Primality proof for n = 4079:

Take b = 2.

b^(n-1) mod n = 1.

2039 is prime.
b^((n-1)/2039)-1 mod n = 3, which is a unit, inverse 1360.

(2039) divides n-1.

(2039)^2 > n.

n is prime by Pocklington's theorem.