Note On The Catalan Constant And Prime Triples

N. A. Carella

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arXiv · 2203.01832

Note On The Catalan Constant And Prime Triples

N. A. Carella

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Abstract

The existence of infinitely many consecutive prime triples $p_n$, $ p_{n+1}$, and $p_{n+2}$ as $n \to \infty$, is sufficient to prove that the Catalan constant $\beta(2)=0.9159655941\ldots $ is an irrational number. This note provides the detailed analysis. Moreover, the numerical data suggests that the irrationality measure is $\mu(\beta(2))=2$, the same as almost every irrational real numbers.

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N. A. Carella. 2022-02-28. Note On The Catalan Constant And Prime Triples. https://arxiv.org/abs/2203.01832

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