Primality proof for n = 1451:
Take b = 2.
b^(n-1) mod n = 1.
29 is prime.
b^((n-1)/29)-1 mod n = 346, which is a unit, inverse 1321.
5 is prime.
b^((n-1)/5)-1 mod n = 711, which is a unit, inverse 100.
(5^2 * 29) divides n-1.
(5^2 * 29)^2 > n.
n is prime by Pocklington's theorem.