Primality proof for n = 915473063:

Take b = 2.

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

65390933 is prime.
b^((n-1)/65390933)-1 mod n = 16383, which is a unit, inverse 4079200.

(65390933) divides n-1.

(65390933)^2 > n.

n is prime by Pocklington's theorem.