Our readers’ contributions

Do you have an idea for proving the Goldbach’s Conjecture, or are you looking for a starting point? Then this is the right page for you. We collected here the contributions we received from some of our readers, because we wish to foster diffusion and exchange of ideas about the Conjecture.
The contributions we received so far are listed below. They are sorted by year and, with equal year, by author’s surname:

Ultima, About the exceptions to Goldbach’s conjecture, 2020
Is it possible to prove Goldbach’s Conjecture by contradiction, starting from the existence on a hypothetical set of exceptions? Our reader Ultima tries to sketch out an argument of this kind. The starting point is that every even number greater than 6 can be expressed as a sum of four prime numbers, which is a consequence of the weak Goldbach’s Conjecture, proved by Helfgott.
Francesco Di Noto and Michele Nardelli, Theorem about the number of Goldbach’s pairs up to even N, 2019 Italian
Discussion, with numerical examples, of some estimates for the number of Goldbach’s pairs. These estimates are based on some interesting correlations, for every even number N \geq 4, between the number of Goldbach’s pairs and the number of prime divisors.
Francesco Di Noto and Michele Nardelli, Weak Goldbach’s conjecture already proved. The strong conjecture follows, 2016 Italian
Proof sketch of the strong Goldbach’s Conjecture based on its weak version. Also some numerical evidences are discussed, for example about the number of Goldbach’s pairs (this topic will be studied in detail in a later paper by the same authors, see above). The paper ends with some mentions about Fermat’s factorization and Lagarias’ equivalent of the Riemann Hypothesis, RH1.

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