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.