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.