Primality proof for n = 665290456380049:

Take b = 2.

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

43936391 is prime.
b^((n-1)/43936391)-1 mod n = 441204432317574, which is a unit, inverse 27740430352642.

(43936391) divides n-1.

(43936391)^2 > n.

n is prime by Pocklington's theorem.