Primality proof for n = 66417393611:

Take b = 2.

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

3677 is prime.
b^((n-1)/3677)-1 mod n = 66219752669, which is a unit, inverse 49445954925.

197 is prime.
b^((n-1)/197)-1 mod n = 34676449720, which is a unit, inverse 51215684949.

(197 * 3677) divides n-1.

(197 * 3677)^2 > n.

n is prime by Pocklington's theorem.