21-digit factor of (M+2)24036583 by ECM by mprime287-OSX
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bearnol
Mar 25, 2016, 4:42:56 PM3/25/16
to Mersenneplustwo
[Fri Mar 25 20:14:38 2016]
ECM found a factor in curve #16, stage #2
Sigma=5314873301490973, B1=50000, B2=5000000.
2^24036583+1 has a factor: 455181217684410622619 (ECM curve 16, B1=50000, B2=5000000)
bearnol
Mar 25, 2016, 5:08:44 PM3/25/16
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Last login: Fri Mar 25 20:39:43 on ttys009
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
? allocatemem()
*** Warning: new stack size = 8000000 (7.629 Mbytes).
? allocatemem()
*** Warning: new stack size = 16000000 (15.259 Mbytes).
? (2^24036583+1)%455181217684410622619
%1 = 0
Last login: Fri Mar 25 20:44:23 on ttys009
Desmond:~ james$ time (echo '455181217684410622619' | bc | tr -d '\\\n';echo) | math/superfac13.gmp-5.0.1.intelOSX.64.static -e
random seed = 1459253457
base = 334743767880155
number to be tested:
455181217684410622619
real 0m0.102s
user 0m0.003s
sys 0m0.008s
Last login: Fri Mar 25 20:46:50 on ttys009
Desmond:~ james$ time (echo '455181217684410622619' | bc | tr -d '\\\n';echo) | math/gmp-ecpp/atkin249.gmp-5.0.1.intelOSX.64.static -q
random seed = 1459733368
error_shift = 1000
precision = 10000
Bmax = 2000
Dmax = 20
D = -7, dT = 1, T = 1 3375
j = 455181217684410619244
N[0] = 455181217684410622619
a = 188457790620877978551
b = 215257913531894796876
m = 455181217692645779344
q = 49822812794729179
P = (3255586162, 54906830921564357010)
P1 = (0, 1)
P2 = (359474768629975765988, 141895521847808930582)
Bmax = 2000
Dmax = 20
N[1] = 49822812794729179
a = 0
b = 37923282798539717
m = 49822813240715277
q = 384718777
P = (3469781179, 9622552739963585)
P1 = (0, 1)
P2 = (30508691094970981, 17720035939055317)
proven prime
real 0m27.680s
user 0m7.285s
sys 0m0.072s
Last login: Fri Mar 25 20:51:47 on ttys009
Desmond:~ james$ time (echo '455181217684410622618' | bc | tr -d '\\\n';echo) | math/superfac13.gmp-5.0.1.intelOSX.64.static -e
random seed = 1459666525
base = 802567581021567
number to be tested:
2
151
B=1000, curve#4, a=465303791772859
62705359373
24036583
real 0m0.174s
user 0m0.091s
sys 0m0.006s
Last login: Fri Mar 25 20:52:03 on ttys009
Desmond:~ james$ time (echo '455181217684410622620' | bc | tr -d '\\\n';echo) | math/superfac13.gmp-5.0.1.intelOSX.64.static -e
random seed = 1459302543
base = 1059909689910419
number to be tested:
2
2
3
5
7586353628073510377
real 0m0.015s
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(455181217684410622619,5314873301490973)
2^4 * 3^2 * 5 * 13 * 19 * 23 * 587 * 46103 * 4112063
bearnol
May 15, 2016, 3:26:04 AM5/15/16
to Mersenneplustwo
[Sun May 15 03:44:58 2016]
2^24036583+1/known_factors is not prime. RES64: 6E7F4102939E99AC. Wd9: 1165A6A9,00000000
Known factors used for PRP test were: 3,11681779339,455181217684410622619,228826184600325074341662763
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