Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Hyperbolic Primality Test and Catalan–Mersenne Number Conjecture

Version 1 : Received: 10 May 2024 / Approved: 14 May 2024 / Online: 14 May 2024 (13:53:44 CEST)

How to cite: Lee, Y. Hyperbolic Primality Test and Catalan–Mersenne Number Conjecture. Preprints 2024, 2024050952. https://doi.org/10.20944/preprints202405.0952.v1 Lee, Y. Hyperbolic Primality Test and Catalan–Mersenne Number Conjecture. Preprints 2024, 2024050952. https://doi.org/10.20944/preprints202405.0952.v1

Abstract

We develop a primality test for Mersenne numbers and investigate the primality of the sequence of Catalan-Mersenne numbers. We use induction as a proof to show that the 5th Catalan-Mersenne number is a prime number, thus demonstrating the infinitude of Mersenne primes.

Keywords

Catalan-Mersenne conjecture; Mersenne prime; double Mersenne prime

Subject

Computer Science and Mathematics, Algebra and Number Theory

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