Primality proof for n = 8803:

Take b = 2.

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

163 is prime.
b^((n-1)/163)-1 mod n = 4883, which is a unit, inverse 4013.

(163) divides n-1.

(163)^2 > n.

n is prime by Pocklington's theorem.