English

A logarithmic inequality involving prime numbers

Number Theory 2019-12-17 v5

Abstract

Assume that NN is a sufficiently large positive number. In this paper we show that for a small constant ε>0\varepsilon>0, the logarithmic inequality \begin{equation*} \big|p_1\log p_1+p_2\log p_2+p_3\log p_3-N\big|<\varepsilon \end{equation*} has a solution in prime numbers p1,p2,p3p_1,\,p_2,\,p_3.

Keywords

Cite

@article{arxiv.1911.08865,
  title  = {A logarithmic inequality involving prime numbers},
  author = {S. I. Dimitrov},
  journal= {arXiv preprint arXiv:1911.08865},
  year   = {2019}
}
R2 v1 2026-06-23T12:22:10.164Z