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.