Results 1 to 10 of about 106 (99)
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 +3 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
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
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
doaj +1 more source
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
openaire +1 more source
Walailak Journal of Science and Technology, 2021 In this paper, we explain all non-negative integer solutions for the nonlinear Diophantine equation of type 8x + py = z2 when p is an arbitrary odd prime number and incongruent with 1 modulo 8.
Boorapa SINGHA
doaj +3 more sources
The Power of Hashing with Mersenne Primes
CoRR, 2020 The classic way of computing a $k$-universal hash function is to use a random degree-$(k-1)$ polynomial over a prime field $\mathbb Z_p$. For a fast computation of the polynomial, the prime $p$ is often chosen as a Mersenne prime $p=2^b-1$. In this paper, we show that there are other nice advantages to using Mersenne primes.
Thomas Dybdahl Ahle +2 more
openaire +2 more sources
Features of digital signal processing algorithms using Galois fields GF(2n+1).
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 +1 more source