Primality proof for n = 16826333:

Take b = 2.

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

4206583 is prime.
b^((n-1)/4206583)-1 mod n = 15, which is a unit, inverse 14582822.

(4206583) divides n-1.

(4206583)^2 > n.

n is prime by Pocklington's theorem.