Results 1 to 10 of about 11,551,206 (206)
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 +3 more
doaj +2 more sources
Computational challenges and solutions: Prime number generation for enhanced data security. [PDF]
PLoS ONEThis 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 +6 more
doaj +2 more sources
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
Some explicit estimates for the error term in the prime number theorem [PDF]
Journal of Mathematical Analysis and Applications, 2022 By combining and improving recent techniques and results, we provide explicit estimates for the error terms $|\pi(x)-\text{li}(x)|$, $|\theta(x)-x|$ and $|\psi(x)-x|$ appearing in the prime number theorem.
D. Johnston, Andrew Yang
semanticscholar +1 more source
Highly uniform prime number theorems [PDF]
Annales de l'Institut Fourier, 2022 We prove a highly uniform version of the prime number theorem for a certain class of $L$-functions. The range of $x$ depends polynomially on the analytic conductor, and the error term is expressed in terms of an optimization problem depending explicitly ...
I. Kaneko, Jesse Thorner
semanticscholar +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
A variant of the prime number theorem [PDF]
Indagationes mathematicae, 2021 Let Λ(n) be the von Mangoldt function, and let [t] be the integral part of real number t. In this note, we prove that for any ε > 0 the asymptotic formula ∑ n6x Λ ([x n ]) = x ∑ d>1 Λ(d) d(d+ 1) +Oε ( x ) (x → ∞) holds.
Kui Liu, Jie Wu, Zhi-Shan Yang
semanticscholar +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
ALTERNATIVE PROOF OF THE INFINITUDE PRIMES AND PRIME PROPERTIES
Barekeng, 2023 Prime numbers is one of kind number that have many uses, one of which is cryptography. The uniqueness of prime numbers in their divisors and distributions causes prime numbers to be widely used in digital security systems. In number theory, one of famous
Dinni Rahma Oktaviani +2 more
doaj +1 more source