Fwd: p41 factor of P110503 found by ECMNet!

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James Wanless

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Nov 25, 2017, 5:13:51 AM11/25/17
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---------- Forwarded message ----------
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

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Nov 25, 2017, 6:28:45 AM11/25/17
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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                    

3392374757

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

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Nov 25, 2017, 6:35:17 AM11/25/17
to Mersenneplustwo

? #

   timer = 1 (on)

? isprime((2^110503+1)/(3*48832113344350037579071829046935480686609))

time = 22min, 13,813 ms.

%4 = 0


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