A lucky number of Euler is a number p such that the prime-generating polynomial n^2 - n + p is prime for n = 1, 2, ..., p - 1. Such numbers are related to the imaginary quadratic field in which the ring of integers is factorable. Specifically, the lucky numbers of Euler (excluding the trivial case p = 3) are those numbers p such that the imaginary quadratic field Q(sqrt(1 - 4p)) has class number 1 (Rabinowitz 1913, Le Lionnais 1983, Conway and Guy 1996, Ribenboim 2000).

class number | Gauss's class number problem | Heegner number | prime-generating polynomial