La cometa di Goldbach e ... le altre

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.