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.