Quote:
Originally Posted by schickel
PS. Clifford has mentioned the required form for a factorization to result in losing the 3, but I'm haven't been able to find that email yet....

I think it's something like this:
All primes congruent to 1 mod 3 must be raised to
an odd power Edit: a power n with n != 2 mod 3. (since nearly all large factors will be ^1, this is the more important of the two; Edit: simplistically, in practice, this means you want the factors to be 1 mod 3)
All primes congruent to 2 mod 3 must be raised to an even power
Quote:
Originally Posted by Batalov
Don't forget  3 comes and goes... See for example 611156.

Yes, it does. Still, it's more hopeful when it's gone.