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.