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.