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The Selberg Sieve and prime pairs Duarte, Martin Christopher

Abstract

This paper gives an exposition of the Selberg Sieve and its application to the sifting of prime pairs. In particular, Selberg's methods are applied to the sifting approach of Eratosthenes and to an alternate sifting approach presented by the author. The results obtained are then used to show that the sum of the reciprocals of the twin primes (and similarly for general prime pairs) is convergent or finite. This paper is intended to be mostly self-contained and will hopefully be readable to someone with little background in the area of Sieve Theory.

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