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).
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.