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The first efficient general primality proving method was proposed in the year1980 by Adleman, Pomerance and Rumely and it used Jacobi sums. The method wasfurther developed by H. W. Lenstra Jr. and more of his students and theresulting primality proving algorithms are often referred to under the genericname of Cyclotomy Primality Proving (CPP). In the present paper we give anoverview of the theoretical background and implementation specifics of CPP,such as we understand them in the year 2007.

Cyclotomy Primality Proofs and their Certificates