Primality proof for n = 13843970897:
Take b = 2.
b^(n-1) mod n = 1.
123606883 is prime.
b^((n-1)/123606883)-1 mod n = 11497946632, which is a unit, inverse 6609093613.
(123606883) divides n-1.
(123606883)^2 > n.
n is prime by Pocklington's theorem.