Primality proof for n = 599:
Take b = 2.
b^(n-1) mod n = 1.
23 is prime.
b^((n-1)/23)-1 mod n = 497, which is a unit, inverse 276.
13 is prime.
b^((n-1)/13)-1 mod n = 18, which is a unit, inverse 233.
(13 * 23) divides n-1.
(13 * 23)^2 > n.
n is prime by Pocklington's theorem.