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

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Tag: dash

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…
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…
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

Posted on August 16, 2019May 2, 2020
Posted 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

Posted on July 27, 2019February 20, 2023
Posted 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

Posted on July 13, 2019May 1, 2020
Posted 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…
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…
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Tools

  • Dashed line viewer

    Dashed line viewer

  • Goldbach pairs viewer

    Goldbach pairs viewer

  • Bidimensional sieve of Eratosthenes

    Bidimensional sieve of Eratosthenes

  • Factorizer

    Factorizer

  • Maximum space distance calculator

    Maximum space distance calculator

References

  • Number theory statements

  • Number theory definitions and symbols

  • Dashed line theory definitions and symbols

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

Categories

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  • Goldbach's conjecture (21)
  • Mathematical analysis (4)
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    • Fun facts (3)
  • Sieve theory (10)

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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