Quote:
Originally Posted by science_man_88
well for the 1/1 mod 8 as well if p=3 mod 8 as I've listed before k = 1,5,9,etc. for 7(1) mod 8 and k=0,4,8,12,16 etc. for 1 mod 8, if p=5 mod 6 to get 1 mod 6 use k=0,3,6,9,etc. ? and for 5 mod 6 k= 1,4,7,etc. ? is so when do k match up for the given mod 8 and mod 6 such that they can equal a common thing number that can be a factor.

Since only primes need to be considered for potential factors, all factors that are not 1 or 5 mod 6 are ignored anyway (all primes over 3 are 1 or 5 mod 6 because all other values mod 6 have 2 and/or 3 as factors). Factors that are 1 mod 6 still have to be tested, as do factors that are 5 mod 6. In the event that it'd be better to test 1 mod 6 and 5 mod 6 factors separately, it might be useful to find out which k's produce which sort of factor and work with that. IIRC, Prime95 does factors within a bit level according to their value mod 120 for efficiency, in which case the value mod 6 isn't at all helpful except in simple implementations.
I don't see any way this can be an improvement on current methods.