COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS

Yahia Awad; Ramiz Hindi; Haissam Chehade

doi:10.21123/bsj.2023.7791

Baghdad Science Journal (Oct 2023)

COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS

Yahia Awad,
Ramiz Hindi,
Haissam Chehade

Affiliations

Yahia Awad: Department of Mathematics and Physics, School of Arts and Sciences, Lebanese International University, Bekaa, Lebanon
Ramiz Hindi: Department of Mathematics and Physics, School of Arts and Sciences, Lebanese International University, Saida, Lebanon
Haissam Chehade: Department of Mathematics and Physics, School of Arts and Sciences, Lebanese International University, Saida, Lebanon and Department of Mathematics and Physics, School of Arts and Sciences, The International University of Beirut, Beirut, Lebanon.

DOI: https://doi.org/10.21123/bsj.2023.7791
Journal volume & issue: Vol. 20, no. 5(Suppl.)

Abstract

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In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test. Moreover, new modiﬁcations are suggested in order to eliminate pseudoprimes. The study covers random primes such as Mersenne primes and Proth primes. Finally, these tests are arranged from the best to the worst according to strength, speed, and effectiveness based on the results obtained through programs prepared and operated by Mathematica, and the results are presented through tables and graphs.

Deterministic test, Mersenne numbers, Primality test, Probabilistic test, Proth numbers.

Published in Baghdad Science Journal

ISSN: 2078-8665 (Print); 2411-7986 (Online)
Publisher: College of Science for Women, University of Baghdad
Country of publisher: Iraq
LCC subjects: Science
Website: http://bsj.uobaghdad.edu.iq/index.php/BSJ

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