  In the first article of this series we have presented the history of
auxiliary primes from Legendre's proof of the quadratic reciprocity law up to
Artin's reciprocity law. We have also seen that the proof of Artin's
reciprocity law consists of several steps, the first of which is the
verification of the reciprocity law for cyclotomic extensions. In this article
we will show that this step can be identified with one of Dedekind's proofs of
the irreducibility of the cyclotomic polynomial.

Number Theory;History and Overview