Primality proof for n = 13721:

Take b = 2.

b^(n-1) mod n = 1.

7 is prime.
b^((n-1)/7)-1 mod n = 2222, which is a unit, inverse 11393.

(7^3) divides n-1.

(7^3)^2 > n.

n is prime by Pocklington's theorem.