Primality proof for n = 87559:

Take b = 2.

b^(n-1) mod n = 1.

14593 is prime.
b^((n-1)/14593)-1 mod n = 63, which is a unit, inverse 31966.

(14593) divides n-1.

(14593)^2 > n.

n is prime by Pocklington's theorem.