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Multa non quia difficilia sunt non audemus sed quia non audemus sunt difficilia

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Tag: space

Geometric representation of Goldbach pairs

Geometric representation of Goldbach pairs

Posted on April 26, 2025April 27, 2025
Posted inDashed line theory , Goldbach's conjecture
When working with numbers, a geometric representation is often helpful in trying to highlight trends or properties that are less…
Overestimation of the number of spaces up to a column included into the validity interval

Overestimation of the number of spaces up to a column included into the validity interval

Posted on March 26, 2025March 27, 2025
Posted inDashed line theory , Goldbach's conjecture
In the previous article we tried to increase the number of spaces contained in a dashed line up to a…
Proof strategy based on spaces: method based on the concept of maximum distance between consecutive spaces

Proof strategy based on spaces: method based on the concept of maximum distance between consecutive spaces

Posted on February 15, 2025February 22, 2025
Posted inDashed line theory , Goldbach's conjecture
Prerequisite: Proof strategy based on spaces As we stated in the previous post, our intent is to find the conditions…
Proof strategy based on spaces: method based on the approximate calculation of spaces

Proof strategy based on spaces: method based on the approximate calculation of spaces

Posted on February 15, 2025March 27, 2025
Posted inDashed line theory , Goldbach's conjecture
In this formulation of the proof strategy based on spaces, we will look for conditions that allow us to conclude…
21. Characterization of spaces: insights

21. Characterization of spaces: insights

Posted on January 29, 2025March 27, 2025
Posted inDashed line theory
In the characterization of spaces we saw, for the first three orders of linear dashed lines, the formulas which calculate…
Study about the existence of complementary space pairs based on second order dashed lines

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

Posted on February 8, 2023June 16, 2023
Posted 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 aim…
Proof strategy based on dashes

Proof strategy based on dashes

Posted on February 8, 2023April 27, 2025
Posted inDashed line theory , Goldbach's conjecture
Prerequisite: Our proof strategies: an overview The proof strategy set out here starts from one of the assumptions of the…
Proof strategy based on spaces

Proof strategy based on spaces

Posted on February 8, 2023February 22, 2025
Posted inDashed line theory , Goldbach's conjecture
Prerequisite: Our proof strategies: an overview The proof strategy which will be exposed here has the goal of proving Hypothesis…
Maximum space distance calculator

Maximum space distance calculator

Posted on December 21, 2021November 5, 2024
Posted inDashed line theory , Goldbach's conjecture
The Maximum space distance calculator is a program which we developed for computing the value of the maximum distance between…
16. Characterization of spaces

16. Characterization of spaces

Posted on December 29, 2019April 26, 2025
Posted inDashed line theory
One of the open problems of dashed line theory is "characterizing" spaces, i.e. looking for a criterion that tells us…
13. Computation of spaces in second order linear dashed lines

13. Computation of spaces in second order linear dashed lines

Posted on October 28, 2019February 8, 2025
Posted 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…
2. Dashed lines, dashes and spaces: some definitions and simple properties

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

Posted on December 21, 2018February 8, 2025
Posted 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

Posted on December 20, 2018November 18, 2023
Posted 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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Complementary Material

  • Elements of asymptotic analysis

  • Properties of asymptotic orders

  • The limit inferior and the limit superior of a sequence

  • Numerical series and prime numbers

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      Molte cose non è perché sono difficili che non osiamo farle,
      ma è perché non osiamo farle che sono difficili

      Many times, it is not because things are difficult that we do not dare,
      but it is because we do not dare that things are difficult

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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 research
          • Dashed line theory
          • Proof strategies
            • Proof strategy based on dashes
            • Proof strategy based on spaces
            • Proof strategy based on factorization
        • 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
        • Fun facts
      • Sieve theory
        • An overestimate of the number of Goldbach pairs
        • Chen’s Theorem
      • Tools
        • Dashed line viewer
        • Goldbach pairs viewer
        • Bidimensional sieve of Eratosthenes
        • Factorizer
        • Maximum space distance calculator
      • Info and contacts
        • About us
        • The project
        • Donations
        • Bookshop
        • Prizes
        • Send us a contribution
      • Italiano