AN EXPLORATION ON GOLDBACH'S CONJECTURE

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.

Locations

• International Journal of Pure and Apllied Mathematics - View - PDF