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.