Primality proof for n = 5585233:
Take b = 2.
b^(n-1) mod n = 1.
116359 is prime. b^((n-1)/116359)-1 mod n = 4992182, which is a unit, inverse 1927333.
(116359) divides n-1.
(116359)^2 > n.
n is prime by Pocklington's theorem.