Primality proof for n = 11699:

Take b = 2.

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

5849 is prime.
b^((n-1)/5849)-1 mod n = 3, which is a unit, inverse 3900.

(5849) divides n-1.

(5849)^2 > n.

n is prime by Pocklington's theorem.