A Conjecture about the Density of Prime Numbers

TL;DR

This paper proposes a heuristic function for prime number density that aligns with known data up to 1010, featuring discontinuities precisely at prime numbers, offering a novel approach compared to traditional constant-based formulas.

Contribution

Introduces a new heuristic function for prime density with discontinuities at primes, improving data fit over existing constant-based models.

Findings

Function closely matches prime density data up to 1010

Discontinuities occur exactly at prime numbers

Provides an alternative to classical prime density formulas

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.