Primality proof for n = 13759:

Take b = 2.

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

2293 is prime.
b^((n-1)/2293)-1 mod n = 63, which is a unit, inverse 1092.

(2293) divides n-1.

(2293)^2 > n.

n is prime by Pocklington's theorem.