Results 1 to 10 of about 384 (160)
On the Eight Levels theorem and applications towards Lucas-Lehmer primality test for Mersenne primes, I [PDF]
Arab Journal of Basic and Applied Sciences, 2023 Lucas-Lehmer test is the current standard algorithm used for testing the primality of Mersenne numbers, but it may have limitations in terms of its efficiency and accuracy.
Moustafa Mohamed
exaly +4 more sources
Minimality Conditions Equivalent to the Finitude of Fermat and Mersenne Primes [PDF]
Axioms, 2023 The question is still open as to whether there exist infinitely many Fermat primes or infinitely many composite Fermat numbers. The same question concerning Mersenne numbers is also unanswered.
Menachem Shlossberg
exaly +4 more sources
BiEntropy, TriEntropy and Primality [PDF]
Entropy, 2020 The order and disorder of binary representations of the natural numbers < 28 is measured using the BiEntropy function. Significant differences are detected between the primes and the non-primes.
Grenville J. Croll
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Proceedings of the National Academy of Sciences, 1971 The 24th Mersenne prime M p = 2 p - 1, and currently the largest known prime, is 2 19937 - 1. Primality
Tuckerman B.
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COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS [PDF]
مجلة بغداد للعلوم, 2023 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.
Yahia Awad, Ramiz Hindi, Haissam Chehade
doaj +3 more sources
Characterizations of Mersenne and 2-rooted primes
Finite Fields and Their Applications, 2015 We give several characterizations of Mersenne primes (Theorem 1.1) and of primes for which 2 is a primitive root (Theorem 1.2). These characterizations involve group algebras, circulant matrices, binomial coefficients, and bipartite graphs.
Gaywalee Yamskulna +2 more
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On the Sum of Reciprocals of Mersenne Primes
American Journal of Computational Mathematics, 2017 The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where is the set of perfect powers of prime numbers.
exaly +3 more sources
Gaussian Mersenne and Eisenstein Mersenne primes [PDF]
Mathematics of Computation, 2010 The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas–Lehmer test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the Quadratic Reciprocity Law and Proth’s Theorem.
Pedro Berrizbeitia, Boris Iskra
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A study on the number of edges of some families of graphs and generalized Mersenne numbers
Ratio Mathematica, 2022 The relationship between the Nandu sequence of the SM family of graphs and the Generalized Mersenne numbers is demonstrated in this study. Nandu sequences are related to the two families of SM sum graphs and SM Balancing graphs.
K.G. Sreekumar +3 more
doaj +1 more source
Mathematics of Computation, 1991 The number 2 110503
W. N. Colquitt, L. Welsh
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