### 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 C∞ and is readily seen to be monotonic.

Original language | English (US) |
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Pages (from-to) | 109-121 |

Number of pages | 13 |

Journal | Ramanujan Journal |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2008 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Vaughan, R. C. (2008). On the number of partitions into primes.

*Ramanujan Journal*,*15*(1), 109-121. https://doi.org/10.1007/s11139-007-9037-5