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.