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Primes in short intervals

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Abstract

Let π(x) stand for the number of primes not exceedingx. In the present work it is shown that if 23/42≤Θ≤1,y≤x θ andx>x(Θ) then π(x)−π(x−y)>y/(100 logx). This implies for the difference between consecutive primes the inequalityp n+1−p n ≪p 23/42 n .

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Authors and Affiliations

  1. Mathematics Institute, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950, Warszawa, Poland

    Henryk Iwaniec

  2. Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13-15, H-1053, Budapest, Hungary

    János Pintz

Authors
  1. Henryk Iwaniec
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  2. János Pintz
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Iwaniec, H., Pintz, J. Primes in short intervals. Monatshefte für Mathematik 98, 115–143 (1984). https://doi.org/10.1007/BF01637280

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  • DOI: https://doi.org/10.1007/BF01637280

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