Primality proof for n = 1103:
Take b = 3.
b^(n-1) mod n = 1.
29 is prime.
b^((n-1)/29)-1 mod n = 362, which is a unit, inverse 454.
19 is prime.
b^((n-1)/19)-1 mod n = 619, which is a unit, inverse 335.
(19 * 29) divides n-1.
(19 * 29)^2 > n.
n is prime by Pocklington's theorem.