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.