Prime Sums

TL;DR

This paper explores graphs based on prime sums, revealing their connection to prime gap distribution and Cramér's model, and extends the discussion to Gaussian integers.

Contribution

It introduces a novel graph-theoretic framework for analyzing prime sums and their relation to prime gaps, including generalizations to Gaussian integers.

Findings

Graph properties relate to prime gap distribution

Connections to Cramér's probabilistic model

Extensions to Gaussian integers discussed

Abstract

We study the properties of certain graphs involving the sums of primes. Their structure largely turns out to relate to the distribution of prime gaps and can be roughly seen in Cram\'er's model as well. We also discuss generalizations to the Gaussian integers.