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

Abstract

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.

Keywords

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

AMS Classification

• 11A35
• 11N05

References

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