Study of some equivalence classes of primes

Sadani Idir
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 2, Pages 21–29
Full paper (PDF, 236 Kb)
Corrigendum

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Authors and affiliations

Sadani Idir
Department of Mathematics
University of Mouloud Mammeri
15000 Tizi-Ouzou, Algeria

Abstract

In this paper, we introduce an equivalence relation ~ on ℙ for studying some specific classes of prime numbers. This relation and the famous prime number theorem allows us to estimate the number of prime numbers of each equivalence class, the number of the different equivalence classes and to show some other results.

Keywords

• Equivalence relation
• Prime number theorem
• Recurrence relation

AMS Classification

• 11A41

References

1. De la Vallée Poussin, C. J. (1896) Recherche analytique sur la théorie des nombres, Ann. Soc. Sci. Bruxelle, 20, 183–256.
2. Hadamard, J. (1896) Sur la distribution des zéros de la fonction ζ(s) et ses conséquences arithmétiques, Bull. Soc. Math. France, 24, 199–220.