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.