Primality proof for n = 65427463921:

Take b = 3.

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

2995763 is prime.
b^((n-1)/2995763)-1 mod n = 42122182385, which is a unit, inverse 11681146965.

(2995763) divides n-1.

(2995763)^2 > n.

n is prime by Pocklington's theorem.