Primality proof for n = 65390933:
Take b = 2.
b^(n-1) mod n = 1.
37409 is prime. b^((n-1)/37409)-1 mod n = 52265216, which is a unit, inverse 21561354.
(37409) divides n-1.
(37409)^2 > n.
n is prime by Pocklington's theorem.