### 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) |
---|---|

Pages (from-to) | 109-121 |

Number of pages | 13 |

Journal | Ramanujan Journal |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2008 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Ramanujan Journal*,

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

}

*Ramanujan Journal*, vol. 15, no. 1, pp. 109-121. https://doi.org/10.1007/s11139-007-9037-5

**On the number of partitions into primes.** / Vaughan, Robert Charles.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the number of partitions into primes

AU - Vaughan, Robert Charles

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38349025618&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38349025618&partnerID=8YFLogxK

U2 - 10.1007/s11139-007-9037-5

DO - 10.1007/s11139-007-9037-5

M3 - Article

AN - SCOPUS:38349025618

VL - 15

SP - 109

EP - 121

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 1

ER -