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Category: Dashed line theory

Maximum space distance calculator

Maximum space distance calculator

Scritto il December 21, 2021December 21, 2021
Pubblicato inDashed line theory , Goldbach's conjecture , Number theory
The Maximum space distance calculator is a program which we developed for computing the value of the maximum distance between…
14. A recursive property of linear dashed lines with two by two coprime components

14. A recursive property of linear dashed lines with two by two coprime components

Scritto il July 24, 2020November 4, 2020
Pubblicato inDashed line theory
In this post we'll talk about a recursive property, that is true for all linear dashed lines with two by…
19. Calculation of t_value for dashed lines of arbitrary order

19. Calculation of t_value for dashed lines of arbitrary order

Scritto il January 11, 2020June 28, 2022
Pubblicato inDashed line theory , Goldbach's conjecture
The function [latex]\mathrm{t\_value}[/latex], by definition, indicates which column of a dashed line a dash belongs to. For this reason, in…
Proof strategy based on factorization

Proof strategy based on factorization

Scritto il January 2, 2020November 20, 2020
Pubblicato inDashed line theory , Goldbach's conjecture
Prerequisites: Our proof strategies Factorization dashed lines Properties of the spaces of the factorization dashed lines can be used to…
15. Factorization dashed lines

15. Factorization dashed lines

Scritto il January 2, 2020June 28, 2022
Pubblicato inDashed line theory
When constructing a linear dashed line, the sequence of primes is usually used as a list of components, until it…
Study of existence of complementary space pairs based on second order dashed lines

Study of existence of complementary space pairs based on second order dashed lines

Scritto il December 30, 2019December 7, 2020
Pubblicato inDashed line theory , Goldbach's conjecture
Prerequisites: Dashed line theory definitions and symbols Our proof strategies Proof strategy based on dashes Characterization of spaces The purpose…
18. Calculation of t_space for dashed lines of arbitrary order

18. Calculation of t_space for dashed lines of arbitrary order

Scritto il December 29, 2019June 28, 2022
Pubblicato inDashed line theory
By now, the formula for calculation of [latex]\mathrm{t\_space}[/latex] for a linear dashed line of any order is not yet known,…
16. Characterization of spaces

16. Characterization of spaces

Scritto il December 29, 2019January 22, 2023
Pubblicato inDashed line theory
One of the open problems of dashed line theory is "characterizing" spaces, i.e. looking for a criterion that tells us…
17. Upper bound for maximum distance between consecutive spaces

17. Upper bound for maximum distance between consecutive spaces

Scritto il December 29, 2019June 28, 2022
Pubblicato inDashed line theory , Goldbach's conjecture
One of the still open problems of dashed line theory is, given a linear dashed line [latex]T = (p_1, p_2,…
Proof strategy based on spaces

Proof strategy based on spaces

Scritto il December 29, 2019December 21, 2021
Pubblicato inDashed line theory , Goldbach's conjecture
Prerequisite: Our proof strategies The proof strategy shown here is aimed at proving the Hypothesis H.1 (Hypothesis of existence of…
Our proof strategies: an overview

Our proof strategies: an overview

Scritto il December 18, 2019November 20, 2020
Pubblicato inDashed line theory , Goldbach's conjecture
Prerequisites: Goldbach’s conjecture From prime numbers to dashed lines Periodicity and symmetry in linear dashed lines As already stated, our…
Proof strategy based on dashes

Proof strategy based on dashes

Scritto il December 17, 2019November 20, 2020
Pubblicato inDashed line theory , Goldbach's conjecture
Prerequisite: Our proof strategies The proof strategy which will be exposed here starts from one of the premises of Hypothesis…
Dashed line theory

Dashed line theory

Scritto il November 25, 2019January 20, 2020
Pubblicato inDashed line theory
Dashed line theory is a new mathematical theory which studies the connection between the sequence of natural numbers and their…
13. Computation of spaces in second order linear dashed lines

13. Computation of spaces in second order linear dashed lines

Scritto il October 28, 2019May 3, 2020
Pubblicato inDashed line theory
In this post we'll see how to obtain a formula for computing the t_space function for second order linear dashed…
12. Computation of a dash value in a linear third order dashed line

12. Computation of a dash value in a linear third order dashed line

Scritto il August 16, 2019May 2, 2020
Pubblicato inDashed line theory
In order to compute the x-th dash value in a third order linear dashed line, we can proceed in a…
11. Computation of a dash value in a linear second order dashed line

11. Computation of a dash value in a linear second order dashed line

Scritto il July 27, 2019May 1, 2020
Pubblicato inDashed line theory
In this post we'll see how it's possible to compute the x-th dash value in a second order linear dashed…
10. Row computation and differences between dash values

10. Row computation and differences between dash values

Scritto il July 13, 2019May 1, 2020
Pubblicato inDashed line theory
It's worth, before passing to the formulas of t_value, pausing for a while and looking closely to the moduli we…
9. Row computation in third order linear dashed lines

9. Row computation in third order linear dashed lines

Scritto il June 23, 2019April 26, 2020
Pubblicato inDashed line theory
For third order linear dashed lines, like second order ones, there exist some particular moduli which, by evaluating proper conditions,…
8. Row computation in second order linear dashed lines

8. Row computation in second order linear dashed lines

Scritto il June 18, 2019April 26, 2020
Pubblicato inDashed line theory
It may sound strange, but it's possible to compute a dash row without having an idea of its value (that…
3. Periodicity and symmetry in linear dashed lines

3. Periodicity and symmetry in linear dashed lines

Scritto il June 14, 2019October 6, 2020
Pubblicato inDashed line theory
In this post we'll talk about two fundamental properties of linear dashed lines: periodicity and symmetry. When we talk about…
7. Downcast characteristic equations of t and t_value for linear dashed lines

7. Downcast characteristic equations of t and t_value for linear dashed lines

Scritto il May 18, 2019April 25, 2020
Pubblicato inDashed line theory
Solving the downcast problem, for linear dashed lines, means finding the solution of particular equations, called "downcast characteristic equations". In…
5. First order linear dashed lines

5. First order linear dashed lines

Scritto il May 16, 2019April 18, 2020
Pubblicato inDashed line theory
We saw that one of the main problems of dashed line theory is computing the t, t_value and t_space functions.…
6. The downcast problem

6. The downcast problem

Scritto il April 21, 2019April 19, 2020
Pubblicato inDashed line theory
The difficulty of computing the t, t_value and t_space functions, increases as the order of the dashed line does. Their…
4. From a problem about jogging to dashed lines

4. From a problem about jogging to dashed lines

Scritto il March 12, 2019April 13, 2020
Pubblicato inDashed line theory
Charles, Mary and Tom are three friends who like jogging. Today they went jogging together, but each of them follow…
Dashed line viewer

Dashed line viewer

Scritto il December 30, 2018March 24, 2021
Pubblicato inDashed line theory
The dashed line viewer lets you to show a dashed line at your choice, with the possibility to highlight spaces…
2. Dashed lines, dashes and spaces: some definitions and simple properties

2. Dashed lines, dashes and spaces: some definitions and simple properties

Scritto il December 21, 2018September 11, 2020
Pubblicato inDashed line theory
In the formal definition of dashed line, a dash is a couple of natural numbers (i, n), where i identifies…
1. From prime numbers to dashed lines

1. From prime numbers to dashed lines

Scritto il December 20, 2018March 29, 2020
Pubblicato inDashed line theory
A dashed line can be represented as a table having a fixed number of rows, and, potentially, infinite columns, numbered…

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  • t_value
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      • Home
      • Goldbach’s conjecture
        • Origins of the two Goldbach’s conjectures
        • Some important results
        • Other conjectures related to sums of primes
        • Our proof strategies
        • Our readers’ contributions
          • Send us a contribution
      • Number theory
        • Foundations of number theory
        • Bertrand’s Postulate
        • Chebyshev’s Theorem (weak version)
        • Chebyshev’s Theorem (strong version)
        • The Prime Number Theorem: the “elementary” proof
        • Complementary material
        • Fun facts
      • Dashed line theory
      • Tools
        • Dashed line viewer
        • Goldbach pairs viewer
        • Bidimensional sieve of Eratosthenes
        • Factorizer
        • Maximum space distance calculator
      • Info and contacts
        • About us
        • The project
        • Donations
        • Prizes
        • Send us a contribution
      • ItalianoItaliano