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
Download full paper: PDF, 194 Kb


Authors and affiliations

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


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.


  • Numerical analysis
  • Number theory
  • Sieves

2020 Mathematics Subject Classification

  • 11N35


  1. Brun, V. (1920). Le crible d’Eratosthène et le théorème de Goldbach. Kristiania: En Commission chez J. Dybwad.
  2. De la Vallée Poussin, C. J. (1896). Recherches analytiques la théorie des nombres premiers. Annales de la Société scientifique de Bruxelles, 20, 183–256.
  3. Derbyshire, J. (2004). Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, New York: Penguin.
  4. Erdős, P. (1940). The difference of consecutive primes. Duke Mathematical Journal, 6(2), 438–441.
  5. Gauss, C. F. (1863). Werke, Band 10, Teil I. p. 10.
  6. Goldston, D. A., Motohahi, Y., Pintz, J., & Yıldırım, C. Y. (2006). Small gaps between primes exist. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 82(4), 61–65. DOI: 10.3792/pjaa.82.61.
  7. Greaves, G. (2001). Sieves in Number Theory. Springer, Berlin.
  8. Hadamard, J. (1896). Sur la distribution des zéros de la fonction ζ(s) et ses consequences arithmé Bulletin de la Société Mathématique de France, 24, 199–220.
  9. Hardy, G. H., & Wright, E. M. (1979). An Introduction to the Theory of Numbers, 5th ed., Oxford Science Publications, Oxford, England: Clarendon Press, pp. 354–358.
  10. Havil, J., & Dyson, F. (2003). Problems with Primes. In: Gamma: Exploring Euler’s Constant. Princeton; Oxford: Princeton University Press, pp. 163–188.
  11. Iverson, K. E. (1962). A Programming Language. New York: Wiley, p. 12.
  12. Littlewood, J. E. (1914). Sur les distribution des nombres premiers. Comptes rendus de l’Académie des Sciences, 158, 1869–1872.
  13. Naldi, G., & Pareschi, L. (2008). Matlab, Concetti e Progetti, Apogeo Education.
  14. Pintz, J. (1997). Very large gaps between consecutive primes. Journal of Number Theory, 63(2), 286–301.
  15. Riesel, H. (1994). Prime Numbers and Computer Methods for Factorization. Series Progress in Mathematics. Vol. 126 (second ed.). Boston, MA: Birkhäuser.

Related papers

Cite this paper

Di Pietro, G. (2021). Numerical analysis approach to twin primes conjecture. Notes on Number Theory and Discrete Mathematics, 27(3), 175-183, doi: 10.7546/nntdm.2021.27.3.175-183.

Comments are closed.