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.