Note on the cardinality difference between primes and twin primes and its impact on function x/ln(x) in prime number theorem

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

We provide a simple explanation and test that the emblematic function x/ln(x) in prime number theorem estimates roughly the prime-counting as 1 for each isolated primes and 1 for each twin primes, and not 2 for twins as it should be. By this reason, for a more proper counting the function (x/ln(x))[1+ln(x)-1] should replace x/ln(x) in the prime number theorem.

Original languageEnglish
Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017
PublisherAmerican Institute of Physics Inc.
Volume1978
ISBN (Electronic)9780735416901
DOIs
Publication statusPublished - Jul 10 2018
EventInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017 - Thessaloniki, Greece
Duration: Sep 25 2017Sep 30 2017

Other

OtherInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017
CountryGreece
CityThessaloniki
Period9/25/179/30/17

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Keywords

  • analysis of x/ln(x) in relation to twin primes and PNT
  • prime number theorem

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Kristyán, S. (2018). Note on the cardinality difference between primes and twin primes and its impact on function x/ln(x) in prime number theorem. In International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017 (Vol. 1978). [470064] American Institute of Physics Inc.. https://doi.org/10.1063/1.5044134