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The Ramanujan Journal

, Volume 15, Issue 1, pp 109–121 | Cite as

On the number of partitions into primes

  • R. C. Vaughan
Article

Abstract

There is, apparently, a persistent belief that in the current state of knowledge it is not possible to obtain an asymptotic formula for the number of partitions of a number n into primes when n is large. In this paper such a formula is obtained. Since the distribution of primes can only be described accurately by the use of the logarithmic integral and a sum over zeros of the Riemann zeta-function one cannot expect the main term to involve only elementary functions. However the formula obtained, when n is replaced by a real variable, is in \({\mathcal{C}}^{\infty}\) and is readily seen to be monotonic.

Keywords

Prime numbers Partitions 

Mathematics Subject Classification (2000)

11P82 11P55 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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