Results 1 to 10 of about 39,822 (114)
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
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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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
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Arab Journal of Basic and Applied SciencesMersenne primes, renowned for their captivating form as [Formula: see text] have intrigued mathematicians for centuries. In this paper, we embark on a captivating quest to unveil the intricate nature of Mersenne primes, seamlessly integrating methods ...
Moustafa Mohamed
exaly +3 more sources
Arab Journal of Basic and Applied SciencesThis paper introduces a new key geometric way to understand Mersenne prime numbers. It discovers a shape called the Mersenne Star, which appears naturally from a special sequence named the Quanta Prime Sequence (QPS).
Moustafa Mohamed
exaly +3 more sources
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
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Public key cryptographic algorithm SM2 optimized implementation on low power embedded platform
网络与信息安全学报, 2022 With the development of wireless communication technology and the popularization of intelligent terminals, more and more cryptographic algorithms are applied to IoT devices to ensure the security of communication and data.Among them, the SM2 elliptic ...
Ganqin LIU +4 more
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Splitting Sequences for Coding and Hybrid Incremental ARQ with Fragment Retransmission
Mathematics, 2021 This paper proposes a code defined on a finite ring ℤpM, where pM = 2m−1 is a Mersenne prime, and m is a binary size of ring elements. The code is based on a splitting sequence (splitting set) S, defined for the given multiplier set E=±20, ±21,…, ±2m−1 ...
Dragana Bajić +2 more
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Mersenne Primes in Certain Lucas Sequences [PDF]
EPJ Web of ConferencesPrime numbers are the most important numbers in number theory and cryptography. One of such special primes are given by the set of Mersenne primes, that are derived from the form Mn = 2n − 1, where n is a prime number.
Hadi Ahmed H., Hashim Hayder R.
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