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.