On complex quadratic fields with class number equal to one
Harold M. Stark · Transactions of the American Mathematical Society · 1966
Let R(V p) be a quadratic extension of the rationals, where p is a positive square free integer. For nine values of p, namely 1, 2, 3, 7, 11, 19, 43, 67, 163, the integers of R(/ p) form a unique factorization domain. Heilbronn and Linfoot [1] have shown that there is at most one more such value of p, and Lehmer [2] has shown that p must be a prime greater than 5 * 109. In the present paper we verify and extend the lower bound of 5 * 109 for p. The result is