COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS
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Abstract
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.
Received 18/9/2022
Revised 22/11/2022
Accepted 23/11/2022
Published Online First 20/3/2023
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