Primality proof for n = 2384153:

Take b = 2.

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

5623 is prime.
b^((n-1)/5623)-1 mod n = 1249200, which is a unit, inverse 711091.

(5623) divides n-1.

(5623)^2 > n.

n is prime by Pocklington's theorem.