Primality proof for n = 45297277:

Take b = 2.

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

3774773 is prime.
b^((n-1)/3774773)-1 mod n = 4095, which is a unit, inverse 37686892.

(3774773) divides n-1.

(3774773)^2 > n.

n is prime by Pocklington's theorem.