IJPAM: Volume 84, No. 1 (2013)


E. Markakis1, C. Provatidis2, N. Markakis3
1Vassilissis Olgas 129B
54643, Thessaloniki, GREECE
2National Technical University of Athens
9, Heroes of Polytechnion Ave., Zografou Campus
157 80, Athens, GREECE
3Cram School ``Methodiko''
Vouliagmenis and Kyprou 2,
16452 Argyroupolis, GREECE

Abstract. This paper divides the set of natural numbers in six equivalence classes and determines two of them as candidate to include all prime numbers. Concerning the even numbers themselves, these were divided into three subsets using a basic cell (6n-2, 6n and 6n+2). Based on the aforementioned tools, this paper proposes a deterministic process of finding all pairs (p,q) of odd numbers (composites and primes) of natural numbers ≥3 whose sum (p + q) is equal to a given even natural number 2n≥6. Based on this procedure and also relying on the distribution of primes in the set N of natural numbers, a closed analytical formula is proposed for the estimation of the number of primes that satisfy Goldbach's conjecture for positive integers ≥6.

Received: September 27, 2012

AMS Subject Classification: 11-XX

Key Words and Phrases: Goldbach's conjecture, prime numbers, statistics

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DOI: 10.12732/ijpam.v84i1.3 How to cite this paper?
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 84
Issue: 1