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.