Results 21 to 30 of about 451,593 (141)

The Numbers of Lakh Place of Mersenne Primes

Journal of Computational Mathematica, 2018
The numbers Mn = 2 n − 1, n > 1 are called Mersenne numbers. A Mersenne number which is also a prime is called Mersenne prime. In this paper, the numbers of lakh place of Mersenne primes Mp = 2 p − 1, where p = 8r+ 1, 8r+ 3, 8r+ 5, 8r+ 7 for r = 1, 2, ...
A. Arockiasamy, R. Srinath
semanticscholar   +2 more sources

Some new results on the largest cycle consisting of quadratic residues [PDF]

Notes on Number Theory and Discrete Mathematics
The length of the largest cycle consisting of quadratic residues of a positive integer n is denoted by L(n). In this paper, we have obtained a formula for finding L(p), where p is a prime. Also, we attempt to characterize a prime number p in terms of the
Prabin Das, Pinkimani Goswami
doaj   +1 more source

A Technique for Image Encryption Using the Modular Multiplicative Inverse Property of Mersenne Primes

Symmetry
Mersenne prime numbers, expressed in the form (2n − 1), have long captivated researchers due to their unique properties. The presented work aims to develop a symmetric cryptographic algorithm using a novel technique based on the logical properties of ...
Shanooja M. A., A. N.
semanticscholar   +1 more source

Generalizing the eight levels theorem: a journey to Mersenne prime discoveries and new polynomial classes

Arab Journal of Basic and Applied Sciences
Mersenne 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
doaj   +1 more source

Complexity Lower Bound for Boolean Functions in the Class of Extended Operator Forms

Известия Иркутского государственного университета: Серия "Математика", 2019
Starting with the fundamental work of D.E.Muller in 1954, the polynomial representations of Boolean functions are widely investigated in connection with the theory of coding and for the synthesis of circuits of digital devices.
A.S. Baliuk
doaj   +1 more source

Acerca de algunos exponentes de Mersenne (About some Mersenne exponents)

Revista Digital Matemática, Educación e Internet
Los números primos de Mersenne crecen de manera vertiginosa y se vuelven intratables con las herramientas de cómputo actuales. En este trabajo se repasan brevemente las cadenas de Mersenne para mostrar cómo ese crecimiento exponencial impone un límite en
Gerardo Miramontes de León
doaj   +1 more source

On the intersections of nilpotent subgroups in simple groups

Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.
Abstract Let G$G$ be a finite group and let Hp$H_p$ be a Sylow p$p$‐subgroup of G$G$. A recent conjecture of Lisi and Sabatini asserts the existence of an element x∈G$x \in G$ such that Hp∩Hpx$H_p \cap H_p^x$ is inclusion‐minimal in the set {Hp∩Hpg:g∈G}$\lbrace H_p \cap H_p^g \,:\, g \in G\rbrace$ for every prime p$p$.
Timothy C. Burness, Hong Yi Huang
wiley   +1 more source

FPGA Realization of a Novel Hyperchaos Augmented Image Encryption Algorithm

IET Computers &Digital Techniques, Volume 2026, Issue 1, 2026.
With the rapid growth of multimedia communication, protecting image data has become increasingly critical. This article proposes a novel 3‐stage hyperchaos‐based augmented image encryption technique (3SHAIET) that utilizes a three‐stage process with chaotic systems of increasing dimensionality (e.g., six‐dimensional [6D], 8D, and 9D) to enhance ...
Wassim Alexan, Noura H. Elshabasy, Eyad Mamdouh, Remas Osama, Mohamed A. Abd El Ghany, Dina El-Damak, Jim Harkin   +6 more
wiley   +1 more source

Assessing the problem of excitation light scattering in high‐viscosity jets used in serial crystallography sample delivery

Journal of Applied Crystallography, Volume 58, Issue 6, Page 2078-2089, December 2025.
We experimentally demonstrate that the scattering‐induced decrease in light intensity experienced by a crystal embedded in a high‐viscosity jet is very limited in materials such as lipidic cubic phase or hydroxyethyl cellulose, and therefore cannot justify the use of pump energies exceeding the linear excitation regime under realistic experimental ...
Stanisław Niziński, Bogdan Marekha, Jochen Reinstein, Robert L. Shoeman, R. Bruce Doak, Ilme Schlichting   +5 more
wiley   +1 more source

Energy Dissipation in Hilbert Envelopes on Motion Waveforms Detected in Vibrating Dynamical Systems: An Axiomatic Approach

Communications in Advanced Mathematical Sciences
This paper introduces an axiomatic approach in the theory of energy dissipation in Hilbert envelopes on motion waveforms emanating from various vibrating dynamical systems. A Hilbert envelope is a curve tangent to peak points on a motion waveform.
Tharaka Liyanage, James F. Peters
doaj   +1 more source