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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

A Simple and Accurate Relation Between the Logarithm Integral Li(x) and the Primes Counting Function π(x) is Derived Making use of the O.E.I.S. Prime Numbers “Sequences”

Paolo Ascarelli1
  • 1 C.N.R retired, Italy

Abstract

Today the prime numbers π(x) contained under the number x appears to be somewhat overestimated by the logarithm integral function Li(x) and underestimated by the function x/ln(x), both originally proposed by Gauss around 1792-1796. However, a simple and accurate expression, relating Li(x) and π(x), may be derived using the data reported on the O.E.I.S. “Sequences”. This relation can also suggest the possibility that for very big numbers the Li(x) may oscillate around π(x).

Journal of Mathematics and Statistics
Volume 17 No. 1, 2021, 59-60

DOI: https://doi.org/10.3844/jmssp.2021.59.60

Submitted On: 22 July 2021 Published On: 30 September 2021

How to Cite: Ascarelli, P. (2021). A Simple and Accurate Relation Between the Logarithm Integral Li(x) and the Primes Counting Function π(x) is Derived Making use of the O.E.I.S. Prime Numbers “Sequences”. Journal of Mathematics and Statistics, 17(1), 59-60. https://doi.org/10.3844/jmssp.2021.59.60

Open AccessCopyright: © 2021 Paolo Ascarelli. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Numbers Theory
  • Mathematics History in Grammar School