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.