Sunday, February 25, 2018

[xucvjwda] Pari/GP first-stage ECM time

Number of seconds pari/gp's factorint function spends on other algorithms before trying MPQS for factoring numbers of various sizes (in bits).  Most of that time is spent on the Elliptic Curve Method.  Hardware and software info:

Intel(R) Core(TM)2 Duo CPU E8600 @ 3.33GHz
GP/PARI CALCULATOR Version 2.9.4 (released)
amd64 running linux (x86-64 kernel) 64-bit version
compiled: Jan 16 2018, gcc version 5.4.0 (Funtoo 5.4.0)
threading engine: single

for(n=95,151,p=precprime(2^n);q=precprime(p-1);T=gettime();factorint(p*q,9);print(2*n," ",(gettime()-T)/1e3))

bitsseconds
1900.705
1920.845
1941.060
1961.476
1981.465
2001.868
2021.873
2042.569
2062.584
2083.024
2103.037
2124.180
2144.212
2164.873
2184.869
2206.740
2226.749
2247.681
2268.296
22811.545
23011.524
23213.004
23413.016
23618.164
23818.241
24020.224
24220.256
24425.368
24625.401
24827.845
25034.656
25243.112
25453.389
25669.324
258101.525
260124.821
262154.692
264208.060
266260.192
268325.405
270407.176
272551.669
274692.544
276869.249
2781094.428
2801486.557
2821875.436
2842344.476
2862948.697
2883786.453
2904642.560
2925319.753
2945968.460
2966642.749
2987310.425
3008004.968
3028700.257

One additional data point from a different computer and different software version: 299 bits (10^90-81), 5767.238 s.

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