Significant Digits of Primes in Subsets

TL;DR

This paper proves a variant of Benford's Law for positive-density subsets of primes, extending the law's applicability to primes within number fields, revealing patterns in the distribution of their leading digits.

Contribution

It establishes a new variant of Benford's Law for primes in subsets of positive density, generalizing the result to number fields.

Findings

Benford's Law applies to primes in certain subsets

The result extends to primes in number fields

Provides a new understanding of digit distribution in primes

Abstract

Benford's Law describes the prevalence of small numbers as the leading digits of numbers in many sets of integers. We prove a variant of Benford's law for many positive-density subsets of the primes. This follows from a more general result over number fields.