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.