Primality proof for n = 1033843:

Take b = 2.

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

172307 is prime.
b^((n-1)/172307)-1 mod n = 63, which is a unit, inverse 475896.

(172307) divides n-1.

(172307)^2 > n.

n is prime by Pocklington's theorem.