Primality proof for n = 599219167:
Take b = 2.
b^(n-1) mod n = 1.
20707 is prime.
b^((n-1)/20707)-1 mod n = 5330079, which is a unit, inverse 512598205.
53 is prime.
b^((n-1)/53)-1 mod n = 147598986, which is a unit, inverse 123777092.
(53 * 20707) divides n-1.
(53 * 20707)^2 > n.
n is prime by Pocklington's theorem.