Primality proof for n = 598729:
Take b = 2.
b^(n-1) mod n = 1.
101 is prime.
b^((n-1)/101)-1 mod n = 94230, which is a unit, inverse 177344.
19 is prime.
b^((n-1)/19)-1 mod n = 112540, which is a unit, inverse 298625.
(19 * 101) divides n-1.
(19 * 101)^2 > n.
n is prime by Pocklington's theorem.