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Irregularities in the Distribution of Prime Numbers pp 45–67Cite as

Distribution of Large Gaps Between Primes

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Abstract

We survey some past conditional results on the distribution of large gaps between consecutive primes and examine how the Hardy–Littlewood prime k-tuples conjecture can be applied to this question.

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Notes

  1. 1.

    Selberg also proved an unconditional estimate that we are not concerned with in this paper.

  2. 2.

    Recent work [1] has determined that C = 0.84 is acceptable.

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Acknowledgements

The authors wish to express their sincere gratitude and appreciation to the anonymous referee for carefully reading the original version of this paper and for making a number of very helpful comments and suggestions.

Author information

Authors and Affiliations

  1. Space and Naval Warfare Systems Center Atlantic, North Charleston, SC, USA

    Scott Funkhouser

  2. Department of Mathematics and Statistics, San José State University, San José, CA, USA

    Daniel A. Goldston

  3. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    Andrew H. Ledoan

Authors
  1. Scott Funkhouser
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  2. Daniel A. Goldston
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  3. Andrew H. Ledoan
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Corresponding author

Correspondence to Daniel A. Goldston .

Editor information

Editors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    János Pintz

  2. Institute of Mathematics, University of Zürich, Zürich, Switzerland

    Michael Th. Rassias

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Funkhouser, S., Goldston, D.A., Ledoan, A.H. (2018). Distribution of Large Gaps Between Primes. In: Pintz, J., Rassias, M. (eds) Irregularities in the Distribution of Prime Numbers. Springer, Cham. https://doi.org/10.1007/978-3-319-92777-0_3

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