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April 28, 2026 2026 年 4 月 28 日 (Kurt Beschorner)

n=4079: c4046(1527972583......) = 426915461085826624259143920722034774479 * c4007(3579098726......)

# ECM B1=1e6, sigma=7104292139681039

n=12223: c11477(9127227149......) = 6369097247405237468604340064437 * c11447(1433048797......)

# ECM B1=1e6, sigma=4266251454290015

n=12233: c11274(3606443994......) = 22472722653715903146492540430914710329 * c11237(1604809550......)

# ECM B1=1e6, sigma=4346254638954307

n=12247: c11867(2095401124......) = 2776545656296308111024907187 * c11839(7546791531......)

# ECM B1=1e6, sigma=5666394773832634

n=12250: c4188(3669243430......) = 621878902495839421287137521938451694251 * c4149(5900253916......)

# ECM B1=3e6, sigma=5389300061366745

n=12264: c3418(4082981731......) = 3141173557231484342233218217422101569 * c3382(1299826850......)

# ECM B1=5e6, sigma=3950502677650097

April 27, 2026 2026 年 4 月 27 日 (Alfred Eichhorn)

# via Kurt Beschorner

n=57077: c57077(1111111111......) = 3848471893272271808963508973 * c57049(2887148826......)

# ECM B1=1e6, sigma=0:4742462032411031

n=61469: c61469(1111111111......) = 698138979099137779882713720563 * c61439(1591532838......)

# ECM B1=1e6, sigma=7844869317150916

n=61519: c61519(1111111111......) = 3592374185368400157663594959 * c61491(3092971538......)

# ECM B1=1e6, sigma=0:2912591680432495

April 27, 2026 2026 年 4 月 27 日 (A.C.)

n=1909: p1763(3987531140......) is proven

# https://stdkmd.net/nrr/cert/Phi/#CERT_PHI_1909_10

April 27, 2026 2026 年 4 月 27 日 (Kurt Beschorner)

n=1909: c1804(9000000000......) = 225703566525345000237290241654276163965649 * p1763(3987531140......)

# ECM B1=20e6, sigma=5168216469123288

n=12240: c3064(4079663740......) = 263000468346705414367562319148772641 * c3029(1551200180......)

# ECM B1=3e6, sigma=4513911137171856

n=12256: c6107(8159202356......) = 43376467754503927150112444601064993 * c6073(1881020465......)

# ECM B1=1.5e6, sigma=6872108156273792

n=20163: c10995(4623079054......) = 721292645808181608827351401 * c10968(6409436005......)

# P-1 B1=50e6

n=33606: c11186(2623476399......) = 230893953674075061463927 * c11163(1136225682......)

# P-1 B1=120e6

n=33607: c28800(9000000900......) = 5964387365159475570403 * c28779(1508956469......)

# P-1 B1=50e6

n=33609: c21051(1501219233......) = 48248595085802769587549417191 * c21022(3111425795......)

# P-1 B1=50e6

n=100814: c40824(9090910000......) = 776396116921274123891 * c40804(1170911317......)

# P-1 B1=120e6

n=100818: c33578(3047841132......) = 54821518733674447939 * c33558(5559570773......)

# P-1 B1=120e6

n=100822: c50379(8914460306......) = 8152588103725941068097397481 * c50352(1093451575......)

# P-1 B1=120e6

n=100830: c26852(1949028251......) = 394392699271528282561 * c26831(4941846680......)

# P-1 B1=120e6

April 26, 2026 2026 年 4 月 26 日 (NFS@Home)

n=784: c265(7992725630......) = 289541217302474902147738712574747645681665598761448687795987839125906245176246519610151449976343537460699905766689 * p152(2760479390......)

# snfs

April 9, 2026 2026 年 4 月 9 日 (Kurt Beschorner)

n=12183: c7784(1199104518......) = 109821907852656265834529348424560071 * c7749(1091862763......)

# ECM B1=1e6, sigma=7051987285101674

n=12185: c9744(9000090000......) = 130322056866604174556330887201 * c9715(6906037410......)

# ECM B1=1e6, sigma=2275484587771368

n=12187: c10372(3947440503......) = 4331894187607779562471947940622489759 * c10335(9112504444......)

# ECM B1=1e6, sigma=899074588164263

n=12197: c12139(1125672810......) = 281192396724953094378341698240982668717 * c12100(4003212118......)

# ECM B1=1e6, sigma=1544402678692367

n=12198: c3785(8911801886......) = 100121059314668298378348902933673188089 * p3747(8901026365......)

# ECM B1=3e6, sigma=6858696947538165

$ ./pfgw64 -tc -q"91*(10^19+1)*(10^107+1)*(10^4066-10^2033+1)/1022354010291092039862560981007071415649878538699338460526954692249201/(10^57+1)/(10^321+1)"
PFGW Version 4.0.3.64BIT.20220704.Win_Dev [GWNUM 29.8]

Primality testing 91*(10^19+1)*(10^107+1)*(10^4066-10^2033+1)/1022354010291092039862560981007071415649878538699338460526954692249201/(10^57+1)/(10^321+1) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 2+sqrt(11)

Calling N-1 BLS with factored part 0.27% and helper 0.12% (0.94% proof)
91*(10^19+1)*(10^107+1)*(10^4066-10^2033+1)/1022354010291092039862560981007071415649878538699338460526954692249201/(10^57+1)/(10^321+1) is Fermat and Lucas PRP! (0.6468s+0.0005s)

n=12199: c11062(1042569824......) = 1739280392832343482352334226643081 * c11028(5994259627......)

# ECM B1=1e6, sigma=1208315919345894

n=12201: c6878(5298946632......) = 109836927317630094632408443 * c6852(4824376247......)

# ECM B1=1e6, sigma=3736292984657857

n=12220L: c2182(6756713074......) = 6973238477503511321447740394630472080633701 * c2139(9689490896......)

# ECM B1=11e6, sigma=1197379811455370

n=33604: c16180(2877998774......) = 291531278012433218181442837529809 * c16147(9872006854......)

# P-1 B1=120e6

n=100807: c86393(1867772414......) = 760773901018618018808663640224203 * c86360(2455095280......)

# P-1 B1=50e6

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