695444679761 * c3173(1443807682......)

# ECM B1=1e6, sigma=0:17455056067453863873

n=4103: c3700(2530510939......) = 1741547372143431977118494290270117837 * c3664(1453024465......)

# ECM B1=1e6, sigma=0:5025907934834844875

n=4165: c2653(4958384644......) = 14502689303731246267058119792968671 * c2619(3418941508......)

# ECM B1=1e6, sigma=0:5727017555073026671

n=4191: c2516(4414045412......) = 22984383232857352472100689865991849 * c2482(1920454148......)

# ECM B1=1e6, sigma=0:12310506994298116883

n=4265: c3375(6599422633......) = 14287864954281769595031262840766686391 * c3338(4618900482......)

# ECM B1=1e6, sigma=0:16892259785869631342

n=4507: c4480(1938486490......) = 144033826328835512829127544710780565639 * c4442(1345855025......)

# ECM B1=1e6, sigma=0:449790939880095147

n=4509: c2949(4345615927......) = 2460235364293681340814960094035702961 * c2913(1766341542......)

# ECM B1=3e6, sigma=0:15501487315860969557

n=4739: c4003(1851058454......) = 169909323009560405443119802808507 * c3971(1089439014......)

# ECM B1=1e6, sigma=0:5951338009732668807

n=4869: c3226(1332576993......) = 486782628447541143585231274986757711 * c3190(2737519614......)

# ECM B1=1e6, sigma=0:7300925068061572311

n=4919: c4915(1129292723......) = 6530957056632063748192085275662319 * c4881(1729138186......)

# ECM B1=1e6, sigma=0:6603285319019973935

n=5215: c3545(1383496501......) = 125442818692110058393659177580154599647431 * c3504(1102890157......)

# ECM B1=1e6, sigma=1:177897093

n=5465: c4360(8719080911......) = 165659419307517545705863974768344231 * c4325(5263256956......)

# ECM B1=1e6, sigma=0:6603285319019973935

n=5593: c4391(2314946094......) = 30774474478303908730228394315801 * c4359(7522292854......)

# ECM B1=1e6, sigma=0:78372119094033

n=5651: c5610(1041194805......) = 253153202072068480481374624902090462157 * c5571(4112903951......)

# ECM B1=1e6, sigma=0:12798764993499092605

n=5711: c5686(1258915791......) = 1458424360860342794605064778192559441 * c5649(8632026625......)

# ECM B1=1e6, sigma=0:5963013522829996799

n=5743: c5691(2198576767......) = 14811624013463002360724048056372841 * c5657(1484359018......)

# ECM B1=1e6, sigma=0:78372119094033

n=5831: c4692(5762935117......) = 318654001333309317352041936803 * c4663(1808524322......)

# ECM B1=1e6, sigma=1:3393956487

n=5917: c5738(2633244994......) = 62128869315196783538931039009211738481 * c5700(4238359757......)

# ECM B1=1e6, sigma=1:1474470163

n=6011: c5998(1011571216......) = 5656607367075011571023869359496363 * c5964(1788300214......)

# ECM B1=1e6, sigma=1:273908683

n=6093: c4028(2817843599......) = 1336143863663099786889758180375119 * c3995(2108937275......)

# ECM B1=1e6, sigma=1:3616795357

n=6173: c6128(1436951503......) = 5053071098890826667938286305293 * c6097(2843719147......)

# ECM B1=1e6, sigma=0:199762724765272745

n=6237: c3235(6680517606......) = 14089779120825363590790687940304359 * c3201(4741392713......)

# ECM B1=1e6, sigma=0:15637767851225334323

n=6327: c3829(1583590286......) = 1596489365351468828532617242104403 * c3795(9919203480......)

# ECM B1=1e6, sigma=1:759148817

n=6407: c6216(9000000000......) = 373939098107201919765478843483 * c6187(2406809035......)

# ECM B1=1e6, sigma=0:11362242212281988111

n=6417: c3961(1001000999......) = 294088177038615753783998327225437 * c3928(3403744448......)

# ECM B1=1e6, sigma=1:3425686205

n=6465: c3433(2078092657......) = 221112688029324217201473060951751 * c3400(9398341975......)

# ECM B1=1e6, sigma=0:8473284529095742021

n=6509: c6148(7475606839......) = 100936144535747450211445731409 * c6119(7406273415......)

# ECM B1=1e6, sigma=0:1532057093235231923

n=6579: c3934(4633018317......) = 14928911404373501386802247002821217191 * c3897(3103386571......)

# ECM B1=1e6, sigma=0:1532057093235231923

n=6747: c4120(1930821339......) = 6723829837620032920626623393563 * c4089(2871609464......)

# ECM B1=1e6, sigma=0:11914725518606056737

n=6767: c6586(3790989235......) = 1943538884462222777971431975683519 * c6553(1950560015......)

# ECM B1=1e6, sigma=0:11914725518606056737

n=6775: c5370(1015626397......) = 7651560979032194699667735601 * c5342(1327345362......)

# ECM B1=1e6, sigma=0:7938031375900419525

n=6785: c5091(5413631108......) = 8367957136701535535458360493059871 * c5057(6469477580......)

# ECM B1=1e6, sigma=0:8253462866479087135

n=6799: c6252(8641990996......) = 170625890566634686201590537198169 * c6220(5064876712......)

# ECM B1=1e6, sigma=0:189873710409027

n=6827: c6789(4710762911......) = 605563853021030672629776013561 * c6759(7779134914......)

# ECM B1=1e6, sigma=0:15042871998340189925

n=6873: c4343(1445891162......) = 11732138724635366578685236204921 * c4312(1232419080......)

# ECM B1=1e6, sigma=1:77461235

n=6933: c4555(1025887252......) = 2056666694145181286351906929282494283 * c4518(4988106510......)

# ECM B1=1e6, sigma=1:1753592501

n=6955: c5083(4698673410......) = 4770123797091402986659534165081 * c5052(9850212720......)

# ECM B1=1e6, sigma=0:7545309159719229623

n=7011: c4251(1084317287......) = 40932492158522147916939842503117 * c4219(2649038038......)

# ECM B1=1e6, sigma=0:15428700728936867661

n=7047: c4486(1079798263......) = 2721713105317415253764995487154864151 * c4449(3967347851......)

# ECM B1=1e6, sigma=0:14957306403135743853

n=7203: c4106(5121299051......) = 358477182201157632404210989262323 * c4074(1428626229......)

# ECM B1=1e6, sigma=0:1899485105162830283

n=7225: c5391(3354548116......) = 4302621570884152909003933564616551 * c5357(7796521403......)

# ECM B1=1e6, sigma=0:263415883537725

n=7389: c4858(1160698409......) = 2898661596886202374101295254853 * c4827(4004256346......)

# ECM B1=1e6, sigma=0:18401888294117552977

n=7405: c5906(8447240300......) = 1000777605747316235823378402467201 * c5873(8440676781......)

# ECM B1=1e6, sigma=1:182620923

n=7435: c5925(4335080638......) = 31538057598641330421637379793605858911 * c5888(1374555368......)

# ECM B1=1e6, sigma=0:17646512381195540761

n=7453: c7144(6132896153......) = 519352817483043973396038245141801 * c7112(1180872799......)

# ECM B1=1e6, sigma=0:17646512381195540761

n=7455: c3320(3044893699......) = 491214058175515798301044852544161 * c3287(6198710418......)

# ECM B1=1e6, sigma=0:1038547052753189993

n=7481: c7451(1299806526......) = 4972615427247872817986627484420443 * c7417(2613929320......)

# ECM B1=1e6, sigma=0:12798764993499092605

n=7497: c4020(9596480253......) = 120992296050473892227494196483557 * c3988(7931480405......)

# ECM B1=1e6, sigma=0:3207401511136924985

n=7571: c7351(3403547135......) = 18698117426765456482515727025468521 * c7317(1820261932......)

# ECM B1=1e6, sigma=0:8906779298094550009

n=7579: c6199(2521757591......) = 19746693354511063241762048385799 * c6168(1277053097......)

# ECM B1=1e6, sigma=1:2923719129

n=7657: c6413(1724850336......) = 23156299845678068145104500838792479 * c6378(7448730357......)

# ECM B1=1e6, sigma=0:11914725518606056737

n=7707: c4365(1056153842......) = 10239935254977661685645752476121 * c4334(1031406758......)

# ECM B1=1e6, sigma=0:14778809121148116955

n=7709: c7104(9000000000......) = 3603902959985554170713863151227 * c7074(2497292546......)

# ECM B1=1e6, sigma=0:78372119094033

n=7735: c4561(6040367395......) = 7852631810215021420841043096031 * c4530(7692156643......)

# ECM B1=1e6, sigma=1:1664073337

n=7751: c7286(1112440926......) = 2508815958146815988829093095690279 * c7252(4434127275......)

# ECM B1=1e6, sigma=0:10977665072412782587

n=7885: c5868(3751352944......) = 19715636275865932733299589027883883203241 * c5828(1902729839......)

# ECM B1=1e6, sigma=1:3605802901

n=8065: c6427(2000194131......) = 60524026956189845504863462287391241 * c6392(3304793536......)

# ECM B1=1e6, sigma=0:13156499177556375355

n=8087: c8087(1111111111......) = 676176399587129808611509701831277 * c8054(1643226696......)

# ECM B1=1e6, sigma=0:7093308573280539123

n=8123: c8116(4652576524......) = 4814330511191140848342973783129 * c8085(9664015617......)

# ECM B1=1e6, sigma=0:10440896923169321451

n=8357: c8138(8736351484......) = 20176718421494524195035668600213 * c8107(4329916938......)

# ECM B1=1e6, sigma=0:12798764993499092605

n=8377: c8377(1111111111......) = 5687690333174390215382594316043 * c8346(1953536578......)

# ECM B1=1e6, sigma=1:1156762131

n=8387: c8364(1579400177......) = 10938520602149818569869171575609 * c8333(1443888287......)

# ECM B1=1e6, sigma=1:1664073337

n=8449: c6675(1387692313......) = 1866759297062204231700511602262397 * c6641(7433697082......)

# ECM B1=1e6, sigma=0:10547514346612664537

n=8527: c8494(4882485445......) = 243375472861762690397991792264917 * c8462(2006153450......)

# ECM B1=1e6, sigma=0:11990104957816418499

n=8549: c8323(3640430113......) = 15925358773101069259411105353519319 * c8289(2285932872......)

# ECM B1=1e6, sigma=0:6603285319019973935

n=8665: c6921(5874839366......) = 25409864545263329255648473295928871 * c6887(2312030965......)

# ECM B1=1e6, sigma=0:9616308672479705735

n=8781: c5827(1484496198......) = 416828196947164610392504584224599 * c5794(3561410214......)

# ECM B1=1e6, sigma=0:17365221873064881403

n=8833: c7865(3873036547......) = 1063599702251709943979714751587 * c7835(3641441925......)

# ECM B1=1e6, sigma=1:1652174903

n=8857: c8296(2462064908......) = 3112229527773266800727250108835512151 * c8259(7910936153......)

# ECM B1=1e6, sigma=0:12466699163099994441

n=8861: c8842(1020803831......) = 514228458427027657041198238405757 * c8809(1985117344......)

# ECM B1=1e6, sigma=0:8906779298094550009

n=9295: c6234(3039115544......) = 13812317980966297693444361767795561 * c6200(2200293642......)

# ECM B1=1e6, sigma=0:5963013522829996799

n=9581: c7899(1228011972......) = 95233941496960508695109319521 * c7870(1289468810......)

# ECM B1=1e6, sigma=1:1751343877

n=9879: c6307(9011312099......) = 622083644065230480047758412090677 * c6275(1448569205......)

# ECM B1=1e6, sigma=0:1038547052753189993

n=9965: c7948(6248166555......) = 50664542210486897314398938301663311 * c7914(1233242477......)

# ECM B1=1e6, sigma=0:17127812835675519603

n=8655: c4609(1109988900......) = 127381682260506697042031958031 * c4579(8713881621......)

# ECM B1=1e6, sigma=0:9616308672479705735

September 11, 2024 2024 年 9 月 11 日 (Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Oliver Kruse and Kurt Beschorner)

n=471: c301(1965855492......) = 1640259175221723797786233348156700513564345502781851447654042775375772294825108377125627674387206196531834389323135517030822828838413 * p169(1198502969......)

# 1275 of 300000 Φn(10) factorizations were finished. 300000 個中 1275 個の Φn(10) の素因数分解が終わりました。

September 9, 2024 2024 年 9 月 9 日 (Alfred Eichhorn)

# via Kurt Beschorner

n=15091: c15091(1111111111......) = 14845413823789711008287828293 * c15062(7484541180......)

# ECM B1=1e6, sigma=2136717002765025

n=15149: c15149(1111111111......) = 12301910027669319512906185199 * c15120(9032021113......)

# ECM B1=1e6, sigma=8122641535983119

September 6, 2024 2024 年 9 月 6 日 (Kurt Beschorner)

n=6655: c4840(9999999999......) = 47002315541332120475432927835118351 * c4806(2127554756......)

# ECM B1=1e6, sigma=0:3671949798087517

n=13908: c4320(9901000000......) = 4796645886147946366365200759449 * c4290(2064150707......)

# P-1 B1=500e6

n=13917: c9270(5993870416......) = 1946882395844921741959 * x9249(3078701841......)

# P-1: B1 =150e6

n=13917: x9249(3078701841......) = 479634834466543489354729 * p9225(6418845379......)

# P-1: B1 =150e6

$ ./pfgw64 -tc -q"(10^13917-1)/155791258534161207680682613894702422837812665874936877/(10^4639-1)"
PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8]

Primality testing (10^13917-1)/155791258534161207680682613894702422837812665874936877/(10^4639-1) [N-1/N+1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)

Calling N-1 BLS with factored part 0.14% and helper 0.01% (0.42% proof)
(10^13917-1)/155791258534161207680682613894702422837812665874936877/(10^4639-1) is Fermat and Lucas PRP! (2.9458s+0.0005s)

n=33423: c20526(9385343668......) = 1431696564802773760921 * c20505(6555400005......)

# P-1 B1=23e6

n=100256: c46061(5043816717......) = 2129531546192902994273 * c46040(2368509978......)

# P-1 B1=55e6

n=100259: c99199(1185283307......) = 7373367128510290221763 * c99177(1607519721......)

# P-1 B1=23e6

n=100261: c85932(9000000900......) = 2578509001157321 * c85917(3490389560......)

# P-1 B1=23e6

n=100265: c72875(1846935875......) = 1081414204698376192537440361 * c72848(1707889416......)

# P-1 B1=23e6

n=100268: c42952(3623382846......) = 510114955101536530235729 * c42928(7103071199......)

# P-1 B1=55e6

n=100270: c38880(9091000000......) = 92110972364038616356834631775642121 * c38845(9869616796......)

# P-1 B1=55e6

n=100271: c100234(7103395288......) = 22605675903598064150949502733 * c100206(3142306082......)

# P-1 B1=23e6

n=159977: c159960(6332816691......) = 16055910264628866119 * c159941(3944227756......)

n=160481: c160472(3074436173......) = 3061777772635910203 * c160454(1004134330......)

n=160619: c160599(8018608022......) = 12625299179729486347 * c160580(6351222183......)

n=160637: c160628(9222541937......) = 6622464926200147133 * c160610(1392614689......)

n=160687: c160675(1034381616......) = 14217364466292133721 * c160655(7275480761......)

n=160723: c160698(1881339432......) = 1053461002320903707 * c160680(1785865284......)

n=160781: c160773(8638388745......) = 10091891125422883573 * c160754(8559732401......)

n=160879: c160853(5522722568......) = 1363625823793966609 * c160835(4050027854......)

# gr-mfaktc

# 1274 of 300000 Φn(10) factorizations were finished. 300000 個中 1274 個の Φn(10) の素因数分解が終わりました。

# 213293 of 300000 Φn(10) factorizations were cracked. 300000 個中 213293 個の Φn(10) の素因数が見つかりました。

August 30, 2024 2024 年 8 月 30 日 (Kurt Beschorner)

n=9382: c4654(5850746026......) = 9300968916181881256379682557271761 * c4620(6290469389......)

# ECM B1=1e6, sigma=0:5919480135446658

n=9388: c4663(2486558516......) = 6367464694402438045010892622442009 * c4629(3905099809......)

# ECM B1=1e6, sigma=0:7946659145174239

n=9404: c4684(1593586001......) = 22051978558725308479114046671949 * c4652(7226498959......)

# ECM B1=1e6, sigma=0:5927629009860808

n=13891: c13351(5654989593......) = 3783946127200973031121 * c13330(1494468843......)

# P-1 B1=150e6

n=100243: c83993(1539468945......) = 2801869717572335479993639 * c83968(5494434434......)

# P-1 B1=23e6

n=100247: c85896(2605876004......) = 2270707106604318898415803 * c85872(1147605517......)

# P-1 B1=23e6

n=100248: c33409(1000099999......) = 137328742232380242793 * c33388(7282525010......)

# P-1 B1=55e6

n=100249: c94320(1895935945......) = 3589469193300853 * c94304(5281939594......)

# P-1 B1=23e6

n=100251: c64570(5898663677......) = 57734074812011041 * c64554(1021695367......)

# P-1 B1=23e6

n=100252: c49281(1009999999......) = 288219713789126385282941 * c49257(3504271053......)

# P-1 B1=55e6

n=158761: c158748(3660574234......) = 672701845713258917 * c158730(5441599807......)

n=158849: c158831(2868561497......) = 1725374401029737483 * c158813(1662573349......)

n=159233: c159199(5220278980......) = 529647323937549359 * c159181(9856141519......)

n=159589: c159581(1822599165......) = 5519361762904215599 * c159562(3302191890......)

n=159673: c159642(4600104144......) = 86101299875254837 * x159625(5342665152......)

n=159673: x159625(5342665152......) = 4106033786290026523 * c159607(1301174181......)

# gr-mfaktc

August 22, 2024 2024 年 8 月 22 日 (-)

# via factordb.com

n=2342: c1135(4552526416......) = 1277793770824393367115298917352334092381609 * c1093(3562802167......)

n=2966: c1482(9090909090......) = 95981284857953712560599708643474527 * c1447(9471543441......)

n=110158: c55078(9090909090......) = 745282464034481898056474303437 * c55049(1219793773......)

n=111854: c55926(9090909090......) = 177644219562011245398893 * c55903(5117480947......)

July 31, 2024 2024 年 7 月 31 日 (-)

# via factordb.com

n=1322: c652(1498294678......) = 32428891213264191224745951834819424405467767 * p608(4620246399......)

n=1322: p608(4620246399......) is proven prime

# 1273 of 300000 Φn(10) factorizations were finished. 300000 個中 1273 個の Φn(10) の素因数分解が終わりました。

August 21, 2024 2024 年 8 月 21 日 (Kurt Beschorner)

n=5681: c4753(1111111111......) = 107401683479315589206835972735096277 * c4718(1034537890......)

# ECM B1=1e6, sigma=0:4319425451299188

n=9374: c4537(1099999999......) = 106678980116741885690755417326646783 * c4502(1031130967......)

# ECM B1=1e6, sigma=0:5204325677688199

n=13855: c10360(8545915907......) = 456647776571096966682457032601 * c10331(1871445859......)

# P-1 B1=200e6

n=13865: c10673(1111099999......) = 18952458289368990140570605351 * c10644(5862564016......)

# P-1 B1=175e6

n=13875: c7152(2513747859......) = 20231400133345763391573474001 * c7124(1242498217......)

# P-1 B1=175e6

n=13877: c13863(1217055110......) = 2665599110827931151219887243864069553535617569 * c13817(4565784501......)

# P-1 B1=175e6

n=13881: c7911(3600326525......) = 613342693696505872009 * c7890(5870008011......)

# P-1 B1=175e6

n=14319: c9073(1001000999......) = 10344827787841879150524132169 * c9044(9676342811......)

# P-1 B1=23e6

n=33411: c18144(9009009909......) = 3967059885436254664099519 * c18120(2270953847......)

# P-1 B1=23e6

n=157561: c157523(1328933416......) = 5998484463028396333 * c157504(2215448627......)

n=157889: c157881(8377728803......) = 6489787974242716681 * c157863(1290909477......)

n=157999: c157942(9459748359......) = 98725868644107347 * c157925(9581833504......)

n=158591: c158555(2790751960......) = 1270898937718055791 * c158537(2195888184......)

n=158731: c158703(1611068019......) = 2774590512897177347 * c158684(5806507347......)

# gr-mfaktc

August 20, 2024 2024 年 8 月 20 日 (Torbjörn Granlund)

# via Kurt Beschorner

n=1651: c1481(3265062187......) = 275217017911139624191776255507977127851519 * c1440(1186359118......)

# ECM B1=1e6, sigma=1:2194818103

n=1841: c1572(9000000900......) = 13025697981837238885482617576986077347 * c1535(6909419297......)

# ECM B1=2e6, sigma=1:2177576267

n=1891: c1765(1234886272......) = 25728430999471065289640031125872987 * c1730(4799695219......)

# ECM B1=5e5, sigma=1:3646079215

n=2099: c2070(1623529005......) = 904895108749261583158479086319155797 * c2034(1794162648......)

# ECM B1=1e6, sigma=120529647102471

n=2305: c1790(8887563402......) = 216435273116164865199941012008081 * c1758(4106337785......)

# ECM B1=1e6, sigma=1:2792610879

n=2321: c2090(8139938846......) = 7819586608885407861280912213052933 * c2057(1040967925......)

# ECM B1=2e6, sigma=144531525929635

n=2361: c1520(9099634074......) = 15093661730388660744164111101395889 * c1486(6028778328......)

# ECM

n=2413: c2268(9000000000......) = 945153149166264948533842733420136547 * c2232(9522266320......)

# ECM B1=1e6, sigma=30278076774429

n=2453: c2199(1414011668......) = 805882633277252112088879931097297947 * p2163(1754612408......)

# ECM B1=2e6, sigma=116639200445373

$ ./pfgw64 -tc -q"9*(10^2453-1)/5129337941570220915834482952864279885533502777195040484557/(10^11-1)/(10^223-1)"
PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8]

Primality testing 9*(10^2453-1)/5129337941570220915834482952864279885533502777195040484557/(10^11-1)/(10^223-1) [N-1/N+1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 2
Running N+1 test using discriminant 5, base 1+sqrt(5)

Calling N+1 BLS with factored part 0.50% and helper 0.36% (1.87% proof)
9*(10^2453-1)/5129337941570220915834482952864279885533502777195040484557/(10^11-1)/(10^223-1) is Fermat and Lucas PRP! (0.1964s+0.0004s)

n=2495: c1955(7429792655......) = 14339967467738136676523658916529111 * c1921(5181178180......)

# ECM B1=1e6, sigma=1:3516144215

n=2817: c1806(6171071017......) = 19763398523108376154207863498493214803 * c1769(3122474614......)

# ECM B1=2e6, sigma=1:1298358369

n=2849: c2129(7867546209......) = 1066161704325642263898000395207191477 * c2093(7379317956......)

# P-1 B1=1e8

n=2921: c2769(1540304638......) = 2318555267727405835742851813721 * p2738(6643381158......)

# ECM B1=5e5, sigma=1:4248825949

$ ./pfgw64 -tc -q"9*(10^2921-1)/13547318429331232298245483147571803/(10^23-1)/(10^127-1)"
PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8]

Primality testing 9*(10^2921-1)/13547318429331232298245483147571803/(10^23-1)/(10^127-1) [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 0.32% and helper 0.04% (1.03% proof)
9*(10^2921-1)/13547318429331232298245483147571803/(10^23-1)/(10^127-1) is Fermat and Lucas PRP! (0.3019s+0.0004s)

n=2995: c2359(7378562894......) = 284277203341019855415851097076878001 * c2324(2595552090......)

# ECM B1=2e6, sigma=53292640982751

n=3303: c2159(1953694834......) = 17001394447702258475801953896133 * c2128(1149137995......)

# ECM B1=1e6, sigma=1:164161343

n=3403: c3265(1137149558......) = 7709805385433232909996248569396122289 * c3228(1474939381......)

# ECM B1=1e6, sigma=756340299292

n=3613: c3578(1935038392......) = 791933522809774878033488285297044583803 * c3539(2443435385......)

# ECM B1=5e5, sigma=1:799608949

n=3811: c3579(9488882300......) = 29858372234782008133506150260148517 * c3545(3177963696......)

# ECM B1=1e6, sigma=1:2792610879

n=3911: c3882(1605469189......) = 18918639432157448162617460631131878973 * c3844(8486176793......)

# ECM B1=5e5, sigma=1:443161973

n=3923: c3908(4950216854......) = 44626167058457804083500990661961 * c3877(1109263282......)

# ECM B1=5e5, sigma=1:2340622139

n=3941: c3369(1141697437......) = 156231445687689775996693860568271 * c3336(7307731375......)

# ECM B1=1e6, sigma=1:121282519

n=3977: c3833(8604608762......) = 2354312200678631452069214594821314015641 * c3794(3654829108......)

# ECM B1=1e6, sigma=756340299292

n=4125: c1986(1432401381......) = 86059536640000496045815898721001 * c1954(1664430738......)

# ECM B1=1e6, sigma=1:2200366123

n=4319: c3696(9000000900......) = 9422301660512506090795954466290799 * c3662(9551807216......)

# ECM B1=3e6, sigma=1:177065869

n=4393: c4155(4081433798......) = 865255910975605274092556312523773 * c4122(4717025040......)

# ECM B1=3e6, sigma=1:173734405

n=4543: c3475(1421954525......) = 588604060502740427330089290043351 * c3442(2415808215......)

# ECM B1=1e6, sigma=1:2991743399

n=4673: c4673(1111111111......) = 4345443283056620687247864599302382797 * c4636(2556956882......)

# ECM B1=1e6, sigma=1:3966327997

n=4757: c4553(3182703923......) = 2801002227013271452145195299558637776841 * c4514(1136273257......)

# ECM B1=1e6, sigma=192084558329613

n=4805: c3660(1999411967......) = 110892774637887477659990433599099441 * c3625(1803013743......)

# ECM B1=5e5, sigma=1:3281332265

n=5239: c4666(1231844950......) = 48210422609883103613072789653231729 * c4631(2555142402......)

# ECM B1=1e6, sigma=80482442127625

n=5331: c3521(1587458188......) = 2816300997574793172646729775188850191 * c3484(5636678003......)

# ECM B1=5e5, sigma=1:1564726371

n=5699: c5494(9302446663......) = 64766941561181774734373002834423813 * c5460(1436295498......)

# ECM B1=5e5, sigma=1:1274567173

n=5785: c4212(3320266223......) = 39654135024926477843166872734614906521 * c4174(8373064300......)

# ECM B1=5e5, sigma=1:1199392889

n=5871: c3662(1711309222......) = 65942014250649795606197848118521 * c3630(2595172806......)

# ECM B1=1e6, sigma=52967061287689

n=5935: c4726(1243689235......) = 712210020588854919195548201211311 * c4693(1746239451......)

# ECM B1=5e5, sigma=1:3855436389

n=5989: c5818(1109863268......) = 36923066507963101716971022287147 * c5786(3005880533......)

# ECM B1=1e6, sigma=52967061287689

n=6001: c5574(1804192358......) = 695816812023656477562394175892797 * c5541(2592912857......)

# ECM B1=5e5, sigma=1:1088594985

n=6323: c6311(2450716538......) = 315438813996319438031657566306729 * c6278(7769229497......)

# ECM B1=25e4, sigma=1:1373130007

n=6367: c6361(4847504771......) = 21345380483323818968803525877502810443 * c6324(2270985412......)

# ECM B1=5e5, sigma=1:1564726371

n=6413: c5693(2171762018......) = 69615667805021500294627143908293 * c5661(3119645457......)

# ECM B1=5e5, sigma=1:1064874425

n=6425: c5095(6969606177......) = 27345173228035282739638463755096201 * c5061(2548751883......)

# ECM B1=5e5, sigma=1:916047441

n=6459: c4251(2429998820......) = 4627697372220068903113651202699449 * c4217(5250989045......)

# ECM

n=6463: c6138(6060549797......) = 33976933348129210891637803696471 * c6107(1783724780......)

# ECM B1=5e5, sigma=1:1064874425

n=6505: c5200(9000090000......) = 771799133272450765286793118681 * c5171(1166118179......)

# ECM

n=6531: c3715(1023846294......) = 20515216490975134970589492865957 * c3683(4990667757......)

# ECM B1=5e5, sigma=1:3134844861

n=6547: c6538(3850113763......) = 26082784537768285040784962616203 * c6507(1476113011......)

# ECM B1=5e5, sigma=1:3186806677

n=6579: c3972(1413158239......) = 30501891916761369005083200765507831649 * c3934(4633018317......)

# P-1 B1=1e8

n=6627: c4292(5732038696......) = 207229602677110354999505334024037 * c4260(2766032759......)

# ECM B1=1e6, sigma=1:3318069251

n=6633: c3953(2376570918......) = 59925833228400736755484667890693 * c3921(3965853773......)

# ECM B1=5e5, sigma=1:4049122495

n=6635: c5228(1365387565......) = 496404891911358902350041179362831 * c5195(2750552195......)

# ECM B1=5e5, sigma=1:1293962689

n=6711: c4437(8966957367......) = 7144586569612918208700259798639 * c4407(1255070154......)

# ECM B1=1e6, sigma=1:1318957861

n=6749: c6320(6409836124......) = 10793463478838927967624074051197 * c6289(5938627705......)

# ECM B1=1e6, sigma=0:180146487010777

n=6827: c6821(2393413517......) = 50807343997336659532852562053547 * c6789(4710762911......)

# ECM B1=1e6, sigma=1:4261948433

n=6853: c5244(2799689690......) = 4407897845005598926599049755323 * c5213(6351530341......)

# ECM B1=1e6, sigma=1:105806636643035

n=6855: c3631(1596817267......) = 813532341364371691666368330069631 * c3598(1962819652......)

# ECM B1=5e5, sigma=1:3404967785

n=6863: c6840(3225399979......) = 45576442660261405454027843005099279363 * c6802(7076901554......)

# ECM B1=5e5, sigma=1:4017018739

n=6885: c3441(3430902391......) = 1199045447656509408148014511681 * c3411(2861361425......)

# ECM B1=1e6, sigma=0:105806636643035

n=6895: c4698(6294751968......) = 345254099442479690466807243161 * c4669(1823222947......)

# ECM B1=5e5, sigma=1:3951530911

n=6983: c6983(1111111111......) = 1016624078655033790209211909154053 * c6950(1092941958......)

# ECM B1=5e5, sigma=1:562663719

n=7011: c4283(3345911144......) = 308573070164753259193607112742747 * c4251(1084317287......)

# ECM B1=5e5, sigma=1:3092943329

n=7027: c6978(1415865114......) = 3270662421470064751270391979111641 * c6944(4328985790......)

# ECM B1=25e4, sigma=1:1767257015

n=7041: c4682(2226830614......) = 350676874085293214078098349707 * c4652(6350092575......)

# ECM B1=1e6, sigma=0:145129032457365

n=7077: c4021(2265560723......) = 13016598920031794002941702559 * c3993(1740516656......)

# ECM B1=5e5, sigma=1:2078807511

n=7079: c7030(3066144079......) = 211936457265809995565760245520973 * c6998(1446728004......)

# ECM B1=5e5, sigma=1:262151673

n=7115: c5637(4620212515......) = 69481578807619036204623270154076561 * c5602(6649550276......)

# ECM B1=5e5, sigma=1:1051968875

n=7155: c3738(6719341833......) = 2363421643121012840509778918901271 * c3705(2843056740......)

# ECM B1=5e5, sigma=1:3855436389

n=7259: c5722(2237391972......) = 8189484816570707340091163330635453 * c5688(2732030185......)

# ECM B1=5e5, sigma=1:3485439623

n=7371: c3825(1969061401......) = 7595905095301842399593540737711 * c3794(2592266987......)

# ECM B1=5e5, sigma=1:3087225587

n=7403: c6713(1195166475......) = 102810485748819791639879926615169 * c6681(1162494727......)

# ECM B1=5e5, sigma=1:714400689

n=7451: c7405(5685462840......) = 1258746002886628455412882180639 * c7375(4516767343......)

# ECM B1=5e5, sigma=1:1210794309

n=7505: c5582(4112525354......) = 1744960597338433533447362115952081 * c5549(2356801271......)

# ECM B1=1e6, sigma=1:1393014461

n=7627: c7286(1606118442......) = 10280281551935956005167840871450787 * c7252(1562329235......)

# ECM B1=5e5, sigma=1:1559371313

n=7751: c7324(1636456105......) = 147104989244161239270656842614006284071 * c7286(1112440926......)

# ECM B1=5e5, sigma=1:4130667131

n=7773: c5155(6223681136......) = 624701770395169312585090935732649 * c5122(9962643666......)

# ECM B1=5e5, sigma=1:1157681981

n=7827: c5199(3019977937......) = 7293854796500084099657229729157 * c5168(4140441538......)

# ECM B1=1e6, sigma=1:1156762131

n=7847: c6238(8915168484......) = 99557767070717924371208413000293881 * c6203(8954769423......)

# ECM

n=7861: c6732(9000000900......) = 898119705955942710848729642627 * c6703(1002093689......)

# ECM B1=5e5, sigma=1:2790569943

n=7889: c6441(2337642263......) = 215231103155467706279277026425453 * c6409(1086108015......)

# ECM B1=5e5, sigma=1:202868745

n=7897: c7696(9000000000......) = 385449578021310700390256413787 * c7667(2334935751......)

# ECM

n=7987: c6769(6351212283......) = 8883682708391634937679236698173 * c6738(7149301131......)

# ECM B1=5e5, sigma=1:2489921303

n=8041: c6708(1005694142......) = 15477413700845533672594920389159 * c6676(6497817798......)

# ECM B1=5e5, sigma=1:3116732165

n=8053: c8026(3692782853......) = 41902595593620392086855271026079 * c7994(8812778305......)

# ECM B1=1e6, sigma=1:1368566913

n=8115: c4291(1475343226......) = 1769701865578466450153518679881 * c4260(8336676675......)

# ECM B1=5e5, sigma=1:3003735203

n=8201: c7966(5430050611......) = 17770709819243095708975667749958463949643 * c7926(3055618299......)

# ECM B1=5e5, sigma=1:3446626047

n=8237: c8205(3084098720......) = 219464278700937029463657983203 * c8176(1405285060......)

# ECM B1=5e5, sigma=1:2790569943

n=8245: c6110(1685109817......) = 4595241096933927040005468109324991 * c6076(3667075963......)

# ECM B1=5e5, sigma=1:4134148097

n=8257: c7863(1008815527......) = 29619972904892450273922341588641 * c7831(3405862424......)

# ECM B1=1e6, sigma=80482442127625

n=8421: c4757(3427432356......) = 891574094727581152824232840516519 * c4724(3844248477......)

# ECM B1=5e5, sigma=1:1903005545

n=8457: c5612(1320470901......) = 16591431242812670951237114925751 * c5580(7958752214......)

# ECM B1=1e6, sigma=9291063370823

n=8477: c7206(4594348897......) = 13155977065160004722127813180227 * c7175(3492214127......)

# ECM B1=5e5, sigma=1:1088594985

n=8537: c8483(1297062658......) = 7068078234757599410245923277 * c8455(1835099465......)

# ECM B1=5e5, sigma=1:1428254743

n=8545: c6832(9000090000......) = 101646283310197475908829512121 * c6803(8854322763......)

# ECM B1=5e5, sigma=1:3087225587

n=8575: c5851(5318117368......) = 5293740271005338383592716601 * c5824(1004604891......)

# ECM B1=5e5, sigma=1:190540483

n=8577: c5707(8319522989......) = 634815482288444139636540572011003 * c5675(1310541916......)

# ECM B1=5e5, sigma=1:149514197612885

n=8639: c8396(1476185028......) = 818877774370128142691864096231 * c8366(1802692752......)

# ECM B1=5e5, sigma=1:2043845067

n=8735: c6947(9297620100......) = 12192865776540531965438812912547431 * c6913(7625459240......)

# ECM B1=5e5, sigma=1:2256808913

n=8737: c8640(1945322428......) = 13361685887895082160085395228039 * c8609(1455895943......)

# ECM B1=5e5, sigma=1:3738655573

n=8745: c4150(1439024999......) = 2272528654159007646526616145391 * c4119(6332263385......)

# ECM B1=1e6, sigma=1:2923719129

n=8829: c5797(2634244196......) = 1513085581534586859396871232498095957759 * c5758(1740975017......)

# ECM B1=5e5, sigma=1:2044862669

n=8869: c7553(1603872975......) = 1628099806387144273085256658529 * c7522(9851195662......)

# ECM B1=5e5, sigma=1:1772750603

n=8959: c8118(8220033671......) = 749539463454661849173837786563 * c8089(1096677903......)

# ECM B1=1e6, sigma=1:2780467357

n=9283: c9218(5725231413......) = 8013308143108550298429503948087441 * c9184(7144654006......)

# ECM B1=5e5, sigma=1:562663719

n=9419: c9414(5897930416......) = 5684469744053776020964152035591 * c9384(1037551553......)

# ECM B1=5e5, sigma=1:121282519

n=9437: c9354(1809502077......) = 1624851391389487899053479556237 * c9324(1113641583......)

# ECM B1=5e5, sigma=1:799608949

n=9473: c9443(4789578625......) = 136213632400294112039787697679 * c9414(3516225609......)

# ECM B1=1e6, sigma=113918028976573

n=9485: c6383(5317559409......) = 308062384945102512389982980881 * c6354(1726130702......)

# ECM B1=25e4, sigma=1:3226404411

n=9655: c7714(3128082216......) = 304548237530189995568241284486281 * c7682(1027122088......)

# ECM B1=5e5, sigma=1:4248825949

n=9725: c7747(6302689926......) = 6266679657139037831692848478951 * c7717(1005746307......)

# ECM B1=5e5, sigma=1:153953135

n=9777: c6470(1306966923......) = 1707913452762899722866250746001 * c6439(7652418928......)

# ECM B1=1e6, sigma=1:1368566913

n=9885: c5256(5500647940......) = 1373181471814143351694865705521 * c5226(4005769123......)

# ECM B1=5e5, sigma=1:2610241785

n=9935: c7899(1373142975......) = 7881330031472834202922901774150160151 * c7862(1742273156......)

# ECM B1=5e5, sigma=1:153953135

# 1272 of 300000 Φn(10) factorizations were finished. 300000 個中 1272 個の Φn(10) の素因数分解が終わりました。

# 213279 of 300000 Φn(10) factorizations were cracked. 300000 個中 213279 個の Φn(10) の素因数が見つかりました。

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