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Let d be the discriminant of a quadratic field, h(d) the class-number of the field and Xd the character (mod I dj) given by Xd(n) = (d/n) (Kronecker symbol). If we restrict d to values <-8 with h(d) = 1 then I dj is a prime_3 (mod 8) and it has recently been proved [I], [4] that d ? 163. The purpose of this note is to show that Gelfond and Linnik missed an opportunity to prove this result in 1949. Let k be the discriminant of a real quadratic field and Ec the fundamental unit of Q(x/k). In the sequel, we assume d < -8 and h(d) = 1. The following expansion was known for prime k by Heilbronn and Linfoot [31 and has recently been established [5] for all k such that (k, d) = 1,

A historical note on complex quadratic fields with class-number one.