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.