Results 11 to 20 of about 14,932 (263)

Lattice Points on the Fermat Factorization Method

Journal of Mathematics, 2022
In this paper, we study algebraic properties of lattice points of the arc on the conics x2−dy2=N especially for d=1, which is the Fermat factorization equation that is the main idea of many important factorization methods like the quadratic field sieve ...
Regis Freguin Babindamana, Gilda Rech Bansimba, Basile Guy Richard Bossoto   +2 more
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The Density of Primes Less or Equal to a Positive Integer up to 20,000: Fractal Approximation

Recoletos Multidisciplinary Research Journal, 2013
The highly irregular and rough fluctuations of the number of primes less or equal to a positive integer x for smaller values of x ( x≤20,000) renders the approximations through the Prime Number Theorem quite unreliable. A fractal probability distribution
Rodel B. Azura, Dennis A. Tarepe, Mark S. Borres, Jocelyn T. Panduyos   +3 more
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A note on Chebyshev's theorem [PDF]

Notes on Number Theory and Discrete Mathematics
We revisit a classical theorem of Chebyshev about distribution of primes on intervals (n, 2n), n∈ℕ, and prove a generalization of it. Extending Erdős' arithmetical-combinatorial argument, we show that for all k∈ℕ, there is nₖ∈ℕ such that the intervals ...
A. Bërdëllima
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Modeling the Dirichlet distribution using multiplicative functions

Nonlinear Analysis, 2020
For q,m,n,d ∈ N and some multiplicative function f > 0, we denote by T3(n) the sum of f(d) over the ordered triples (q,m,d) with qmd = n. We prove that Cesaro mean of distribution functions defined by means of T3 uniformly converges to the one-parameter ...
Gintautas Bareikis, Algirdas Mačiulis
doaj   +1 more source

Amodal completion of partly occluded figures: Effect of contour orientation [PDF]

Psihologija, 2003
In present study the temporal dimension of amodal completion in visual occlusion was investigated. We supposed that the visual system prefers to complete normally (vertically-horizontally) oriented contours than the oblique ones. Using the prime-matching
Marković Slobodan S., Gvozdenović Vasilije P.   +1 more
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On the prime distribution

, 2021
In this paper, the estimation formula of the number of primes in a given interval is obtained by using the prime distribution property. For any prime pairs $p>5$ and $ q>5 $, construct a disjoint infinite set sequence $A_1, A_2, \ldots, A_i. \ldots $, such that the number of prime pairs ($p_i$ and $q_i $, $p_i-q_i = p-q $) in $A_i $ increases ...
Zhao, Yong, Zhou, Jianqin
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Some Density Results on Sets of Primes for Hecke Eigenvalues

Journal of Mathematics, 2021
Let f and g be two distinct holomorphic cusp forms for SL2ℤ, and we writeλfn and λgn for their corresponding Hecke eigenvalues. Firstly, we study the behavior of the signs of the sequences λfpλfpj for any even positive integer j.
Aiyue Zou, Huixue Lao, Shu Luo
doaj   +1 more source

The Distribution of Prime Numbers

, 2022
In this paper, we discovered a new sequence of all prime numbers which end with a 1 or 9, the sequence defined by 𝑎(𝑛) = (𝑛^2 − 𝑛 − 1)/gcd (𝑏(𝑛), 𝑛^2 − 𝑛 − 1), with 𝑏(𝑛) satisfying the recurcive formula 𝑏(𝑛)=(𝑛 − 1). 𝑏(𝑛 − 1) − 𝑛. 𝑏(𝑛 − 2) and 𝑏(1) = 𝑏(2) = −1, the sequence 𝑎(𝑛) takes only 1’s and primes.
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A conceptual proposal on the undecidability of the distribution law of prime numbers and theoretical consequences

Ratio Mathematica, 2019
Within the conceptual framework of number theory, we consider prime numbers and the classic still unsolved problem to find a complete law of their distribution.
Gianfranco Minati
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New estimations for numerical analysis approach to twin primes conjecture [PDF]

Notes on Number Theory and Discrete Mathematics
This paper provides a better approximation of the functions presented in the article “Numerical Analysis Approach to Twin Primes Conjecture” (see [3]).
Gabriele Di Pietro
doaj   +1 more source