Primality proof for n = 4909:

Take b = 2.

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

409 is prime.
b^((n-1)/409)-1 mod n = 4095, which is a unit, inverse 3142.

(409) divides n-1.

(409)^2 > n.

n is prime by Pocklington's theorem.