An elementary heuristic for Hardy-Littlewood extended Goldbach's conjecture
Abstract
The goal of this paper is to describe an elementary combinatorial heuristic that predicts Hardy and Littlewood's extended Goldbach's conjecture. We examine common features of other heuristics in additive prime number theory, such as Cram\'er's model and density-type arguments, both of which our heuristic draws from. Apart from the prime number theorem, our argument is entirely elementary, in the sense of not involving complex analysis. The idea is to model sums of two primes by a hypergeometric probability distribution, and then draw heuristic conclusions from its concentration behavior, which follows from Hoeffding-type bounds.
Keywords
Cite
@article{arxiv.1508.05702,
title = {An elementary heuristic for Hardy-Littlewood extended Goldbach's conjecture},
author = {Christian Táfula},
journal= {arXiv preprint arXiv:1508.05702},
year = {2024}
}
Comments
13 pages, 3 figures. The old version of this article ([v1], [v2]) has been expanded and split into two separate papers: arXiv:1807.10200 and the present one. From [v3], [v4] to this version: grammar was corrected, references were added, and figures were adjusted. For the scripts used to generate the figures, see https://github.com/tafula/hl_ext_gb_conj