# The density of integers representable as the sum of four prime cubes

## TL;DR

This paper establishes a new lower bound on the density of integers that can be expressed as the sum of four prime cubes, improving previous bounds and advancing understanding of prime representations.

## Contribution

It provides an improved lower bound on the density of integers representable as the sum of four prime cubes, surpassing earlier known bounds.

## Key findings

- Lower density bound at least 0.009664
- Improves previous bounds of 0.003125 and 0.005776
- Advances knowledge on prime sum representations

## Abstract

The set of integers which can be written as the sum of four prime cubes has lower density at least $0.009664$. This improves earlier bounds of $0.003125$ by Ren and $0.005776$ by Liu.