Primality proof for n = 1399417:
Take b = 2.
b^(n-1) mod n = 1.
58309 is prime. b^((n-1)/58309)-1 mod n = 1383628, which is a unit, inverse 79326.
(58309) divides n-1.
(58309)^2 > n.
n is prime by Pocklington's theorem.