Primality proof for n = 1024633:
Take b = 2.
b^(n-1) mod n = 1.
107 is prime.
b^((n-1)/107)-1 mod n = 83987, which is a unit, inverse 561110.
19 is prime.
b^((n-1)/19)-1 mod n = 247037, which is a unit, inverse 868572.
(19 * 107) divides n-1.
(19 * 107)^2 > n.
n is prime by Pocklington's theorem.