Remark on the irrationality of the Brun's constant

TL;DR

This paper numerically investigates the Brun's constant B2, finding evidence of its irrationality through continued fraction analysis and convergence to known mathematical constants.

Contribution

It introduces a novel numerical approach to support the conjecture that Brun's constant is irrational, based on continued fraction approximations.

Findings

Denominators' means close to Khinchin constant

Square roots of denominators near Khinchin-Levy constant

Supports the belief in infinite twin primes

Abstract

We have calculated numerically geometrical means of the denominators of the continued fraction approximations to the Brun constant B2. We get values close to the Khinchin constant. Next we calculated the n-th square roots of the denominators of the n-th convergents of these continued fractions obtaining values close to the Khinchin-Levy constant. These two results suggests that B2 is irrational, supporting the common believe that there is an infinity of twins.