I have uploaded version 1.5.5x which takes the switch `sr2sieve x X' and only tests for factors of the form p1 (mod X). X doesn't have to be a power of 2 but it is more efficient if it is.
I speculated in another thread about modifying the Sieve of Eratosthenes so that it only sieved numbers of the form N*x+1 for some constant N, but I haven't found a way to do this efficiently, except when N is a power of 2.
Citrix, even if this were done, you talk about finding the factors of (p1)%N, which is another problem altogether. Sr2sieve doesn't need to do this, it only ever looks at the value gcd(p1,N).
Here is the general technique I would use to find the factors of gcd(p1,N).
0. Precompute T[0] ... T[N1] where T[i] contains the factors of gcd(i,N).
1. For any p > 0, the factors of gcd(p1,N) are T[(p1)%N].
This only requires one division per p and so is a huge improvement over computing (p1)%n for each divisor n of N. However it can't be used to find factors of (p1)%N that are not themselves divisors of N.
