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.