Results 21 to 30 of about 11,676,412 (344)
A conditional explicit result for the prime number theorem in short intervals [PDF]
Research in Number Theory, 2019 This paper gives an explicit bound for the prime number theorem in short intervals under the assumption of the Riemann hypothesis.
Michaela Cully-Hugill, Adrian W. Dudek
semanticscholar +1 more source
Prime number decomposition using the Talbot effect. [PDF]
Optics Express, 2018 We report on prime number decomposition by use of the Talbot effect, a well-known phenomenon in classical near field optics whose description is closely related to Gauss sums.
K. Pelka +3 more
semanticscholar +1 more source
About finding of prime numbers that follow after given prime number without using computer
Дифференциальная геометрия многообразий фигур, 2020 It is shown how to define one or several prime numbers following after given prime number without using computer only by calculating several arithmetic progressions. Five examples of finding such prime numbers are given.
V.S. Malakhovsky
doaj +1 more source
Counting rational points of two classes of algebraic varieties over finite fields
AIMS Mathematics, 2023 Let $ p $ stand for an odd prime and let $ \eta\in \mathbb Z^+ $ (the set of positive integers). Let $ \mathbb F_q $ denote the finite field having $ q = p^\eta $ elements and $ \mathbb F_q^* = \mathbb F_q\setminus \{0\} $.
Guangyan Zhu, Shiyuan Qiang, Mao Li
doaj +1 more source
Jacob’s Ladder: Prime Numbers in 2D
Mathematical and Computational Applications, 2020 Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense variety of problems.
Alberto Fraile +2 more
doaj +1 more source
Inclusive prime number races [PDF]
Transactions of the American Mathematical Society, 2017 Let $\pi(x;q,a)$ denote the number of primes up to $x$ that are congruent to $a$ modulo $q$. A prime number race, for fixed modulus $q$ and residue classes $a_1, \ldots, a_r$, investigates the system of inequalities $\pi(x;q,a_1) > \pi(x;q,a_2) > \cdots >
G. Martin, Nathan Ng
semanticscholar +1 more source
On some characteristics of subset of prime numbers
Дифференциальная геометрия многообразий фигур, 2019 The set of prime numbers p ≥ 5 is divided into two nonoverlapping subset P1 = {6k1 - 1}, P2 = {6k2 + 1}, where ki ⋲ A (i = 1,2). Subsets A1, A2 of natural numbers is defined by differences Ai = N\Bi, where B1, B2 are subset {j1}, {j2} defining subsets ...
V. Malakhovsky
doaj +1 more source
Ratio Mathematica, 2023 In prime labeling, vertices are labeled from 1 to n, with the condition that any two adjacent vertices have relatively prime labels. Coprime labeling maintains the same criterion as prime labeling with adjacent vertices using any set of distinct positive
Janani R, Ramachandran T
doaj +1 more source
Harmonic sets and the harmonic prime number theorem [PDF]
, 2005 We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+
Broughan, Kevin A., Casey, Rory J.
core +2 more sources
The concept of prime number and the strategies used in explaining prime numbers
South African Journal of Education, 2020 The teaching of mathematics does not only require the teacher to have knowledge about the subject, but the teacher also needs mathematical knowledge that is useful for the teaching and explaining thereof, as the teacher’s knowledge effects the students ...
Nejla Gürefe, Gülfem Sarpkaya Aktaş
doaj +1 more source