A Comparative Study between aNovel Deterministic Test for MersennePrimes and the Well-Known Primality Tests

Authors

Yahia Awad, Department of Mathematics and Physics, School of Arts and Sciences, Lebanese International University, Bekaa, LebanonFollow
Ramiz Hindi, Department of Mathematics and Physics, School of Arts and Sciences, Lebanese International University, Saida, LebanonFollow
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.Follow

Abstract

In this article, we propose a new deterministic primality test for the Mersenne numbers 2^��−1which is introduced by theHindi Awad test (HAT). The idea of this test is related to that of Pepin’s primality test for Fermat numbers 2^2��+1. In addition, a modification to solve the weaknesses in the Selfridge-Lucas Test (SLT) is presented and used to suggest a new modified test called Hindi Selfridge-Lucas test (HLT) with the help of base 3. Finally, a comparative study betweensome well-known primality tests and the new test is done in order to identify and classify them from the least to the most powerful and reliable tests according to their level of strength, speed, and effectiveness based on the results obtained through programs prepared and operated by Mathematicawhere the results are presented through tables and graphs.

Keywords

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

Article Type

Supplemental Issue

How to Cite this Article

Awad, Yahia; Hindi, Ramiz; and Chehade, Haissam (2023) "A Comparative Study between aNovel Deterministic Test for MersennePrimes and the Well-Known Primality Tests," Baghdad Science Journal: Vol. 20: Iss. 5, Article 50.
DOI: https://doi.org/10.21123/bsj.2023.7791