Primality proof for n = 15803:
Take b = 2.
b^(n-1) mod n = 1.
7901 is prime. b^((n-1)/7901)-1 mod n = 3, which is a unit, inverse 5268.
(7901) divides n-1.
(7901)^2 > n.
n is prime by Pocklington's theorem.