Primality proof for n = 15773:

Take b = 2.

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

3943 is prime.
b^((n-1)/3943)-1 mod n = 15, which is a unit, inverse 13670.

(3943) divides n-1.

(3943)^2 > n.

n is prime by Pocklington's theorem.