Primality proof for n = 22871:
Take b = 2.
b^(n-1) mod n = 1.
2287 is prime. b^((n-1)/2287)-1 mod n = 1023, which is a unit, inverse 9211.
(2287) divides n-1.
(2287)^2 > n.
n is prime by Pocklington's theorem.