Primality proof for n = 181:
Take b = 2.
b^(n-1) mod n = 1.
5 is prime.
b^((n-1)/5)-1 mod n = 58, which is a unit, inverse 103.
3 is prime.
b^((n-1)/3)-1 mod n = 47, which is a unit, inverse 104.
(3^2 * 5) divides n-1.
(3^2 * 5)^2 > n.
n is prime by Pocklington's theorem.