Fwd: p41 factor of P110503 found by ECMNet!
James Wanless
From: bea...@gmail.com
Date: Sat, 25 Nov 2017 03:11:51
Subject: p41 factor of P110503 found by ECMNet!
To: bea...@gmail.com, ja...@grok.ltd.uk
A factor was found for P110503 using GMP-ECM using factor method ECM
Candidate number: (2^110503+1)/(3)
Factor: 48832113344350037579071829046935480686609
Factor Type: probable
Factor Length: 41
Co-Factor: ((2^110503+1)/(3))/48832113344350037579071829046935480686609
Co-Factor Type: Composite
Co-Factor Length: 60
B1: 11000000
Sigma: 3406623784
Finder: ja...@grok.ltd.uk
Found on machine: simply151
bearnol
simply15 is a 2013 Mac Pro running OS X El Capitan
James-Wanlesss-iMac:~ james$ gp
GP/PARI CALCULATOR Version 2.9.3 (released)
i386 running darwin (ix86/GMP-6.1.2 kernel) 32-bit version
compiled: Aug 6 2017, gcc version 4.2.1 (Apple Inc. build 5566)
threading engine: single
(readline v7.0 enabled, extended help enabled)
Copyright (C) 2000-2017 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 ?15 for how to get moral (and possibly technical) support.
parisize = 4000000, primelimit = 500000
? (2^110503+1)%48832113344350037579071829046935480686609
%1 = 0
James-Wanlesss-iMac:~ james$ time (echo '48832113344350037579071829046935480686609' | bc | tr -d '\\\n';echo) | math/superfac13.gmp-5.0.1.intelOSX.64.static -erandom seed = 1511924281base = 835905351153474
number to be tested:
48832113344350037579071829046935480686609
real 0m0.120s
user 0m0.003s
sys 0m0.008s
James-Wanlesss-iMac:~ james$ time (echo '48832113344350037579071829046935480686609' | bc | tr -d '\\\n';echo) | math/gmp-ecpp/atkin249.gmp-5.0.1.intelOSX.64.static -q
random seed = 1512600179
error_shift = 1000
precision = 10000
Bmax = 2000
Dmax = 20
N[0] = 48832113344350037579071829046935480686609
a = 0
b = 48832113344350037579071829046935480686608
m = 48832113344350037579459708146112303642916
q = 7663854484999687501449518245549
P = (2490310922, 31355246817231292866851838447157978268557)
P1 = (0, 1)
P2 = (29308242383031782077788666367852866715432, 27829858038012516711045073975601067032556)
Bmax = 2000
Dmax = 20
N[1] = 7663854484999687501449518245549
a = 0
b = 6657947519172774395554284478305
m = 7663854484999682260431615485383
q = 228778604883718387427434117
P = (3389354290, 2138960044604277682139439191608)
P1 = (0, 1)
P2 = (5587609936487760657508455261191, 6688800768502766812488032296410)
Bmax = 2000
Dmax = 20
N[2] = 228778604883718387427434117
a = 0
b = 73138674788851727027151171
m = 228778604883745011832560903
q = 5300364873980612701
P = (3432869928, 134508598441202348032727140)
P1 = (0, 1)
P2 = (121453167460359516912767858, 155790857164186222235361353)
Bmax = 2000
Dmax = 20
N[3] = 5300364873980612701
a = 0
b = 2934354062901869592
m = 5300364878380693081
q = 143253104821099813
P = (2217038959, 2663400417555069150)
P1 = (0, 1)
P2 = (932032347286313910, 3777327221936504224)
Bmax = 2000
Dmax = 20
N[4] = 143253104821099813
a = 0
b = 139157170117027208
m = 143253105542729497
q = 2923532766178153
P = (1326136590, 111231681134269572)
P1 = (0, 1)
P2 = (100317242527704367, 51292949633521736)
Bmax = 2000
Dmax = 20
N[5] = 2923532766178153
a = 0
b = 1362179953127537
m = 2923532663088199
q = 40928065729
P = (472047447, 1626959294526040)
P1 = (0, 1)
P2 = (712874315149114, 1359213352047922)
Bmax = 2000
Dmax = 20
N[6] = 40928065729
a = 0
b = 31187889566
m = 40928469007
q = 560663959
P = (127362889, 34568479681)
P1 = (0, 1)
P2 = (20023181451, 26768795926)
proven prime
real 0m5.996s
user 0m2.469s
sys 0m0.011s
James-Wanlesss-iMac:~ james$ time (echo '48832113344350037579071829046935480686608' | bc | tr -d '\\\n';echo) | math/superfac13.gmp-5.0.1.intelOSX.64.static -e
random seed = 1512252683
base = 687380794183685
number to be tested:
2
2
2
2
3
17
3
11
B=1000, curve#1, a=81109792381474
110503
B=1000, curve#18, a=269750034805679
71096109191
230824295397187136107
real 0m1.068s
user 0m0.509s
sys 0m0.008s
James-Wanlesss-iMac:~ james$ time (echo '48832113344350037579071829046935480686610' | bc | tr -d '\\\n';echo) | math/superfac13.gmp-5.0.1.intelOSX.64.static -e
random seed = 1512434132
base = 1002970983339262
number to be tested:
2
5
7
7
7
B=1000, curve#7, a=868752034803118
B=10000, curve#5, a=970059549974759
38702181493
108435661156566427
real 0m6.728s
user 0m2.772s
sys 0m0.012s
? FindGroupOrder(p,s)=
{
K = Mod(1,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 = ellinit([0,b*A,0,b^2,0],K);
factor(ellcard(E))
}
%2 = (p,s)->K=Mod(1,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=ellinit([0,b*A,0,b^2,0],K);factor(ellcard(E))
? FindGroupOrder(48832113344350037579071829046935480686609,3406623784)
%3 =
[ 2 5]
[ 3 3]
[ 5 1]
[ 23 1]
[ 89 1]
[ 226381 1]
[ 465587 1]
[ 1368841 1]
[ 5388107 1]
[7103524693 1]
bearnol
? #
timer = 1 (on)
? isprime((2^110503+1)/(3*48832113344350037579071829046935480686609))
time = 22min, 13,813 ms.
%4 = 0