Primality proof for n = 716223737:
Take b = 2.
b^(n-1) mod n = 1.
5266351 is prime. b^((n-1)/5266351)-1 mod n = 618493942, which is a unit, inverse 424902569.
(5266351) divides n-1.
(5266351)^2 > n.
n is prime by Pocklington's theorem.