Primality proof for n = 4919:

Take b = 2.

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

2459 is prime.
b^((n-1)/2459)-1 mod n = 3, which is a unit, inverse 1640.

(2459) divides n-1.

(2459)^2 > n.

n is prime by Pocklington's theorem.