Primality proof for n = 3041458943669203:

Take b = 2.

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

457345879 is prime.
b^((n-1)/457345879)-1 mod n = 2754785306633515, which is a unit, inverse 1981054409968951.

(457345879) divides n-1.

(457345879)^2 > n.

n is prime by Pocklington's theorem.