A complete classification of the Mersenne’s primes  and its implications for computing

Yeisson Alexis Acevedo-Agudelo

doi:10.33571/rpolitec.v16n32a10

Authors

Yeisson Alexis Acevedo-Agudelo Universidad EAFIT https://orcid.org/0000-0002-1640-9084

DOI:

https://doi.org/10.33571/rpolitec.v16n32a10

Keywords:

Mersenne’s prime, residual classes, Mersenne’s trapeze, computing, classification

Abstract

A study of Mersenne’s primes is carried out using the multiplicative group modulo 360 and a complete classification is obtained by its residual classes. This allows the search for Mersenne’s primes to be classified into four subgroups mutually exclusive (disjoint) and contributes to the ordered selection of exponents to be computationally tested. According to this idea, Mersenne’s trapeze is presented with the purpose of giving a geometric representation for this classification. Finally, from one of the theorems presented and proven for primes in modulo 360, a conjecture is established that could be solved by computing.

Se realiza un estudio de los números primos de Mersenne utilizando el grupo multiplicativo módulo 360 y se obtiene una clasificación completa mediante sus clases residuales. Esto permite clasificar la búsqueda de los números primos de Mersenne en cuatro subgrupos mutuamente excluyentes (disjuntos) y contribuye a la selección ordenada de exponentes a probar computacionalmente. Acorde a esta idea, el trapecio de Mersenne se presenta con el propósito de dar una representación geométrica para esta clasificación. Finalmente, a partir de uno de los teoremas presentado y demostrado para primos en módulo 360, se establece una conjetura que podría resolverse mediante verificación computacional.

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Author Biography

Yeisson Alexis Acevedo-Agudelo, Universidad EAFIT

Magister en Matemáticas Aplicadas, Universidad EAFIT

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