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.