Let F be an algebraic number field and let P_F(r) denote the number of nonassociated prime elements of absolute field norm less than or equal to r in the corresponding ring of integers. Using information about the absolute field norms of prime elements and Chebotarev's density theorem, we readily show that when F is a Galois extension of Q, it is the case that P_F is asymptotic to (1/h)π, where π is the standard prime-counting function and h is the class number of F. Along the way, we pick up some well-known facts on the realizability of certain prime numbers in terms of those binary quadratic forms associated with the field norm over a ring of integers that is a unique factorization domain.