Congratulations! (and thanks!) to user [P3D] Crashtest of yoyo@home,
who today found the following 45-digit factor:
128201605404515119370139202836664201936768339
http://www.rechenkraft.net/yoyo/show_user.php?userid=18820
[P3D] Crashtest
random seed = 1292328207
iter = 1000
Bmax = 2000
error_shift = 1000
precision = 10000
N[0] = 128201605404515119370139202836664201936768339
a = 0
b = 89688413221901148323265285010785799341246162
m = 128201605404515119370116568715250501262461267
q = 2223291254715649492350652805622697
P = (1965754593, 60889907444088140269567387611684054357943591)
P1 = (0, 1)
P2 = (53898277912729453733086466028166174057829105,
99992884604099290066056253233347269766285331)
N[1] = 2223291254715649492350652805622697
a = 0
b = 517136918933228623427518117209413
m = 2223291254715649580335686599749543
q = 87107074056883833949344277
P = (3421911252, 1602842038559204797474188390599531)
P1 = (0, 1)
P2 = (1088055996380113964229767495009419,
788744077462490401593545836496284)
N[2] = 87107074056883833949344277
a = 0
b = 5202092132633676772984237
m = 87107074056902004187893139
q = 53197211956017391
P =
(2362625119, 84577898739301293212944978)
P1 = (0, 1)
P2 = (33468624707842766025076354, 18137103533850782215747782)
N[3] = 53197211956017391
a = 0
b = 26179771598127550
m = 53197211605949373
q = 13302628558627
P = (2223124758, 18253021777148979)
P1 = (0, 1)
P2 = (4607961748771082, 44289788572053441)
N[4] = 13302628558627
a = 0
b = 9072964657831
m = 13302635814493
q = 1297944757
P = (1377122123, 11800405242477)
P1 = (0, 1)
P2 = (7213009280011, 9725731475168)
N[5] = 1297944757
a = 0
b = 185543736
m = 1298016769
q = 831529
P = (1186518069, 990249340)
P1 = (0, 1)
P2 = (208628686, 90959236)
proven prime
GP/PARI CALCULATOR Version 2.3.5 (released)
i386 running darwin (ix86 kernel) 32-bit version
compiled: Mar 1 2010, gcc-4.0.1 (Apple Inc. build 5490)
(readline v6.1 enabled, extended help available)
Copyright (C) 2000-2006 The PARI Group
PARI/GP is free software, covered by the GNU General Public License,
and
comes WITHOUT ANY WARRANTY WHATSOEVER.
Type ? for help, \q to quit.
Type ?12 for how to get moral (and possibly technical) support.
parisize = 4000000, primelimit = 500000
? (2^23209+1)%128201605404515119370139202836664201936768339
%1 = 0
? isprime((2^23209+1)/
(3*4688219*27665129*128201605404515119370139202836664201936768339))
%2 = 0