Primality proof for n = 302579:
Take b = 2.
b^(n-1) mod n = 1.
151289 is prime. b^((n-1)/151289)-1 mod n = 3, which is a unit, inverse 100860.
(151289) divides n-1.
(151289)^2 > n.
n is prime by Pocklington's theorem.