Primality proof for n = 12721:
Take b = 2.
b^(n-1) mod n = 1.
53 is prime.
b^((n-1)/53)-1 mod n = 9970, which is a unit, inverse 11380.
3 is prime.
b^((n-1)/3)-1 mod n = 4929, which is a unit, inverse 11077.
(3 * 53) divides n-1.
(3 * 53)^2 > n.
n is prime by Pocklington's theorem.