26-digit factor of (M+2)82589933 by ECM by mprime287-OSX
bearnol
[Mon May 25 06:42:23 2020]
ECM found a factor in curve #27, stage #2
Sigma=2912612216072525, B1=250000, B2=25000000.
2^82589933+1 has a factor: 17973642059656480077259129 (ECM curve 27, B1=250000, B2=25000000)
? (2^82589933+1)%17973642059656480077259129
%1 = 0
Jamess-iMac:~ james$ time (echo '17973642059656480077259129' | bc | tr -d '\\\n';echo) | documents/math/gmp-ecpp/atkin251 -q
random seed = 1591114572
error_shift = 1000
precision = 10000
Bmax = 2000
Dmax = 20
N[0] = 17973642059656480077259129
a = 0
b = 11749563742650692115849481
m = 17973642059663872473380901
q = 47013473708893
P = (3929325902, 11080135350800411226844225)
P1 = (0, 1)
P2 = (9977524242683966744807853, 11501345732412404543760482)
Bmax = 2000
Dmax = 20
N[1] = 47013473708893
a = 0
b = 46131236257413
m = 47013460724991
q = 15671153574997
P = (4104368483, 40069241088063)
P1 = (0, 1)
P2 = (16602596174452, 1968292754651)
Bmax = 2000
Dmax = 20
N[2] = 15671153574997
a = 0
b = 10214535812815
m = 15671161340793
q = 248748592711
P = (485075308, 6635568045708)
P1 = (0, 1)
P2 = (12454839960377, 3103851943846)
Bmax = 2000
Dmax = 20
N[3] = 248748592711
a = 0
b = 178189128735
m = 248749580793
q = 1692174019
P = (650158144, 88430893777)
P1 = (0, 1)
P2 = (56587880963, 215354843270)
Bmax = 2000
Dmax = 20
N[4] = 1692174019
a = 0
b = 407224654
m = 1692233292
q = 898213
P = (662673500, 1292498287)
P1 = (0, 1)
P2 = (1351363812, 64130366)
proven prime
real 0m6.412s
user 0m4.079s
sys 0m0.036s
Jamess-iMac:~ james$ time (echo '17973642059656480077259128' | bc | tr -d '\\\n';echo) | documents/math/superfac/superfac13 -e
random seed = 1590555434
base = 351386229831369
number to be tested:
2
2
2
3
743
B=1000, curve#1, a=975427523169956
82589933
B=1000, curve#1, a=96456237293623
12377
986037719
real 0m0.139s
user 0m0.052s
sys 0m0.014s
Jamess-iMac:~ james$ time (echo '17973642059656480077259130' | bc | tr -d '\\\n';echo) | documents/math/superfac/superfac13 -e
random seed = 1590420970
base = 1063110314487780
number to be tested:
2
5
37
B=1000, curve#1, a=254121976639030
338161
143651724983201909
real 0m0.037s
user 0m0.028s
sys 0m0.013s
? 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(17973642059656480077259129,2912612216072525)
%3 =
[ 2 2]
[ 3 4]
[ 13 1]
[ 19 1]
[ 491 1]
[ 859 1]
[ 8539 1]
[ 9103 1]
[6850589 1]
bearnol
[Sat Jul 11 19:21:00 2020]
2^82589933+1/3/17973642059656480077259129 is not prime. RES64: 460157BF4252EB66. We10: C404A363,00000000