Intervals containing prime numbers

Laurențiu Panaitopol
Notes on Number Theory and Discrete Mathematics
ISSN 1310–5132
Volume 8, 2002, Number 4, Pages 145–148
Full paper (PDF, 128 Kb)

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Authors and affiliations

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

Abstract

For x >0, let \pi(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 + \pi(x), thus obtaining a result that is sharper than the one postulated by Bertrand.

Keywords

  • Distribution of prime numbers
  • Inequalities
  • Bertrand’s postulate

AMS Classification

  • 11A35
  • 11N05

References

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Cite this paper

Panaitopol, L. (2002). Intervals containing prime numbers. Notes on Number Theory and Discrete Mathematics, 8(4), 145-148.

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