A prime number theorem for the majority function

TL;DR

This paper proves an unconditionally established prime number theorem related to the distribution of zeros and ones in the binary expansion of prime numbers, revealing new insights into their binary structure.

Contribution

It introduces a prime number theorem specifically for the majority function in the binary expansion of primes, a novel result in number theory.

Findings

Zeros and ones in prime binary expansions are distributed according to the theorem

The proof is unconditional, not relying on unproven hypotheses

Establishes a new connection between prime distribution and binary patterns

Abstract

In the paper, the occurrence of zeros and ones in the binary expansion of the primes is studied. In particular the statement in the title is established. The proof is unconditional.