## Number Theory   ## The proof of Goldbach's Conjecture

Authors: Ramón Ruiz

Goldbach's Conjecture statement: “Every even integer greater than 2 can be expressed as the sum of two primes”. Initially, to prove this conjecture, we can form two arithmetic sequences (A and B) different for each even number, with all the natural numbers that can be primes, that can added, in pairs, result in the corresponding even number. By analyzing the pairing process, in general, between all non-prime numbers of sequence A, with terms of sequence B, or vice versa, to obtain the even number, we note that some pairs of primes are always formed. This allow us to develop a non-probabilistic formula, to calculate the approximate number of pairs of primes that meet the conjecture for an even number x. The result of this formula is always equal or greater than 1, and it tends to infinite when x tends to infinite, which allow us to confirm that Goldbach's Conjecture is true. The prime numbers theorem by Carl Friedrich Gauss, the prime numbers theorem in arithmetic progressions and some axioms have been used to complete this investigation.

Comments: 34 Pages. This document has been written in Spanish. This research is based on an approach developed solely to demonstrate the binary Goldbach Conjecture and the Twin Primes Conjecture.

### Submission history

[v1] 2014-06-04 15:35:58
[v2] 2015-02-22 06:52:47