Heegner number

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In number theory, a Heegner number is a positive integer n such that the imaginary quadratic field

[\mathbb Q(\sqrt) ]

has class number 1. Equivalently, its ring of integers has a unique factorization. The determination of such numbers is a special case of the class number problem.

According to the Stark–Heegner theorem there are precisely nine Heegner numbers:

1, 2, 3, 7, 11, 19, 43, 67, 163

This result was conjectured by Gauss and proven by Kurt Heegner in 1952.

External links

[A003173] from the On-Line Encyclopedia of Integer Sequences

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