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.

The Approximate Number System (ANS) and Discriminating Magnitudes

2020 ◽  
pp. 127-139
Author(s):  
Ellen Peters
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Arithmetic Operations ◽  
Simple Arithmetic ◽  
Math Ability ◽  
Intuitive Sense

This chapter, “The Approximate Number System (ANS) and Discriminating Magnitudes,” discusses our intuitive, rather than deliberative, understanding of numbers. Humans are born with an innate sense of number and an ability to perform simple arithmetic operations with sets of objects without counting. We share this intuitive sense of numeric magnitude (how big one quantity is relative to another) with other species. Non-human animals cannot count as humans do. However, they have a keen sense of quantity that allows them to tell quickly and efficiently which quantity is bigger so that they can make better choices about food, mates, and safety. In humans, this intuitive sense of numbers develops from infancy to adulthood, and it appears to underlie the emergence of symbolic math ability (objective numeracy) in children.

Parallel-sequential adder-subtractor with the highest digits forward on neurons

2021 ◽  
Author(s):  
S.S. Shevelev
Keyword(s):  
Computer System ◽  
Control Unit ◽  
Arithmetic Operations ◽  
Mathematical Functions ◽  
Simple Arithmetic ◽  
Addition And Subtraction

The article deals with the development of a parallel-sequential adder-subtractor that performs arithmetic operations of addition and subtraction of binary numbers in the format with a fixed comma with the highest digits forward. The result of performing arithmetic operations is the sum and difference of binary numbers in the direct code of eight digits. The sum and difference of numbers is calculated on neuropositive elements, the transfer to the highest digits when summing and the loan from the highest digits when subtracting is determined by the majority elements. The algorithm for adding numbers in direct codes allows you to get the result in direct code. The signed digits of numbers determine which operation should be performed on numbers using the sum modulo two operation. If the characters are the same, the result will be zero. Otherwise, the result will be one. After that, the addition or subtraction operation is selected. Summation is performed if the numbers have the same signs, the result is assigned the sign of the first number. Subtraction is performed if the numbers have different signs, the result is assigned the sign of a larger modulo number. The adder-subtracter senior digits forward on neurons contains: block input, block comparatii, the block parallel-serial addersubtracter, the unit registers a larger number, the unit of determining the transfer and loan, a unit registers a smaller number of unit registers a result, the control unit, majority, threshold and neural elements. The device can be used as an arithmetic co-processor in a computer system. It significantly speeds up calculations of both simple arithmetic operations and results of various mathematical functions.

Experimental analysis of large prime numbers generation in residue number system

2017 ◽  
Author(s):  
Nikolay I. Chervyakov ◽  
Mikhail G. Babenko ◽  
Darya S. Konyaeva ◽  
Natalya N. Kuchukova ◽  
Ekaterina A. Kuchukova ◽  
...  
Keyword(s):  
Experimental Analysis ◽  
Number System ◽  
Residue Number System ◽  
Prime Numbers ◽  
Residue Number

scholarly journals A Proposed Fully Homomorphic for Securing Cloud Banking Data at Rest

2020 ◽  
Vol 4 (1) ◽  
pp. 87
Author(s):  
Zana Thalage Omar ◽  
Fadhil Salman Abed
Keyword(s):  
Homomorphic Encryption ◽  
Prime Numbers ◽  
Data Encryption ◽  
Theoretical Research ◽  
Significant Progress ◽  
Arithmetic Operations ◽  
Fully Homomorphic Encryption ◽  
Encrypted Data ◽  
Encryption And Decryption ◽  
Local Cloud

Fully homomorphic encryption (FHE) reaped the importance and amazement of most researchers and followers in data encryption issues, as programs are allowed to perform arithmetic operations on encrypted data without decrypting it and obtain results similar to the effects of arithmetic operations on unencrypted data. The first (FHE) model was introduced by Craig Gentry in 2009, and it was just theoretical research, but later significant progress was made on it, this research offers FHE system based on directly of factoring big prime numbers which consider open problem now, The proposed scheme offers a fully homomorphic system for data encryption and stores it in encrypted form on the cloud based on a new algorithm that has been tried on a local cloud and compared with two previous encryption systems (RSA and Paillier) and shows us that this algorithm reduces the time of encryption and decryption by 5 times compared to other systems.

2. The laws of algebra

2015 ◽  
pp. 11-24
Author(s):  
Peter M. Higgins
Keyword(s):  
Number System ◽  
Arithmetic Operations ◽  
Distributive Law ◽  
Associative Law

‘The laws of algebra’ explores the three laws that govern arithmetic operations and explains how these rules are extended so that they continue to be respected as we pass from one number system to a greater one that subsumes the former. The associative law of addition shows that that (a + b) + c = a + (b + c), and the associative law of multiplication is a(bc) = (ab)c. The distributive law tells us how to multiply out the brackets: a(b + c) = ab + ac. The commutative law of addition is a + b = b + a, a law that holds equally well for multiplication: ab = ba.

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