scholarly journals Prime numbers demystified

2021 ◽  
Vol 9 (6) ◽  
pp. 131-145
Author(s):  
Artwell Ncube
Keyword(s):  
Prime Numbers ◽  
Prime Integer ◽  
Simple Arithmetic ◽  
The Relationship ◽  
Distribution Equation

The paper is the ultimate prime numbers algorithm that gets rid of the unneccessary mystery about prime numbers. All the numerous arithmetic series patterns observed between various prime numbers are clearly explained with an elegant "pattern of remainders". With this algorithm we prove that odd numbers too can make an Ulam spiral contrary to current ""proofs". At the end of the paper this author proves the relationship between a simple arithmetic series pattern and the Riehmann's prime numbers distribution equation. This paper would be important for encryption too. As an example, prime integer 1979 is expressed as 1.2.4.5.10.3.7.3.1.7.26.18.11.1. This makes even smaller primes useful for encryption as well.

scholarly journals Step Pyramid Distribution for Prime Numbers

2022 ◽  
Vol 14 (1) ◽  
pp. 55
Author(s):  
Shaimaa said soltan
Keyword(s):  
Number System ◽  
Prime Numbers ◽  
Classification Algorithm ◽  
Algorithm Complexity ◽  
Arithmetic Operations ◽  
Simple Arithmetic ◽  
Simpler Algorithm

In this document, we will present a new way to visualize the distribution of Prime Numbers in the number system to spot Prime numbers in a subset of numbers using a simpler algorithm. Then we will look throw a classification algorithm to check if a number is prime using only 7 simple arithmetic operations with an algorithm complexity less than or equal to O (7) operations for any number.

Young children’s arithmetic strategies in social context: How parents contribute to children’s strategy development while playing games

2004 ◽  
Vol 28 (4) ◽  
pp. 347-357 ◽  
Author(s):  
David F. Bjorklund ◽  
Martha J. Hubertz ◽  
Andrea C. Reubens
Keyword(s):  
Cognitive Strategies ◽  
Past Research ◽  
Strategy Development ◽  
Development Theory ◽  
Sociocultural Perspective ◽  
Simple Arithmetic ◽  
Parent Child Interactions ◽  
The Social ◽  
The Relationship ◽  
Math Problems

We examined the relationship between parents’ behaviour and children’s use of simple arithmetic strategies while playing a board game in contrast to solving arithmetic problems. In a microgenetic study spanning 3 weeks, 5-year-old children who were just beginning kindergarten played a modified game of “Chutes and Ladders” with one of their parents, computing their moves from the throw of dice. Children also solved math problems (math context) given to them by their parents at the end of each session. Children’s arithmetic strategies and a variety of parental behaviours (prompt, prompt after error, affirmation, disaffirmation, cognitive directives, provide answer) were coded for children’s game moves and the math context. As in past research, children used multiple and variable strategies, both when computing their moves during the game and in solving the math problems. Parents displayed different patterns of behaviours during the game and math contexts and showed different relationships among behaviours and strategies as a function of context, reflecting their sensitivity to the cognitive demands on their children of the different tasks. The results were interpreted in terms of the need to integrate contemporary strategy development theory with a sociocultural perspective and to recognise the dynamic nature of parent–child interactions with respect to the social construction of cognitive strategies.

scholarly journals The relationship between problem size and fixation patterns during addition, subtraction, multiplication, and division

2016 ◽  
Vol 2 (2) ◽  
pp. 91-115 ◽  
Author(s):  
Evan T. Curtis ◽  
Matthew G. Huebner ◽  
Jo-Anne LeFevre
Keyword(s):  
Eye Movements ◽  
Eye Tracking ◽  
Cognitive Processing ◽  
Mental Arithmetic ◽  
Problem Size ◽  
Single Digit ◽  
Simple Arithmetic ◽  
Division Problems ◽  
The Right ◽  
The Relationship

Eye-tracking methods have only rarely been used to examine the online cognitive processing that occurs during mental arithmetic on simple arithmetic problems, that is, addition and multiplication problems with single-digit operands (e.g., operands 2 through 9; 2 + 3, 6 x 8) and the inverse subtraction and division problems (e.g., 5 – 3; 48 ÷ 6). Participants (N = 109) solved arithmetic problems from one of the four operations while their eye movements were recorded. We found three unique fixation patterns. During addition and multiplication, participants allocated half of their fixations to the operator and one-quarter to each operand, independent of problem size. The pattern was similar on small subtraction and division problems. However, on large subtraction problems, fixations were distributed approximately evenly across the three stimulus components. On large division problems, over half of the fixations occurred on the left operand, with the rest distributed between the operation sign and the right operand. We discuss the relations between these eye tracking patterns and other research on the differences in processing across arithmetic operations.

Layman's method to verify Goldbach's conjectures

2013 ◽  
Vol 10 (4) ◽  
pp. 401-404
Author(s):  
Y. Chang
Keyword(s):  
Graphical Method ◽  
Number Line ◽  
Prime Numbers ◽  
Coordinate Frame ◽  
Horizontal Line ◽  
Analytical Geometry ◽  
Mathematical Problems ◽  
Straight Lines ◽  
Relationship Of ◽  
The Relationship

Goldbach conjecture of prime numbers is one of the unsolved mathematical problems. Many trial solutions appeared in the literature, but so far none has been accepted by the mathematics societies. This paper describes a graphical method devised by me to explain the mystery of the said conjecture. My method based on the teachings of analytical geometry using a rectangular coordinate frame with even numbers as ordinates and prime numbers as abscissas. Straight lines with 45 degree slop and intercepets of varying prime numbers on the ordinate are drawn to meet all the vertical straight draw grom the abscissas. These diagonal lines are designated as separation lines and identified by its intercept number. The intersection of vertical abscissa line, the separation line and a horizontal line drawn from the ordinates shows the relationship of an even number and its pair of prime numbers. These intersections vividly appear on the horizontal even number line and can be easily seen. This method is a graphical version of binary combination of prime numbers and can locate the prime-pairs of any even nuber by drawing a family of separation lines.

SIZE EFFECT ON SPECIFIC ENERGY DISTRIBUTION IN PARTICLE COMMINUTION

Fractals ◽  
2017 ◽  
Vol 25 (02) ◽  
pp. 1750016 ◽  
Author(s):  
YONGFU XU ◽  
YIDONG WANG
Keyword(s):  
Particle Size ◽  
Energy Distribution ◽  
Specific Energy ◽  
Reduction Process ◽  
Fractal Model ◽  
Published Data ◽  
Weibull Statistics ◽  
Self Similar ◽  
The Relationship ◽  
Distribution Equation

A theoretical study is made to derive an energy distribution equation for the size reduction process from the fractal model for the particle comminution. Fractal model is employed as a valid measure of the self-similar size distribution of comminution daughter products. The tensile strength of particles varies with particle size in the manner of a power function law. The energy consumption for comminuting single particle is found to be proportional to the 5(D−3)/3rd order of the particle size, [Formula: see text] being the fractal dimension of particle comminution daughter. The Weibull statistics is applied to describe the relationship between the breakage probability and specific energy of particle comminution. A simple equation is derived for the breakage probability of particles in view of the dependence of fracture energy on particle size. The calculated exponents and Weibull coefficients are generally in conformity with published data for fracture of particles.

Relationship between Circadian Rhythm in Body Temperature and Ultradian Variations of Psychological and Physiological States in Arousal

1995 ◽  
Vol 7 (2) ◽  
pp. 151-155
Author(s):  
Yoichi Tsuji ◽  
◽  
Kazuyuki Nagasawa
Keyword(s):  
Circadian Rhythm ◽  
Body Temperature ◽  
Maximum Entropy Method ◽  
Significant Negative Correlation ◽  
Entropy Method ◽  
Diurnal Variations ◽  
Least Square ◽  
Arithmetic Operations ◽  
Simple Arithmetic ◽  
The Relationship

In order to investigate the relationship between the ultradian variations of psychological and physiological states in arousal and circadian rhythm in body temperature, the physiological and psychological testing of seven subjects was carried out continuously for 13 hours from 9am to 10pm. Diurnal variations in physiological and psychological quantities were analyzed by the maximum entropy method and the least square approximation. As a result of the analysis, three kinds of ultradian component (periods of 1.5, 3.0, and 6.0 hour) were detected. In addition, with regard to the 1.5-hour-cycle component for simple arithmetic operations and heart rates, the interrelation between the period of ultradian variations and the amplitude of the rhythm of body temperature was investigated for each subject; as a result, it was recognized that there were a statistical significant negative correlation (r = -0.72, p<0.05) between body temperature and simple arithmetic operations and a positive correlation (r = 0.95, p<0.001) between body temperature and heart rate. This shows that the cycles of ultradian variations are affected by circadian rhythms, and is important knowledge in considering the essence of ultradian rhythm.

scholarly journals Prime Numbers: A Particle in a Box and the Complex Wave Model

2015 ◽  
Vol 7 (4) ◽  
pp. 43
Author(s):  
Raul Alberto Ribeiro Correia de Sousa
Keyword(s):  
Prime Number ◽  
Energy Levels ◽  
Computing Time ◽  
Wave Model ◽  
Prime Numbers ◽  
Integer Number ◽  
Oscillation Modes ◽  
Complex Wave ◽  
New Formula ◽  
The Relationship

<p>Euler{'}s formula establishes the relationship between the trigonometric function and the exponential function. In doing so unifies two waves, a real and an imaginary one, that propagate through the Complex number set, establishing relation between integer numbers. A complex wave, if anchored by zero and by a defined integer number \textit{N}, only can assume certain oscillation modes. The first mode of oscillation corresponds always to a \textit{N} prime number and the other modes to its multiples.</p><p>\begin{center}<br />\(\psi (x)=x e^{i\left(\frac{n \pi }{N}x\right)}\)<br />\end{center}</p><p>Under the above described conditions, these waves and their admissible oscillation modes allows for primality testing of integer numbers, the deduction of a new formula $\pi(x)$ for counting prime numbers and the identification of patterns in the prime numbers distribution with computing time gains in the calculations. In this article, four theorems and one rule of factorizing are put forward with consequences for prime number signaling, counting and distribution. Furthermore, it is establish the relationship between this complex wave with a time independent semi-classical harmonic oscillator, in which the spectrum of the allowed energy levels are always only prime numbers. Thus, it is affirmative the reply to the question if the prime numbers distribution is related to the energy levels of a physical system.</p>

scholarly journals Majorana quanta, string scattering, curved spacetimes and the Riemann Hypothesis

2021 ◽  
Author(s):  
Fabrizio Tamburini ◽  
Ignazio Licata
Keyword(s):  
Riemann Hypothesis ◽  
Open String ◽  
Prime Numbers ◽  
Dirac Particles ◽  
Ideal System ◽  
S Matrix ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Poles And Zeros ◽  
The Relationship

Abstract The Riemann Hypothesis states that the Riemann zeta function ζ(z) admits a set of “non-trivial” zeros that are complex numbers supposed to have real part 1/2. Their distribution on the complex plane is thought to be the key to determine the number of prime numbers before a given number. Hilbert and Pólya suggested that the Riemann Hypothesis could be solved through the mathematical tools of physics, finding a suitable Hermitian or unitary operator that describe classical or quantum systems, whose eigenvalues distribute like the zeros of ζ(z). A different approach is that of finding a correspondence between the distribution of the ζ(z) zeros and the poles of the scattering matrix S of a physical system. Our contribution is articulated in two parts: in the first we apply the infinite-components Majorana equation in a Rindler spacetime and compare the results with those obtained with a Dirac particle following the Hilbert-Pólya approach showing that the Majorana solution has a behavior similar to that of massless Dirac particles and finding a relationship between the zeros of zeta end the energy states. Then, we focus on the S-matrix approach describing the bosonic open string scattering for tachyonic states with the Majorana equation. Here we find that, thanks to the relationship between the angular momentum and energy/mass eigenvalues of the Majorana solution, one can explain the still unclear point for which the poles and zeros of the S-matrix of an ideal system that can satisfy the Riemann Hypothesis, exist always in pairs and are related via complex conjugation. As claimed in the literature, if this occurs and the claim is correct, then the Riemann Hypothesis could be in principle satisfied, tracing a route to a proof.

scholarly journals Teaching Business Statistics: Some Useful Relationships

2020 ◽  
Vol 15 (5) ◽  
pp. 73
Author(s):  
Philip F. Rice ◽  
Chris Brune
Keyword(s):  
Geometric Mean ◽  
Joint Probability ◽  
Arithmetic Mean ◽  
Simple Arithmetic ◽  
Weighted Arithmetic ◽  
Multiplication Rule ◽  
Business Statistics ◽  
Statistics Course ◽  
Compound Interest ◽  
The Relationship

The purpose of this paper is to suggest an instructional approach in the introductory business statistics course that utilizes relationships between separately introduced topics. The paper will explore three &ldquo;useful relationships&rdquo; that can assist classroom instruction: (1) the relationship between the simple arithmetic mean, the weighted arithmetic mean, and the expected value of a discrete probability distribution; (2) the relationship between the use of the multiplication rule to calculate the joint probability associated with two events, use of tree diagrams, and the use of the binomial and hypergeometric distributions; and (3) the relationship between the geometric mean and the compound interest rate. Each discussion includes detailed examples of calculations to demonstrate the relationships.

Mengungkap Konsep Bilangan Prima dalam Surat Al-Kautsar

2016 ◽  
Vol 7 (2) ◽  
pp. 249-256
Author(s):  
Umi Azizatul Mubaroh ◽  
Mujib Mujib ◽  
Muhamad Syazali
Keyword(s):  
Content Analysis ◽  
Prime Numbers ◽  
Scientific Data ◽  
Qualitative Model ◽  
New Horizons ◽  
The Third ◽  
Valid Data ◽  
The Difference ◽  
The Relationship ◽  
Text Images

This study requires to use a qualitative model, while for the type of research, using Content Analysis. Content analysis is a model used to examine the documentation data in the form of text, images, symbols, and so forth. A research technique for making inferences that can be replicated and valid data with the context. As a technique of research, the content analysis includes specific procedures for processing the scientific data with the aim of providing knowledge, open new horizons and presenting the facts. Assessment of the linkages primes 3 includes a discussion on the relationship with the meaning and also lafadznya, apart from Al-Kautsar consists of three paragraphs, including the font used and unused in the letter, the difference between the two is 6 (multiples of prime numbers 3), for the number of repetitions of letters obtained 111.111.111.123.444.510 numbers (multiples of primes 3), in a letter lafadz هللاproduce numbers 15 and 1,040 (multiples of primes 3), the sequence of letters and the number of letters in the Qur'an produced 114 108 numbers (multiples of primes 3), correlation beginning and end of the letter gives the figure 1.515 (multiples of primes 3), and the number of repetitions of letters in each verse, second verse generate numbers 1.111.111.224, 1.111.111.122 generate numbers second paragraph, and paragraph the third 1.111.111.125 produce numbers which are all multiples of primes 3.

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