Primality proof for n = 5121119:

Take b = 2.

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

6977 is prime.
b^((n-1)/6977)-1 mod n = 969211, which is a unit, inverse 2762657.

(6977) divides n-1.

(6977)^2 > n.

n is prime by Pocklington's theorem.