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.