La cometa di Goldbach e ... le altre

TL;DR

This paper explores the structure of Goldbach's comet, a plot of the Goldbach function g(n), analyzing its layers and related conjectures in number theory, with insights into prime representations and similar sequences.

Contribution

It provides an accessible analysis of Goldbach's comet and introduces related conjectures involving sequences of odd integers and prime representations.

Findings

Goldbach's comet reveals layered structures in the Goldbach function

Connections between Goldbach's conjecture and other number theory conjectures

Insights into sequences of odd integers related to prime sums

Abstract

Goldbach's comet is the plot of the Goldbach function g(n), in the interval [3, N], with a large positive integer N. The function g(n) counts the number of different ways in which 2n can be expressed as the sum of two odd primes. An account, hopefully satisfying and accessible, is given for the layers that make up the comet. By means of several (sometimes historical) results of Theory of Number, other conjectures, similar to the Goldbach's one, emerge. These are related with sequences of odd positive integers, like but not quite to the prime sequence.