If you go that way, it opens a rabbit hole that just goes on and on.... rational prime, primitive ideals, prime ideals, primaries and semiprimes... ... if p

If you go that way, it opens a rabbit hole that just goes on and on.... rational prime, primitive ideals, prime ideals, primaries and semiprimes... ... if p is a rational prime and d be a squarefree integer, then p is prime in Z[√d] if and only if f_d(x)= x²-d is irreducible mod p.