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.