Primality proof for n = 1033337:

Take b = 2.

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

3491 is prime.
b^((n-1)/3491)-1 mod n = 785315, which is a unit, inverse 127210.

(3491) divides n-1.

(3491)^2 > n.

n is prime by Pocklington's theorem.