Mathematical Machine for Primality Testing of Numbers: An Advanced Research

2021 ◽  
pp. 83-93
Author(s):  
Takaaki Musha
Keyword(s):  
Primality Testing ◽  
Mathematical Machine

scholarly journals Dreibens Modulo 7: A New Formula for Primality Testing

Elements ◽  
2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Arthur Diep-Nguyen
Keyword(s):  
Number Theory ◽  
Linear Algebra ◽  
Abstract Algebra ◽  
Additional Insight ◽  
Primality Testing ◽  
New Formula ◽  
Insight Into ◽  
Rule Out

In this paper, we discuss strings of 3’s and 7’s, hereby dubbed “dreibens.” As a first step towards determining whether the set of prime dreibens is infinite, we examine the properties of dreibens when divided by 7. by determining the divisibility of a dreiben by 7, we can rule out some composite dreibens in the search for prime dreibens. We are concerned with the number of dreibens of length n that leave a remainder i when divided by 7. By using number theory, linear algebra, and abstract algebra, we arrive at a formula that tells us how many dreibens of length n are divisible by 7. We also find a way to determine the number of dreibens of length n that leave a remainder i when divided by 7. Further investigation from a combinatorial perspective provides additional insight into the properties of dreibens when divided by 7. Overall, this paper helps characterize dreibens, opens up more paths of inquiry into the nature of dreibens, and rules out some composite dreibens from a prime dreiben search.

scholarly journals An open source software package for primality testing of numbers of the form p2^n+1, with no constraints on the relative sizes of p and 2^n

2018 ◽  
Author(s):  
Tejas R. Rao
Keyword(s):  
Open Source ◽  
Open Source Software ◽  
Software Package ◽  
Primality Testing ◽  
Fermat Number ◽  
Open Source Software Package ◽  
Sierpinski Numbers ◽  
Efficient Software

We develop an efficient software package to test for the primality of p2^n+1, p prime and p>2^n. This aids in the determination of large, non-Sierpinski numbers p, for prime p, and in cryptography. It furthermore uniquely allows for the computation of the smallest n such that p2^n+1 is prime when p is large. We compute primes of this form for the first one million primes p and find four primes of the form above 1000 digits. The software may also be used to test whether p2^n+1 divides a generalized fermat number base 3.

Mathematical machine usage in medical information systems

2021 ◽  
Vol 65 (04) ◽  
pp. 75-85
Author(s):  
İradə Hətəm qızı Mirzəzadə ◽  
◽  
Gülçin Gülhüseyn qızı Abdullayeva ◽  
Həsənağa Rauf oğlu Nağızadə ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Integral Equations ◽  
Medical Information ◽  
Simple Approach ◽  
Bayes Method ◽  
Medical Information Systems ◽  
Nonlinear Algebra ◽  
Artifical Neural Networks ◽  
Mathematical Machine ◽  
Differential And Integral Equations

Biosystem of the human body is viewed as a whole. First of all adequate mathematical machine selection and class of biosystems needs to be assigned for creation of mathematical model of biological system. Biosystem has two types of appoach. One of them is supposed to be a simple approach, the other is likely to be very complex – indexed approach. Different biosystems with determination properties are usually described by differential and integral equations, linear and nonlinear algebra. In some cases, algebraic polynoms with timed argument are used for presenting determined biosystem dynamics. Adequate mathematical modeling machine, probability theory, Markov and random processes theory and the laws are applied for the description of likely characterized biosystems. Key words: biosystem, biocybernetic issues, differential and integral equations, mathematical model, Markov chains, Bayes method, artifical neural networks

Sign in / Sign up

Export Citation Format

Share Document