Harbingers of Artin's Reciprocity Law. I. The Continuing Story of   Auxiliary Primes
  In this article we present the history of auxiliary primes used in proofs of reciprocity laws from the quadratic to Artin's reciprocity law. We also show that the gap in Legendre's proof can be closed with a simple application of Gauss's genus theory. 
Franz Lemmermeyer
math.NT math.HO