Results 1 to 10 of about 524 (199)
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 was shown by the Lucas-Lehmer test on an IBM 360/91 computer.
Bryant Tuckerman
exaly +5 more sources
The emergence of the Mersenne Star: a new geometry of prime numbers bridging physics and artificial general intelligence [PDF]
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 Ibrahim
exaly +6 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
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 Ibrahim
exaly +4 more sources
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
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
doaj +2 more sources
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
exaly +2 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
doaj +2 more sources
Cryptographically Strong Elliptic Curves of Prime Order [PDF]
International Journal of Electronics and Telecommunications, 2021 The purpose of this paper is to generate cryptographically strong elliptic curves over prime fields Fp, where p is a Mersenne prime, one of the special primes or a random prime. We search for elliptic curves which orders are also prime numbers.
Marcin Barański +2 more
doaj +1 more source
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