Primality proof for n = 2633:
Take b = 2.
b^(n-1) mod n = 1.
47 is prime.
b^((n-1)/47)-1 mod n = 1523, which is a unit, inverse 2531.
7 is prime.
b^((n-1)/7)-1 mod n = 1503, which is a unit, inverse 2393.
(7 * 47) divides n-1.
(7 * 47)^2 > n.
n is prime by Pocklington's theorem.