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.