Primality proof for n = 66891682553:
Take b = 2.
b^(n-1) mod n = 1.
21384809 is prime. b^((n-1)/21384809)-1 mod n = 60851177397, which is a unit, inverse 32312831146.
(21384809) divides n-1.
(21384809)^2 > n.
n is prime by Pocklington's theorem.