Primality proof for n = 3433:

Take b = 2.

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

13 is prime.
b^((n-1)/13)-1 mod n = 1862, which is a unit, inverse 1746.

11 is prime.
b^((n-1)/11)-1 mod n = 2477, which is a unit, inverse 1756.

(11 * 13) divides n-1.

(11 * 13)^2 > n.

n is prime by Pocklington's theorem.