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.