Primality proof for n = 513928823:

Take b = 2.

b^(n-1) mod n = 1.

661 is prime.
b^((n-1)/661)-1 mod n = 28519645, which is a unit, inverse 65192971.

599 is prime.
b^((n-1)/599)-1 mod n = 314420, which is a unit, inverse 135654522.

(599 * 661) divides n-1.

(599 * 661)^2 > n.

n is prime by Pocklington's theorem.
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