[Cado-nfs-discuss] unbearably slow factorization

mike at mikepage.us mike at mikepage.us
Fri Jan 26 17:07:19 CET 2018

I tried to factor the following with cado-nfs:
> ./cado-nfs.py 45092142015619504885545233428956286716628249204022412001730233506211619093779816252705400749792379537111120400056001524660779352594720896883613951409971968610022842465256891175311

after several hours I killed it
the last few lines of output:
> Info:HTTP server: Sending workunit c180_polyselect1_270000-275000 to client localhost
> Info:Polynomial Selection (size optimized): Adding workunit c180_polyselect1_320000-325000 to database
> Info:Polynomial Selection (size optimized): Parsed 160 polynomials, added 3 to priority queue (has 100)
> Info:Polynomial Selection (size optimized): Worst polynomial in queue now has lognorm 50.620000
> Info:Polynomial Selection (size optimized): Marking workunit c180_polyselect1_260000-265000 as ok (5.3% => ETA Fri Feb  2 10:55:20 2018)

(ETA was 8 days!!!!)

I was trying to verify the factorization that maxima produced in relatively short order:
> (%o1) 17*2652478942095264993267366672291546277448720541413083058925307853306565829045871544276788279399551737477124729415058913215339961917336523346094938318233645212354284850897464186783

maxima uses trial divisions by primes up to 9973, Pollard's rho and p-1 method and elliptic curves but not nfs.

Is this just an issue with suitability of the algorithm? Why is nfs such a poor performer on this input?

Mike Page
Theory and Practice, LLC
mike at mikepage.us

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