Primality proof for n = 105769:

Take b = 2.

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

113 is prime.
b^((n-1)/113)-1 mod n = 17918, which is a unit, inverse 83934.

13 is prime.
b^((n-1)/13)-1 mod n = 50731, which is a unit, inverse 82906.

(13 * 113) divides n-1.

(13 * 113)^2 > n.

n is prime by Pocklington's theorem.