Primality proof for n = 1300347341:
Take b = 2.
b^(n-1) mod n = 1.
3824551 is prime. b^((n-1)/3824551)-1 mod n = 1098383323, which is a unit, inverse 1281468091.
(3824551) divides n-1.
(3824551)^2 > n.
n is prime by Pocklington's theorem.