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Distribution of Large Gaps Between Primes

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Irregularities in the Distribution of Prime Numbers

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.

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Correspondence to Daniel A. Goldston .

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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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