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.