30-digit factor of (M+2)42643801 by ECM by mprime287-OSX
bearnol
[Sun May 12 04:55:25 2019]
ECM found a factor in curve #316, stage #2
Sigma=8871782200919076, B1=250000, B2=25000000.
2^42643801+1 has a factor: 405661842777846034141594389769 (ECM curve 316, B1=250000, B2=25000000)
? (2^42643801+1)%405661842777846034141594389769
%1 = 0
Jamess-iMac:~ james$ time (echo '405661842777846034141594389769' | bc | tr -d '\\\n';echo) | documents/math/gmp-ecpp/atkin249.gmp-5.0.1.intelOSX.64.static -q
random seed = 1558445829
error_shift = 1000
precision = 10000
Bmax = 2000
Dmax = 20
N[0] = 405661842777846034141594389769
a = 0
b = 305957169152383985576123323488
m = 405661842777847306649228653521
q = 61716391720347985189293877
P = (172087199, 24959468906914807928510779403)
P1 = (0, 1)
P2 = (198828239360384528004004808345, 18091630342094185508387189181)
Bmax = 2000
Dmax = 20
N[1] = 61716391720347985189293877
a = 0
b = 46946159022935209131707423
m = 61716391720362558130291317
q = 681802422221161
P = (1819183051, 30288874779996084323037518)
P1 = (0, 1)
P2 = (12683047143957997412904494, 11617497073318558434741179)
Bmax = 2000
Dmax = 20
N[2] = 681802422221161
a = 0
b = 681802422221160
m = 681802472101188
q = 56816872675099
P = (3471062812, 572392737858156)
P1 = (0, 1)
P2 = (449747382754215, 604341223954645)
Bmax = 2000
Dmax = 20
N[3] = 56816872675099
a = 0
b = 17192193375390
m = 56816862437397
q = 18938954145799
P = (1741274583, 16295145393174)
P1 = (0, 1)
P2 = (14399757274374, 53623318225982)
Bmax = 2000
Dmax = 20
N[4] = 18938954145799
a = 0
b = 4635848237997
m = 18938960534773
q = 7058551
P = (309909654, 1057067057897)
P1 = (0, 1)
P2 = (9871670682869, 8131771833836)
proven prime
real 0m2.016s
user 0m1.643s
sys 0m0.009s
Jamess-iMac:~ james$ time (echo '405661842777846034141594389768' | bc | tr -d '\\\n';echo) | documents/math/superfac/superfac13.gmp-5.0.1.intelOSX.64.static -e
random seed = 1558367693
base = 992183559187916
number to be tested:
2
2
2
3
B=1000, curve#2, a=776548786142907
42643801
396366561752087986307
real 0m0.133s
user 0m0.060s
sys 0m0.006s
Jamess-iMac:~ james$ time (echo '405661842777846034141594389770' | bc | tr -d '\\\n';echo) | documents/math/superfac/superfac13.gmp-5.0.1.intelOSX.64.static -e
random seed = 1557978863
base = 1018015964134473
number to be tested:
2
5
23
B=1000, curve#1, a=468166911562995
526627
B=1000, curve#2, a=1020638154989229
1346773
2486788215051769
real 0m0.056s
user 0m0.051s
sys 0m0.006s
? 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(405661842777846034141594389769,8871782200919076)
%3 =
[ 2 4]
[ 3 2]
[ 3037 1]
[ 7589 1]
[ 38183 1]
[ 43777 1]
[ 90803 1]
[805297 1]