Primality proof for n = 479208894057626693:
Take b = 2.
b^(n-1) mod n = 1.
119802223514406673 is prime.
b^((n-1)/119802223514406673)-1 mod n = 15, which is a unit, inverse 415314374849943134.
(119802223514406673) divides n-1.
(119802223514406673)^2 > n.
n is prime by Pocklington's theorem.