Primality proof for n = 88339:

Take b = 2.

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

14723 is prime.
b^((n-1)/14723)-1 mod n = 63, which is a unit, inverse 40664.

(14723) divides n-1.

(14723)^2 > n.

n is prime by Pocklington's theorem.