Primality proof for n = 33191:

Take b = 2.

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

3319 is prime.
b^((n-1)/3319)-1 mod n = 1023, which is a unit, inverse 22030.

(3319) divides n-1.

(3319)^2 > n.

n is prime by Pocklington's theorem.