Primality proof for n = 6299:
Take b = 2.
b^(n-1) mod n = 1.
67 is prime.
b^((n-1)/67)-1 mod n = 4252, which is a unit, inverse 4505.
47 is prime.
b^((n-1)/47)-1 mod n = 1576, which is a unit, inverse 5040.
(47 * 67) divides n-1.
(47 * 67)^2 > n.
n is prime by Pocklington's theorem.