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.