Primality proof for n = 21871:
Take b = 2.
b^(n-1) mod n = 1.
5 is prime.
b^((n-1)/5)-1 mod n = 16388, which is a unit, inverse 9322.
3 is prime.
b^((n-1)/3)-1 mod n = 11706, which is a unit, inverse 17968.
(3^7 * 5) divides n-1.
(3^7 * 5)^2 > n.
n is prime by Pocklington's theorem.