Primality proof for n = 709927:
Take b = 2.
b^(n-1) mod n = 1.
16903 is prime. b^((n-1)/16903)-1 mod n = 471067, which is a unit, inverse 242120.
(16903) divides n-1.
(16903)^2 > n.
n is prime by Pocklington's theorem.