Primality proof for n = 704251:
Take b = 2.
b^(n-1) mod n = 1.
313 is prime.
b^((n-1)/313)-1 mod n = 148688, which is a unit, inverse 512127.
5 is prime.
b^((n-1)/5)-1 mod n = 574806, which is a unit, inverse 306580.
(5^3 * 313) divides n-1.
(5^3 * 313)^2 > n.
n is prime by Pocklington's theorem.