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Old 2020-11-05, 01:38   #11
Batalov
 
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"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

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It takes about 2 hrs for the Stage 1 and another hour for Stage 2 (and not too much RAM) to reproduce this ECM hit.
As it was originally found, it was perhaps a 12-15 CPUhour run, you know, 7 yrs ago, per curve - or in this case the lucky curve.
Code:
GMP-ECM 7.0.4 [configured with GMP 6.1.2, --enable-asm-redc] [ECM]
Tuned for x86_64/k8/params.h
Running on ip-172-31-27-255
Input number is (7^337+1)/808161122051378212567896018011524822258323205672 (237 digits)
Using MODMULN [mulredc:1, sqrredc:1]
Using B1=1150000000, B2=8000000000000, polynomial Dickson(30), sigma=0:3882127693
dF=524288, k=3, d=5705700, d2=17, i0=185
Expected number of curves to find a factor of n digits:
35      40      45      50      55      60      65      70      75      80
15      47      162     624     2636    12164   60183   318529  1793599 1.1e+07
Step 1 took 7573043ms
Using 28 small primes for NTT
Estimated memory usage: 2.64GB
Initializing tables of differences for F took 503ms
Computing roots of F took 89201ms
Building F from its roots took 159581ms
Computing 1/F took 79996ms
Initializing table of differences for G took 694ms
Computing roots of G took 70110ms
Building G from its roots took 167132ms
Computing roots of G took 69881ms
Building G from its roots took 167327ms
Computing G * H took 39791ms
Reducing  G * H mod F took 39970ms
Computing roots of G took 69782ms
Building G from its roots took 168006ms
Computing G * H took 39928ms
Reducing  G * H mod F took 39915ms
Computing polyeval(F,G) took 312713ms
Computing product of all F(g_i) took 367ms
Step 2 took 1517151ms
********** Factor found in step 2: 16559819925107279963180573885975861071762981898238616724384425798932514688349020287
Found prime factor of 83 digits: 16559819925107279963180573885975861071762981898238616724384425798932514688349020287
Prime cofactor ((7^337+1)/808161122051378212567896018011524822258323205672)/16559819925107279963180573885975861071762981898238616724384425798932514688349020287 has 155 digits
Peak memory usage: 3194MB
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