Primality proof for n = 62633:
Take b = 2.
b^(n-1) mod n = 1.
7829 is prime. b^((n-1)/7829)-1 mod n = 255, which is a unit, inverse 40036.
(7829) divides n-1.
(7829)^2 > n.
n is prime by Pocklington's theorem.