Let F be an algebraic number field and let PF (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 PF 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

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... 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.