Intervals containing prime numbers

L. Panaitopol
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 7, 2001, Number 4, Pages 111—114
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Authors and affiliations

L. Panaitopol
University of Bucharest, Faculty of Mathematics
14 Academiei St., RO-70109 Bucharest, Romania


For x > 0, let π(x) be the number of prime numbers not exceeding x. One shows that, for x 7, there exists at least one prime number between x and x + π(x), thus obtaining a result that is sharper than the one postulated by Bertrand.


  • distribution of prime numbers
  • inequalities
  • Bertrand’s postulate

AMS Classification

  • 11A35
  • 11N05


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Cite this paper

Panaitopol, L. (2001). Intervals containing prime numbers. Notes on Number Theory and Discrete Mathematics, 7(4), 111-114.

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