Primality proof for n = 99140441:
Take b = 2.
b^(n-1) mod n = 1.
354073 is prime. b^((n-1)/354073)-1 mod n = 56357391, which is a unit, inverse 60104789.
(354073) divides n-1.
(354073)^2 > n.
n is prime by Pocklington's theorem.