Results 1 to 10 of about 191 (146)
Proceedings of the National Academy of Sciences of the United States of America, 1971 The 24th Mersenne prime M p = 2 p - 1, and currently the largest known prime, is 2 19937 - 1. Primality
Bryant Tuckerman
exaly +5 more sources
Features of digital signal processing algorithms using Galois fields GF(2n+1). [PDF]
PLoS ONE, 2023 An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1 ...
Ibragim E Suleimenov +2 more
doaj +2 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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Computer Assisted Surgery, 2019 Purpose: Encryption of patient information has become an important issue in medical ultrasound instrumentation to secure information when images are accessed off-site.
Hojong Choi
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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
The specifics of the Galois field GF(257) and its use for digital signal processing [PDF]
Scientific ReportsAn algorithm of digital logarithm calculation for the Galois field $$GF(257)$$ G F ( 257 ) is proposed. It is shown that this field is coupled with one of the most important existing standards that uses a digital representation of the signal through 256 ...
Akhat Bakirov +4 more
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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
Mersenne version of Brocard-Ramanujan equation
Journal of New Results in Science, 2023 In this study, we deal with a special form of the Brocard-Ramanujan equation, which is one of the interesting and still open problems of Diophantine analysis.
Ayşe Nalli, Seyran İbrahimov
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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
openaire +2 more sources
Mathematics of Computation, 1991 The number 2 110503
W. N. Colquitt, L. Welsh
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