Primality proof for n = 6599:

Take b = 2.

b^(n-1) mod n = 1.

3299 is prime.
b^((n-1)/3299)-1 mod n = 3, which is a unit, inverse 2200.

(3299) divides n-1.

(3299)^2 > n.

n is prime by Pocklington's theorem.