Primality proof for n = 2999:

Take b = 2.

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

1499 is prime.
b^((n-1)/1499)-1 mod n = 3, which is a unit, inverse 1000.

(1499) divides n-1.

(1499)^2 > n.

n is prime by Pocklington's theorem.