Primality proof for n = 303767:
Take b = 2.
b^(n-1) mod n = 1.
151883 is prime. b^((n-1)/151883)-1 mod n = 3, which is a unit, inverse 101256.
(151883) divides n-1.
(151883)^2 > n.
n is prime by Pocklington's theorem.