COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS
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 prim...
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| Format: | Article |
| Language: | English |
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University of Baghdad, College of Science for Women
2023-10-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7791 |
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| author | Yahia Awad Ramiz Hindi Haissam Chehade |
| author_facet | Yahia Awad Ramiz Hindi Haissam Chehade |
| author_sort | Yahia Awad |
| collection | DOAJ |
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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.
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| format | Article |
| id | doaj-art-e52c36bd4af9425bba4f05121d3a2e93 |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-e52c36bd4af9425bba4f05121d3a2e932025-08-20T03:38:44ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862023-10-01205(Suppl.)10.21123/bsj.2023.7791COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTSYahia Awad0Ramiz Hindi1Haissam Chehade2 Department of Mathematics and Physics, School of Arts and Sciences, Lebanese International University, Bekaa, Lebanon Department of Mathematics and Physics, School of Arts and Sciences, Lebanese International University, Saida, LebanonDepartment 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. 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. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7791Deterministic test, Mersenne numbers, Primality test, Probabilistic test, Proth numbers. |
| spellingShingle | Yahia Awad Ramiz Hindi Haissam Chehade COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS مجلة بغداد للعلوم Deterministic test, Mersenne numbers, Primality test, Probabilistic test, Proth numbers. |
| title | COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS |
| title_full | COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS |
| title_fullStr | COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS |
| title_full_unstemmed | COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS |
| title_short | COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS |
| title_sort | comparative study between a novel deterministic test for mersenne primes and the well known primality tests |
| topic | Deterministic test, Mersenne numbers, Primality test, Probabilistic test, Proth numbers. |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7791 |
| work_keys_str_mv | AT yahiaawad comparativestudybetweenanoveldeterministictestformersenneprimesandthewellknownprimalitytests AT ramizhindi comparativestudybetweenanoveldeterministictestformersenneprimesandthewellknownprimalitytests AT haissamchehade comparativestudybetweenanoveldeterministictestformersenneprimesandthewellknownprimalitytests |