Primality proof for n = 199:

Take b = 2.

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

11 is prime.
b^((n-1)/11)-1 mod n = 60, which is a unit, inverse 136.

3 is prime.
b^((n-1)/3)-1 mod n = 105, which is a unit, inverse 163.

(3^2 * 11) divides n-1.

(3^2 * 11)^2 > n.

n is prime by Pocklington's theorem.