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.