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.