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.