Primality proof for n = 14153:
Take b = 2.
b^(n-1) mod n = 1.
61 is prime.
b^((n-1)/61)-1 mod n = 10466, which is a unit, inverse 4234.
29 is prime.
b^((n-1)/29)-1 mod n = 5482, which is a unit, inverse 1469.
(29 * 61) divides n-1.
(29 * 61)^2 > n.
n is prime by Pocklington's theorem.