L. Panaitopol

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

Volume 7, 2001, Number 4, Pages 111–114

**Full paper (PDF, 122 Kb)**

## Details

### 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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## Cite this paper

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