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.