Primality proof for n = 7151:
Take b = 2.
b^(n-1) mod n = 1.
13 is prime.
b^((n-1)/13)-1 mod n = 1349, which is a unit, inverse 546.
5 is prime.
b^((n-1)/5)-1 mod n = 3594, which is a unit, inverse 4252.
(5^2 * 13) divides n-1.
(5^2 * 13)^2 > n.
n is prime by Pocklington's theorem.