Primality proof for n = 45265241663:

Take b = 2.

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

997 is prime.
b^((n-1)/997)-1 mod n = 25636981309, which is a unit, inverse 38287484439.

661 is prime.
b^((n-1)/661)-1 mod n = 8343847944, which is a unit, inverse 13961776954.

(661 * 997) divides n-1.

(661 * 997)^2 > n.

n is prime by Pocklington's theorem.