Primality proof for n = 8713:

Take b = 2.

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

11 is prime.
b^((n-1)/11)-1 mod n = 1625, which is a unit, inverse 7898.

(11^2) divides n-1.

(11^2)^2 > n.

n is prime by Pocklington's theorem.