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.