Primality proof for n = 24098228377:

Take b = 2.

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

9211861 is prime.
b^((n-1)/9211861)-1 mod n = 7249217956, which is a unit, inverse 20243037454.

(9211861) divides n-1.

(9211861)^2 > n.

n is prime by Pocklington's theorem.