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.