Keywords
primality criterion
deterministic algorithm
pure terms in arithmetic sequences
mixed terms in arithmetic sequences
How to Cite
Abstract
This paper presents the theoretical elements that support the calculation of the prime number counting function, π(x), based on properties of the sequences (6n-1) and (6n+1), n ≥ 1. As a result, Sufficient primality criteria are exposed for the terms of both sequences that support a deterministic computational algorithm that reduces the number of operations in calculating the function π(x) by exonerating all multiples of 3 from the analysis. In analyzing the primality of a particular term, the divisions by factor 3 are excluded. Such an algorithm can be applied to the search for prime numbers in each sequence separately, a possibility that allows approximately half the time of number search in practical applications.
References
[2] R. Martínez Zocón, L. Ortiz Céspedes, J. Horna Mercedes y A. Zavaleta Quipuscoa, «Algoritmos para pruebas de primalidad,» Selecciones Matemáticas, vol. 1, nº 02, p. 8, agosto-diciembre 2014.
[3] S. A. Ramírez Gajardo, Y. F. Vasquez Cea y C. Zenteno Acuña, «Curvas elípticas y test de primalidad,» Chillan, 2019.
[4] Z. Castellanos y Á. SandoVal, «Test de primalidad de secuencia de raíz digital Tesla Zollner,» ResearchGate, p. 8,
septiembre 2022.
[5] M. Allen Weiss, Estructuras de datos en Java, cuarta edición ed., Pearson Educación, S.A., 2013, 2013, p. 945.
This work is licensed under a Creative Commons Attribution 4.0 International License.