Primality proof for n = 22549:

Take b = 2.

b^(n-1) mod n = 1.

1879 is prime.
b^((n-1)/1879)-1 mod n = 4095, which is a unit, inverse 16167.

(1879) divides n-1.

(1879)^2 > n.

n is prime by Pocklington's theorem.