Primality proof for n = 6317:
Take b = 2.
b^(n-1) mod n = 1.
1579 is prime. b^((n-1)/1579)-1 mod n = 15, which is a unit, inverse 2948.
(1579) divides n-1.
(1579)^2 > n.
n is prime by Pocklington's theorem.