Einyen
Dec 2003
Denmark
3×17×59 Posts

You want to combine those factors (2kp+1) = +/ 1 (mod 8) with those that can be prime (2kp+1)= +/ 1 (mod 6).
Prime95 already does this, but instead of using +/ 1 mod 6, it uses those numbers mod 120 which can be prime, i.e. those that are coprime with 120:
1,7,11,13,17,19,23,29,31,37,41,43,47,49,53,59,61,67,71,73,77,79,83,89,91,97,101,103,107,109,113,119
Combining the above list with the requirement +/ 1 mod 8 gives 16 residue classes mod 120, which is those 16 Prime95 uses:
1,7,17,23,31,41,47,49,71,73,79,89,97,103,113,119
Your idea gives 20 residue classes mod 120:
1,7,17,23,25,31,41,47,49,55,65,71,73,79,89,95,97,103,113,119
so what Prime95 already uses is more efficient.
