Using some suitable Lseries for some appropriate ray class group, one can find the Dirichlet density of some set of primes. One can conclude that this set of prime is infinite as long as the density is nonzero. I wonder if this method has been tried for, e.g. regular primes. Perhaps it's not easy to connect the indivisibility with the Frobenius elements? What's so impractical about it for regular primes? (Feel free to close it if this question is too vague of too 'big')
