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.
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https://hal.archives-ouvertes.fr/hal-01467925
Contributor : Rédoane Daoudi <>
Submitted on : Tuesday, February 14, 2017 - 7:28:20 PM
Last modification on : Tuesday, April 2, 2019 - 2:21:58 AM
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Rédoane Daoudi. The distribution of prime numbers: overview of n.ln(n). 2017. ⟨hal-01467925⟩

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