Results 81 to 90 of about 1,699,076 (196)

Distribution of prime numbers Distribution of the prime numbers

This research explores the distribution of prime numbers, which are a fundamental topic in number theory. The study originated from the author's fascination with mathematics and the desire to discover something novel.
Khalil, Lolav Ahmed
core   +1 more source

On an inequality about Euler's totient function [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we show that when Nₖ is a primorial and φ(Nₖ) is Euler's totient function, the inequality φ(Nₖ)44.
Cheng-Ting Wang
doaj   +1 more source

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

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   +1 more source

Mersenne Primes in Certain Lucas Sequences [PDF]

EPJ Web of Conferences
Prime numbers are the most important numbers in number theory and cryptography. One of such special primes are given by the set of Mersenne primes, that are derived from the form Mn = 2n − 1, where n is a prime number.
Hadi Ahmed H., Hashim Hayder R.
doaj   +1 more source

Prime number or Multiple Of Prime number

Research Is Going On.
openaire   +2 more sources

On the emergence of the Quanta Prime sequence

Arab Journal of Basic and Applied Sciences
This paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications.
Moustafa Ibrahim
doaj   +1 more source

A note on Sturm-Liouville problems whose spectrum is the set of prime numbers

Electronic Journal of Differential Equations, 2011
We show that there is no classical regular Sturm-Liouville problem on a finite interval whose spectrum consists of infinitely many distinct primes numbers. In particular, this answers in the negative a question raised by Zettl in his book [9].
Angelo B. Mingarelli
doaj  

The Number of Prime Numbers and Twin Prime Numbers Is Infinite

A prime number graphic method is proposed. In the coordinate system, the prime number and its multiple points are represented by the prime number span-arc. Other points that cannot be determined as the prime number or the composite number are called undetermined points, so as to obtain the prime number generation process diagram represented by the ...
openaire   +1 more source

On a sequence involving the prime numbers

J. Integer Seq., 2015
8 pages, comments are ...
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Prime Numbers and Polynomials.

, 2010
This thesis deals with the classical problem of prime numbers represented by polynomials. It consists of three parts. In the first part I collected many results about the problem. Some of them are quite recent and this part can be considered as a survey of the state of the art of the subject. In the second part I present two results due to P. Pleasants
openaire   +2 more sources