  The first efficient general primality proving method was proposed in the year
1980 by Adleman, Pomerance and Rumely and it used Jacobi sums. The method was
further developed by H. W. Lenstra Jr. and more of his students and the
resulting primality proving algorithms are often referred to under the generic
name of Cyclotomy Primality Proving (CPP). In the present paper we give an
overview of the theoretical background and implementation specifics of CPP,
such as we understand them in the year 2007.
