# Our readers’ contributions

In order to foster the diffusion and exchange of ideas about Goldbach’s Conjecture, we created this page which collects some contributions that have been sent us from our readers for that purpose. They are sorted by year and, with equal year, by author’s surname.

Ultima, About the exceptions to Goldbach’s conjecture II, 2021
Our reader Ultima, after having supposed the existance of exceptions to Goldbach’s Conjecture (see also the other contribution of the same author listed below in this page), continues his argument attempting to find a form for expressing such exceptions, observing that some forms can be reduced to other ones. The final goal is to find a connection between Lemoine’s Conjecture and Goldbach’s weak Conjecture.
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
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
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.