Primality proof for n = 59598109:
Take b = 2.
b^(n-1) mod n = 1.
24709 is prime. b^((n-1)/24709)-1 mod n = 51054277, which is a unit, inverse 6475653.
(24709) divides n-1.
(24709)^2 > n.
n is prime by Pocklington's theorem.