Goldbach's Problem in Primes with Binary Expansions of a Special Form

TL;DR

This paper addresses Goldbach's problem specifically for natural numbers with binary expansions containing an even number of ones, providing a solution within this special class.

Contribution

The paper solves Goldbach's problem for numbers whose binary expansions have an even number of ones, a novel restriction not previously addressed.

Findings

Goldbach's conjecture holds for numbers in class .

Established the distribution of such numbers in relation to Goldbach's problem.

Proved the conjecture for a new subset of natural numbers.

Abstract

Let $\mathbb{N}_0$ be a class of natural numbers whose binary expansions contain even numbers of ones. Goldbach's problem in numbers of class $\mathbb{N}_0$ is solved.