37-digit factor of (M+2)6972593 by ECM by mprime287-OSX
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bearnol
Jul 28, 2016, 9:13:36 AM7/28/16
to Mersenneplustwo
[Thu Jul 28 12:45:55 2016]
ECM found a factor in curve #9, stage #2
Sigma=8552762875224071, B1=250000, B2=25000000.
2^6972593+1 has a factor: 2194866270224408542085820822929656883 (ECM curve 9, B1=250000, B2=25000000)
Desmond:~ james$ gp
GP/PARI CALCULATOR Version 2.7.4 (released)
i386 running darwin (ix86/GMP-6.1.0 kernel) 32-bit version
compiled: Jan 8 2016, gcc version 4.2.1 (Apple Inc. build 5566)
threading engine: single
(readline v6.3 enabled, extended help enabled)
Copyright (C) 2000-2015 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
? (2^6972593+1)%2194866270224408542085820822929656883
%1 = 0
Desmond:~ james$ time (echo '2194866270224408542085820822929656883' | bc | tr -d '\\\n';echo) | math/superfac13.gmp-5.0.1.intelOSX.64.static -e
random seed = 1470363838
base = 5630236039100
number to be tested:
2194866270224408542085820822929656883
real 0m0.149s
user 0m0.003s
sys 0m0.009s
Desmond:~ james$ time (echo '2194866270224408542085820822929656883' | bc | tr -d '\\\n';echo) | math/gmp-ecpp/atkin249.gmp-5.0.1.intelOSX.64.static -q
random seed = 1470137201
error_shift = 1000
precision = 10000
Bmax = 2000
Dmax = 20
D = -7, dT = 1, T = 1 3375
j = 2194866270224408542085820822929653508
N[0] = 2194866270224408542085820822929656883
a = 2194866270224408526780992933140071008
b = 28337836114962828884190647250
m = 2194866270224408545032416859420428216
q = 72910993895488139836517
P = (1135671538, 1741809689898580248188958060507679337)
P1 = (0, 1)
P2 = (1507444324223652903356135995612067124, 2087068925727312392896071726142671611)
Bmax = 2000
Dmax = 20
N[1] = 72910993895488139836517
a = 34368474992492162973699
b = 0
m = 72910993896027949692826
q = 58730716094293
P = (5178518, 3966922935770883953142)
P1 = (0, 1)
P2 = (53172871450457178143871, 25366148950126915395716)
Bmax = 2000
Dmax = 20
N[2] = 58730716094293
a = 0
b = 51259156670498
m = 58730729559327
q = 310744600843
P = (1963021566, 42941379676878)
P1 = (0, 1)
P2 = (26375785484748, 25351985164855)
Bmax = 2000
Dmax = 20
N[3] = 310744600843
a = 0
b = 88066107172
m = 310745644657
q = 1032377557
P = (4155116731, 291096994565)
P1 = (0, 1)
P2 = (119309558636, 227347585524)
proven prime
real 0m15.354s
user 0m7.474s
sys 0m0.090s
Desmond:~ james$ time (echo '2194866270224408542085820822929656882' | bc | tr -d '\\\n';echo) | math/superfac13.gmp-5.0.1.intelOSX.64.static -e
random seed = 1470387723
base = 1073502604706218
number to be tested:
2
41
251
163
B=1000, curve#3, a=1011667363237984
11239
B=1000, curve#2, a=639299761952432
6972593
8348547057289890151
real 0m0.149s
user 0m0.110s
sys 0m0.007s
Desmond:~ james$ time (echo '2194866270224408542085820822929656884' | bc | tr -d '\\\n';echo) | math/superfac13.gmp-5.0.1.intelOSX.64.static -e
random seed = 1470212783
base = 895195987903688
number to be tested:
2
2
3
151
1211294851117223257221755421042857
real 0m0.012s
user 0m0.003s
sys 0m0.006s
sage: def FindGroupOrder(p,s):
... K = GF(p)
... v = K(4*s)
... u = K(s^2-5)
... x = u^3
... b = 4*x*v
... a = (v-u)^3*(3*u+v)
... A = a/b-2
... x = x/v^3
... b = x^3 + A*x^2 + x
... E = EllipticCurve(K,[0,b*A,0,b^2,0])
... return factor(E.cardinality())
sage: FindGroupOrder(2194866270224408542085820822929656883,8552762875224071)
2^3 * 3 * 7 * 127 * 977 * 1607 * 28493 * 130483 * 134807 * 225569 * 579563
bearnol
Oct 12, 2016, 1:35:15 PM10/12/16
to Mersenneplustwo
[Wed Oct 12 18:33:08 2016]
2^6972593+1/known_factors is not prime. RES64: 5D89531357882463. Wd9: A4277B69,00000000
Known factors used for PRP test were: 3,142921867730820791335455211,2194866270224408542085820822929656883
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