Primality proof for n = 3110999:
Take b = 2.
b^(n-1) mod n = 1.
3449 is prime. b^((n-1)/3449)-1 mod n = 1392477, which is a unit, inverse 75646.
(3449) divides n-1.
(3449)^2 > n.
n is prime by Pocklington's theorem.