Producing class numbers for the Atkin–Morain primality test

Abstract. During the precomputation phase of the Atkin--Morain primality test, a rather big set of negative fundamental discriminants, moreover the class numbers related to these discriminants are produced. In this article, we present a method which allows us to quickly produce negative fundamental discriminants representable on at most eight bytes. Furthermore we give two methods to compute the class numbers related to these discriminants. With the first method, we can quickly acquire the exact value of the class numbers related to discriminants with absolute value up to approximately \(2^{40}\) (depending on the underlying processor), while with the second method we can estimate the order of magnitude of the class numbers.