Quote from: bob123 on March 30, 2018, 08:32:46 PM

Quote from: c_demian on March 27, 2018, 10:32:44 PM

It's a challenging proposal.
Prime numbers and numbers having small factors can be ruled out easily. Primality test is much faster than factoring and there are algorithms which are very fast in finding small factors (see elliptic curve factoring).

Factorization of large numbers usually means 1024 bit (obsolte) or 2048 bit numbers (4096 bit would be recommended to be on the safe side).
Those numbers are incredibly big (about 600+ digits long).

Quote from: c_demian on March 27, 2018, 10:32:44 PM

This could also lead to finding new factoring algorithms.

Quite a few organisations have an incentive to find factoring algorithms with a better runtime.
Until now there hasn't been made any considerable progress in solving this problem.

Yup right on. I think for our purposes we will be working primarily on the 100-200 digit range. Still gnfs sieve is the best known way to either look for factors or to determine if these numbers are prime. Finding one factor of a given length is much easier to do (or prove you can't do) than to prove a mumber is prime.