Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Considerations for Goldbach's Strong Conjecture

Version 1 : Received: 8 March 2021 / Approved: 10 March 2021 / Online: 10 March 2021 (13:14:22 CET)
Version 2 : Received: 12 March 2021 / Approved: 12 March 2021 / Online: 12 March 2021 (11:29:49 CET)

How to cite: Severino Silva, C. Considerations for Goldbach's Strong Conjecture. Preprints 2021, 2021030281 (doi: 10.20944/preprints202103.0281.v1). Severino Silva, C. Considerations for Goldbach's Strong Conjecture. Preprints 2021, 2021030281 (doi: 10.20944/preprints202103.0281.v1).

## Abstract

Since 1742, the year in which the Prussian Christian Goldbach wrote a letter to Leonhard Euler with his Conjecture in the weak version, mathematicians have been working on the problem. The tools in number theory become the most sophisticated thanks to the resolution solutions. Euler himself said he was unable to prove it. The weak guess in the modern version states the following: any odd number greater than 5 can be written as the sum of 3 primes. In response to Goldbach's letter, Euler reminded him of a conversation in which he proposed what is now known as Goldbach's strong conjecture: any even number greater than 2 can be written as a sum of 2 prime numbers. The most interesting result came in 2013, with proof of weak version by the Peruvian Mathematician Harald Helfgott, however the strong version remained without a definitive proof. The weak version can be demonstrated without major difficulties and will not be described in this article, as it becomes a corollary of the strong version. Despite the enormous intellectual baggage that great mathematicians have had over the centuries, the Conjecture in question has not been validated or refuted until today.

## Keywords

Goldbach's conjecture; numbers prime; Arithmetic Theorem

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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