Primality proof for n = 1302347:

Take b = 2.

b^(n-1) mod n = 1.

9719 is prime.
b^((n-1)/9719)-1 mod n = 955797, which is a unit, inverse 407495.

(9719) divides n-1.

(9719)^2 > n.

n is prime by Pocklington's theorem.