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.