Laurențiu Panaitopol

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 8, 2002, Number 4, Pages 145—148

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## Details

### Authors and affiliations

Laurențiu 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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## Cite this paper

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