Primality proof for n = 833843:

Take b = 2.

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

18127 is prime.
b^((n-1)/18127)-1 mod n = 459666, which is a unit, inverse 765264.

(18127) divides n-1.

(18127)^2 > n.

n is prime by Pocklington's theorem.