Primality proof for n = 22017043:
Take b = 2.
b^(n-1) mod n = 1.
407723 is prime. b^((n-1)/407723)-1 mod n = 7143676, which is a unit, inverse 13515000.
(407723) divides n-1.
(407723)^2 > n.
n is prime by Pocklington's theorem.