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Tag: third order

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…
17. Upper bound for maximum distance between consecutive spaces

17. Upper bound for maximum distance between consecutive spaces

Posted on December 29, 2019June 28, 2022
Posted 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,…
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…
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…
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…
9. Row computation in third order linear dashed lines

9. Row computation in third order linear dashed lines

Posted on June 23, 2019April 26, 2020
Posted inDashed line theory
For third order linear dashed lines, like second order ones, there exist some particular moduli which, by evaluating proper conditions,…
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Complementary Material

  • Elements of asymptotic analysis

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  • 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