IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v341y2004icp607-617.html
   My bibliography  Save this article

The gaps between the gaps: some patterns in the prime number sequence

Author

Listed:
  • Szpiro, George G

Abstract

It has long been known that the gaps between consecutive prime numbers cluster on multiples of 6. Recently it was shown that the frequency of the gaps between the gaps is lower for multiples of 6 than for other values (P. Kumar et al., Information entropy and correlation in prime numbers, arXiv: cond-mat/0303110). This paper investigates “higher moments” of the prime number series and shows that they exhibit certain peculiarities. In order to remove doubts as to whether these peculiarities are related to the known clustering of the gaps on multiples of 6, the results are compared to a benchmark series of “simulated gaps”.

Suggested Citation

  • Szpiro, George G, 2004. "The gaps between the gaps: some patterns in the prime number sequence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 607-617.
    • Handle: RePEc:eee:phsmap:v:341:y:2004:i:c:p:607-617
    DOI: 10.1016/j.physa.2004.05.073
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104007277
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2004.05.073?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wolf, Marek, 1998. "Random walk on the prime numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 335-344.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Iovane, Gerardo, 2008. "The distribution of prime numbers: The solution comes from dynamical processes and genetic algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 23-42.
    2. Iovane, Gerardo, 2009. "The set of prime numbers: Multifractals and multiscale analysis," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1945-1958.
    3. Gadiyar, H.Gopalkrishna & Padma, R., 1999. "Ramanujan–Fourier series, the Wiener–Khintchine formula and the distribution of prime pairs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(2), pages 503-510.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:341:y:2004:i:c:p:607-617. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.