scholarly journals Remarks on Goldbach’s Conjecture on Prime Numbers

2019 ◽  
Vol 11 (12) ◽  
pp. 336-344
Author(s):  
Silviu Guiasu
Keyword(s):  
Prime Numbers ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

scholarly journals A Study of Authenticated Communication Based on Magic Square and Goldbach’s Conjecture

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Group Learning ◽  
Prime Numbers ◽  
Learning Problems ◽  
Student Group ◽  
Magic Square ◽  
Innovative Method ◽  
Encryption Decryption ◽  
Novel Applications ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

Although the magic square is a historical and universal study, its progress has been limited, to numeric games, which is closer to digital games or word games, and lacks the connection with mainstream mathematics. Recently, its study has extended from exciting mathematical games to various novel applications, such as image encryption, decryption processing, watermarking solutions, and student group learning problems, or different engineering applications. In terms of employment in information security, it is the blue ocean that requires more innovative research to enrich its content. In this study, we engage the magic square and Goldbach’s Conjecture to develop an innovative method to search prime numbers

scholarly journals On the Universal Encoding Optimality of Primes

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3155
Author(s):  
Ioannis N. M. Papadakis
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Optimization Problem ◽  
Prime Numbers ◽  
Prime Factors ◽  
Universal Quantum ◽  
Optimality Properties ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

The factorial-additive optimality of primes, i.e., that the sum of prime factors is always minimum, implies that prime numbers are a solution to an integer linear programming (ILP) encoding optimization problem. The summative optimality of primes follows from Goldbach’s conjecture, and is viewed as an upper efficiency limit for encoding any integer with the fewest possible additions. A consequence of the above is that primes optimally encode—multiplicatively and additively—all integers. Thus, the set P of primes is the unique, irreducible subset of ℤ—in cardinality and values—that optimally encodes all numbers in ℤ, in a factorial and summative sense. Based on these dual irreducibility/optimality properties of P, we conclude that primes are characterized by a universal “quantum type” encoding optimality that also extends to non-integers.

scholarly journals Exploring Goldbach’s conjecture, the Pebonacci sequence and its five-dimensional vortex structure based on the logarithm of the circle

2020 ◽  
Vol 7 (8) ◽  
pp. 398-408
Author(s):  
Yiping Wang
Keyword(s):  
Mathematical Model ◽  
Closed Interval ◽  
Three Dimensional ◽  
Prime Numbers ◽  
Quadratic Equation ◽  
Space Structure ◽  
Number Sequence ◽  
Number Series ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

A method based on circle logarithm to prove Goldbach’s conjecture and Pebonacci sequence is proposed. Its essence is to deal with the real infinite series, each of the finite three elements (prime numbers, number series) has asymmetry problems, forming a basic even function one-variable quadratic equation and odd function one-variable three-dimensional number sequence; it is converted to "The irrelevant mathematical model expands latently in a closed interval of 0 to 1," forming a five-dimensional vortex space structure.

scholarly journals Proof of the Goldbach's Conjecture

2021 ◽  
Author(s):  
K.H.K. Geerasee Wijesuriya
Keyword(s):  
Prime Numbers ◽  
Goldbach’S Conjecture ◽  
Mathematics Problem ◽  
Goldbach's Conjecture

Goldbach’s Conjecture states that every even number greater than 3, can be written as a summation of two prime numbers. This conjecture is roughly 300 years old and a very famous unsolved mathematics problem. To prove the Goldbach’s Conjecture, I use the contradiction method in mathematics as below.

7. Conjectures and theorems

2020 ◽  
pp. 112-129
Author(s):  
Robin Wilson
Keyword(s):  
Prime Numbers ◽  
Unique Factorization ◽  
The 1950S ◽  
Positive Integers ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

‘Conjectures and theorems’ investigates a number of topics, such as the distribution of prime numbers, and two unsolved problems, Goldbach’s conjecture and the twin prime conjecture. The factorization of positive integers into primes is unique, but this does not hold for certain other systems of numbers. A more in-depth look at unique factorization gives deeper results, including a proposed result of Gauss. Mathematicians in the 1950s and 1960s confirmed that he was correct, as shown in the so-called ‘Baker-Heegner-Stark theorem’.

scholarly journals Distribution of the Largest Strong Goldbach Numbers Generated by Primes

2018 ◽  
Vol 10 (5) ◽  
pp. 1
Author(s):  
Pingyuan Zhou ◽  
Rong Ao
Keyword(s):  
Distribution Curve ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

Using the first 4000000 primes to find Ln, the largest strong Goldbach number generated by the n-th prime Pn, we generalize a proposition in our previous work (Zhou 2017) and propose that Ln ≈ 2Pn and Ln/2Pn < 1 for sufficiently large Pn but the limit of Ln/2Pn as n → ∞ is 1, Ln ≈ Pn + n log n and Ln/(Pn + n log n) > 1 for sufficiently large Pn but the limit of Ln/(Pn + n log n) as n → ∞ is 1. There are five corollaries of the generalized proposition for getting Ln → ∞ as n → ∞, which is equivalent to Goldbach’s conjecture. If every step in distribution curve of Ln is called a Goldbach step, a study on the ratio of width to height for Goldbach steps supports the existence of above two limits but a study on distribution of Goldbach steps supports an estimation that Q(n) ≈ (1 + 1/log log n)n/log n and the limit of Q(n)/((1 + 1/log log n)n/log n) as n → ∞ is 1, where Q(n) is the number of Goldbach steps, from which we may expect there are infinitely many Goldbach steps to imply Goldbach’s conjecture.

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