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.