The author gives a method, similar to the sieve of Eratosthenes, for finding the numbers less than a given bound that are norms of primes in a given quadratic field with unique factorization. There are given an extensive background of number theory, and a Pascal program to implement the method and plot the primes \(x+ \omega y\) (where 1, \(\omega\) is a basis of the field) for \(x\) and \(y\) within given bounds. The paper is illustrated with plots for 16 fields.