Primality proof for n = 109:
Take b = 3.
b^(n-1) mod n = 1.
3 is prime. b^((n-1)/3)-1 mod n = 62, which is a unit, inverse 51.
(3^3) divides n-1.
(3^3)^2 > n.
n is prime by Pocklington's theorem.