I'm Interested in finding irreducibles in Dedekind domains, (and especially integer rings) in an efficient manner. I've tried to look around a bit but found no papers on this (admittedly my paper searching skills need more work). So I'll appreciate links to any generalizations of the sieve of Eratosthenes to other rings, even if its just to other PID's.
EDIT: should this be moved to mathoverflow (or is it too basic for there)?