The Heegner numbers are 1, 2, 3, 7, 11, 19, 43, 67, 163. The ring of integers $\textbf{Q}(\sqrt{-d})$ have unique factorizations.
1 gives the Gaussian integers.
3 gives the Eisenstein integers.
7 gives the Kleinian integers.
What happened to 2, 11, 19, and the others? Here are pictures of the primes for 1, 2, 3, 7.
I've decided to call $\mathbb{Q}(\sqrt{-2})$ the Hippasus integers, after Hippasus, who was murdered for proving $\sqrt{2}$'s irrationality.