Primality proof for n = 6719:
Take b = 2.
b^(n-1) mod n = 1.
3359 is prime. b^((n-1)/3359)-1 mod n = 3, which is a unit, inverse 2240.
(3359) divides n-1.
(3359)^2 > n.
n is prime by Pocklington's theorem.