A Heegner number is a number n such that Q(√−n) is an imaginary quadratic field of class number 1.
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The Stark–Heegner theorem identifies the imaginary quadratic fields of class number 1.
Heegner's proof was finally accepted as essentially correct in 1969, after Harold Stark, who had independently arrived at a similar proof, showed that Heegner's proof was more or less equivalent to his own, with only a minor gap in it.