Primality proof for n = 163:
Take b = 2.
b^(n-1) mod n = 1.
3 is prime. b^((n-1)/3)-1 mod n = 103, which is a unit, inverse 19.
(3^4) divides n-1.
(3^4)^2 > n.
n is prime by Pocklington's theorem.