Primality proof for n = 484778929:
Take b = 2.
b^(n-1) mod n = 1.
171179 is prime. b^((n-1)/171179)-1 mod n = 122759329, which is a unit, inverse 302123541.
(171179) divides n-1.
(171179)^2 > n.
n is prime by Pocklington's theorem.