Primality proof for n = 22842497:
Take b = 2.
b^(n-1) mod n = 1.
7759 is prime. b^((n-1)/7759)-1 mod n = 7263322, which is a unit, inverse 16999439.
(7759) divides n-1.
(7759)^2 > n.
n is prime by Pocklington's theorem.