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 Show affiliations
- C.N.R retired, Italy
Journal of Mathematics and Statistics, Volume 17, Issue 1, pp. 59–60 · doi.org/10.3844/jmssp.2021.59.60
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).
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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
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