Primality proof for n = 4048673:

Take b = 2.

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

6659 is prime.
b^((n-1)/6659)-1 mod n = 1785997, which is a unit, inverse 3486811.

(6659) divides n-1.

(6659)^2 > n.

n is prime by Pocklington's theorem.