Prime numbers in typical Continued Fraction Expansions

TL;DR

This paper investigates the statistical behavior of prime numbers appearing as digits in continued fraction expansions of real numbers using tools from metrical number theory and ergodic theory.

Contribution

It introduces a probabilistic framework for understanding how prime numbers occur within continued fraction digits, combining metrical number theory and ergodic theory.

Findings

Prime numbers appear with specific probabilistic laws in continued fractions.

The distribution of prime digits follows certain ergodic properties.

New insights into the frequency and pattern of prime digits in continued fractions.

Abstract

We study, from the viewpoint of metrical number theory and (infinite) ergodic theory, the probabilistic laws governing the occurrence of prime numbers as digits in continued fraction expansions of real numbers.