Primality proof for n = 3079:
Take b = 2.
b^(n-1) mod n = 1.
19 is prime.
b^((n-1)/19)-1 mod n = 1246, which is a unit, inverse 556.
3 is prime.
b^((n-1)/3)-1 mod n = 545, which is a unit, inverse 1870.
(3^4 * 19) divides n-1.
(3^4 * 19)^2 > n.
n is prime by Pocklington's theorem.