Primality proof for n = 11909:

Take b = 2.

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

229 is prime.
b^((n-1)/229)-1 mod n = 3948, which is a unit, inverse 7695.

(229) divides n-1.

(229)^2 > n.

n is prime by Pocklington's theorem.