Primality proof for n = 6679:
Take b = 3.
b^(n-1) mod n = 1.
53 is prime.
b^((n-1)/53)-1 mod n = 3290, which is a unit, inverse 3778.
3 is prime.
b^((n-1)/3)-1 mod n = 941, which is a unit, inverse 4138.
(3^2 * 53) divides n-1.
(3^2 * 53)^2 > n.
n is prime by Pocklington's theorem.