Primality proof for n = 67219:

Take b = 2.

b^(n-1) mod n = 1.

659 is prime.
b^((n-1)/659)-1 mod n = 17348, which is a unit, inverse 20540.

(659) divides n-1.

(659)^2 > n.

n is prime by Pocklington's theorem.