# An equation about sum of primes with digital sum constraints

## TL;DR

This paper explores an equation involving four primes with digital sum constraints, establishing conditions on their digital sums and providing a method to determine perfect squares within the proof.

## Contribution

It introduces new digital sum constraints on primes in sum equations and offers a method to identify perfect squares related to these constraints.

## Key findings

- Square root of digital sum > 4
- Digital sum not multiple of 3
- Method for determining perfect squares

## Abstract

We know that any prime number of form $4s+1$ can be written as a sum of two perfect square numbers. As a consequence of Goldbach's weak conjecture, any number great than $10$ can be represented as a sum of four primes. We are motivated to consider an equation with some constraints about digital sum for the four primes. And we conclude that the square root of the digital sum of the four primes will greater than $4$ and will not be a multiple of $3$ if the equation has solutions. In the proof, we give the method of determining whether a number is a perfect square.