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.