The distribution of prime numbers: overview of n.ln(n)

Abstract : The empirical formula giving the nth prime number p(n) is p(n) = n.ln(n) (from ROSSER (2)). Other studies have been performed (from DUSART for example (1)) in order to better estimate the nth prime number. Unfortunately these formulas don't work since there is a significant difference between the real nth prime number and the number given by the formulas. Here we propose a new model in which the difference is effectively reduced compared to the empirical formula. We discuss about the results and hypothesize that p(n) can be approximated with a constant defined in this work. As prime numbers are important to cryptography and other fields, a better knowledge of the distribution of prime numbers would be very useful. Further investigations are needed to understand the behavior of this constant and therefore to determine the nth prime number with a basic formula that could be used in both theoretical and practical research.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01467925
Contributeur : Rédoane Daoudi <>
Soumis le : mardi 14 février 2017 - 19:28:20
Dernière modification le : vendredi 17 février 2017 - 01:07:49
Document(s) archivé(s) le : lundi 15 mai 2017 - 18:12:54

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  • HAL Id : hal-01467925, version 1

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Rédoane Daoudi. The distribution of prime numbers: overview of n.ln(n). 2017. 〈hal-01467925〉

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