Primality proof for n = 14720401:
Take b = 2.
b^(n-1) mod n = 1.
47 is prime.
b^((n-1)/47)-1 mod n = 8557480, which is a unit, inverse 10629675.
29 is prime.
b^((n-1)/29)-1 mod n = 12453323, which is a unit, inverse 9887646.
5 is prime.
b^((n-1)/5)-1 mod n = 5784941, which is a unit, inverse 1191016.
(5^2 * 29 * 47) divides n-1.
(5^2 * 29 * 47)^2 > n.
n is prime by Pocklington's theorem.