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.