Primality proof for n = 433:

Take b = 3.

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

3 is prime.
b^((n-1)/3)-1 mod n = 197, which is a unit, inverse 222.

(3^3) divides n-1.

(3^3)^2 > n.

n is prime by Pocklington's theorem.