30-digit factor of (M+2)42643801 by ECM by mprime287-OSX

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bearnol

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May 12, 2019, 4:57:02 AM5/12/19
to Mersenneplustwo

[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]


bearnol

unread,
Jun 17, 2019, 6:54:14 AM6/17/19
to Mersenneplustwo
[Mon Jun 17 11:45:51 2019]
2^42643801+1/3/405661842777846034141594389769 is not prime.  RES64: 3C8F4A9ECB47213F. We10: B7E878A9,00000000

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