Results 1 to 10 of about 11,676,412 (344)

Primes in prime number races [PDF]

Proceedings of the American Mathematical Society, 2019
Rubinstein and Sarnak have shown, conditional on the Riemann hypothesis (RH) and the linear independence hypothesis (LI) on the nonreal zeros of ζ ( s ) \zeta (s) , that the set of real numbers x ≥ 2 x\ge 2 for which π ( x ) &
Lichtman, Jared Duker, Martin, Greg, Pomerance, Carl   +2 more
openaire   +3 more sources

Fragile Watermark in Medical Image Based on Prime Number Distribution Theory. [PDF]

J Digit Imaging, 2021
Wei X, Zhang W, Yang B, Wang J, Xia Z.
europepmc   +2 more sources

On a Dynamical Approach to Some Prime Number Sequences [PDF]

Entropy, 2018
We show how the cross-disciplinary transfer of techniques from dynamical systems theory to number theory can be a fruitful avenue for research. We illustrate this idea by exploring from a nonlinear and symbolic dynamics viewpoint certain patterns ...
Lucas Lacasa, Bartolome Luque, Ignacio Gómez, Octavio Miramontes   +3 more
doaj   +2 more sources

Pseudo-prime number simulation and its application for security purpose [PDF]

MATEC Web of Conferences, 2018
Many public cryptography schemes rely on the use of prime numbers like for encryption and decryption. A prime number is one number that is widely used and large and consists of hundreds of digits, so it takes time to test whether the numbers are prime or
Rahim Robbi, Kurniasih Nuning, Pohan Nurmaliana, Sriadhi S, Listyorini Tri, Nanuru Ricardo Freedom, Manurung Rosida Tiurma, Najmurrokhman Asep, Hasibuan Abdurrozzaq, Abdullah Dahlan, Napitupulu Darmawan   +10 more
doaj   +2 more sources

Counting certain quadratic partitions of zero modulo a prime number [PDF]

Open Mathematics, 2021
Consider an odd prime number p≡2(mod3)p\equiv 2\hspace{0.3em}\left(\mathrm{mod}\hspace{0.3em}3). In this paper, the number of certain type of partitions of zero in Z/pZ{\mathbb{Z}}\hspace{-0.1em}\text{/}\hspace{-0.1em}p{\mathbb{Z}} is calculated using a ...
Xiao Wang, Li Aihua
doaj   +2 more sources

Computational challenges and solutions: Prime number generation for enhanced data security. [PDF]

PLoS ONE
This paper addresses the computational methods and challenges associated with prime number generation, a critical component in encryption algorithms for ensuring data security.
Amal Ezz-Eldien, Mohamed Ezz, Amjad Alsirhani, Ayman Mohamed Mostafa, Abdullah Alomari, Faeiz Alserhani, Mohammed Mujib Alshahrani   +6 more
doaj   +2 more sources

Blade prime-number / uniform angular distribution criterion for vibration reduction

Engineering Transactions
Currently, the vibration noise of casting cleaning equipment exceeds 95 dB, which not only impacts the equipment's service life but also jeopardizes workers' health.
Yong Li, Yaao Di, Wenzheng Dong, Fangxiang Yin, Yihao Yin, Shanling Han   +5 more
doaj   +2 more sources

Prime number races [PDF]

ریاضی و جامعه, 2022
Translator's abstractThis paper deals with one of the important and interesting topics in Number Theory under the title of prime number races, which is less discussed in Persian texts. All prime numbers (except 2) can be written in the form 4n+1 or 4n+3.
Mohammad Reza Esfandiari
doaj   +1 more source

A Remark on the Factorization of Factorials [PDF]

Mathematics Interdisciplinary Research, 2021
The subject of this paper is to study distribution of the prime factors p and their exponents, which we denote by vp (n!), in standard factorization of n! into primes. We show that for each θ > 0 the primes p not exceeding nθ eventually assume almost all
Mehdi Hassani, Mahmoud Marie
doaj   +1 more source

The average value of a certain number-theoretic function over the primes [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
We consider functions F:ℤ_{≥0}→ℤ_{≥0} for which there exists a positive integer n such that two conditions hold: F(p) divides n for every prime p, and for each divisor d of n and every prime p, we have that d divides F(p) iff d divides F(p mod d ...
Louis Rubin
doaj   +1 more source