A Conjecture about the Density of Prime Numbers

2008/03/04 by L. A. Amarante Ribeiro, Ribeiro, L. A. Amarante
Mathematics · #History and Theory of Mathematics #math.GM

paper · pdf · doi:10.48550/arxiv.0803.0420

arxiv created 2008/03/04 · arxiv updated 2009/12/01

Abstract

We present in this work a heuristic expression for the density of prime numbers. Our expression leads to results which possesses approximately the same precision of the Riemann's function in the domain that goes from 2 to 1010 at least. Instead of using a constant as was done by Legendre and others in the formula of Gauss, we try to adjust the data through a function. This function has the remarkable property: its points of discontinuity are the prime numbers.

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