Primality proof for n = 9533:

Take b = 2.

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

2383 is prime.
b^((n-1)/2383)-1 mod n = 15, which is a unit, inverse 8262.

(2383) divides n-1.

(2383)^2 > n.

n is prime by Pocklington's theorem.