Numerical analysis approach to twin primes conjecture

Gabriele Di Pietro
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 3, Pages 175–183
DOI: 10.7546/nntdm.2021.27.3.175-183
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Authors and affiliations

Gabriele Di Pietro
Via Annunziata, 42, 64021, Giulianova (TE), Italy

Abstract

The purpose of this paper is to demonstrate how the modified Sieve of Eratosthenes is used to have an approach to twin prime conjecture. If the Sieve is used in its basic form, it does not produce anything new. If it is used through the numerical analysis method explained in this paper, we obtain a specific counting of twin primes. This counting is based on the false assumption that distribution of primes follows punctually the Logarithmic Integral function denoted as Li(x) (see [5] and [10], pp. 174–176). It may be a starting point for future research based on this numerical analysis method technique that can be used in other mathematical branches.

Keywords

• Numerical analysis
• Number theory
• Sieves

2020 Mathematics Subject Classification

• 11N35

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