Interesting news and discussion centered around Mathematics
The Heegner Numbers. These are the n such that ℚ[√-n] has unique factorisation. There are exactly 9 of them:
1, 2, 3, 7, 11, 19, 43, 67, 163.
A famous fact about them is that 163 being a Heegner Number leads to e^(π√163) being very close to a whole number.
262537412640768743.99999999999925…
There are tons of them! For example, the class of numbers n such that there is a Platonic solid made of n-gons. This class only has the numbers 3, 4, and 5. You can get other examples any time there is an interesting mathematical structure with only finitely many examples.
Well, yes, obviously. I was hoping for something number-theoretic, though. Let me reword the title.