A GEOMETRIC APPROACH TO GOLDBACH’S CONJECTURE AND POLIGNAC’S CONJECTURE

2020 ◽  
Vol 9 (12) ◽  
pp. 10983-10988
Author(s):  
Ð. V. Phúc ◽  
S. Nawaz
Keyword(s):  
Geometric Approach ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

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.

scholarly journals Linnik's approximation to Goldbach's conjecture, and other problems

2015 ◽  
Vol 153 ◽  
pp. 54-62 ◽  
Author(s):  
D.J. Platt ◽  
T.S. Trudgian
Keyword(s):  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

The Crystallographic Restriction, Permutations, and Goldbach's Conjecture

2003 ◽  
Vol 110 (3) ◽  
pp. 202 ◽  
Author(s):  
John Bamberg ◽  
Grant Cairns ◽  
Devin Kilminster
Keyword(s):  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

scholarly journals The Complexity of Mathematics

2020 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Number Theory ◽  
Complexity Theory ◽  
Riemann Hypothesis ◽  
Open Problems ◽  
Mathematical Proofs ◽  
Pure Mathematics ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. We prove the Riemann hypothesis using the Complexity Theory. Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. The Goldbach's conjecture is one of the most important and unsolved problems in number theory. Nowadays, it is one of the open problems of Hilbert and Landau. We show the Goldbach's conjecture is true using the Complexity Theory as well. An important complexity class is 1NSPACE(S(n)) for some S(n). These mathematical proofs are based on if some unary language belongs to 1NSPACE(S(log n)), then the binary version of that language belongs to 1NSPACE(S(n)) and vice versa.

scholarly journals An asymptotic formula for Goldbach’s conjecture with monic polynomials in \(\mathbb {Z}[\theta ][x]\)

2017 ◽  
Vol 148 (2) ◽  
pp. 215-223 ◽  
Author(s):  
Abílio Lemos ◽  
Anderson Luís Albuquerque de Araujo
Keyword(s):  
Asymptotic Formula ◽  
Goldbach’S Conjecture ◽  
Goldbach's Conjecture
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