Primality proof for n = 17:

Take b = 3.

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

2 is prime.
b^((n-1)/2)-1 mod n = 15, which is a unit, inverse 8.

(2^4) divides n-1.

(2^4)^2 > n.

n is prime by Pocklington's theorem.