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.