József Sándor

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 4, Pages 149–153

DOI: 10.7546/nntdm.2021.27.4.149-153

**Full paper (PDF, 148 Kb)**

## Details

### Authors and affiliations

József Sándor

*Department of Mathematics, Babeș-Bolyai University
Cluj-Napoca, Romania*

### Abstract

We study certain inequalities for the prime counting function *π*(*x*). Particularly, a new proof and a refinement of an inequality from [1] is provided.

### Keywords

- Prime counting function
- Inequalities
- Hardy–Littlewood conjecture

### 2020 Mathematics Subject Classification

- 11A25
- 11A41

### References

- Alzer, H., Kwong, M. K., & Sándor, J. (2021). Inequalities for
*π*(*x*). Rendiconti del Seminario Matematico della Universita di Padova, 145(2), 1–15 (to appear).

- Panaitopol, L. (2001). Some generalizations for a theorem by Landau. Mathematical Inequalities & Applications, 4(3), 327–330.

- Rosser, J. B., & Schoenfeld, L. (1962). Approximate formulas for some functions of prime numbers. Illinois Journal of Mathematics, 6(1), 64–94.

- Sándor, J., Mitrinovic, D. S., & Crstici, B. (2006). Handbook of Number Theory. I, Springer.

- Sándor, J., & Atanassov, K. T. (2021). Arithmetic Functions, Nova Science Publishers, New York.

- Segal, S. L. (1962). On
*π*(*x*+*y*) ≤*π*(*x*)+*π*(*y*). Transactions of the American Mathematical Society, 104, 523–527.

## Related papers

- Sándor, J. (2022). On certain inequalities for the prime counting function – Part II.
*Notes on Number Theory and Discrete Mathematics*, 28(1), 124-128. - Sándor, J. (2023). On certain inequalities for the prime counting function – Part III.
*Notes on Number Theory and Discrete Mathematics*, 29(3), 454-461.

## Cite this paper

Sándor, J. (2021). On certain inequalities for the prime counting function. *Notes on Number Theory and Discrete Mathematics*, 27(4), 149-153, DOI: 10.7546/nntdm.2021.27.4.149-153.