The values of -d for which imaginary quadratic fields Q(sqrt(-d)) are uniquely factorable into factors of the form a + bsqrt(-d). Here, a and b are half-integers, except for d = 1 and 2, in which case they are integers. The Heegner numbers therefore correspond to binary quadratic form discriminants -d which have class number h(-d) equal to 1, except for Heegner numbers -1 and -2, which correspond to d = - 4 and -8, respectively.

binary quadratic form discriminant | class number | Gauss's class number problem | j-function | prime-generating polynomial | quadratic field | Ramanujan constant