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.