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      The Brocard conjecture

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      research-article
        1 ,
      ScienceOpen Preprints
      ScienceOpen
      Brocard conjecture, Maximal prime gaps bound, Prime Number Theorem, Twin primes, Least number of primes in Brocard's interval
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            Abstract

            The Brocard conjecture asserts that the number of primes, within the interval, between the squares of two subsequent primes is greater than or equal to 4. Although the number of primes within this interval varies to a great degree, there is a common ground, which makes it possible to settle this old conundrum. Three bounds are developed: the least lower bound and the lower/upper bounds. The least lower bound is implemented to prove the conjecture. The lower/upper bounds exploit the shortest such interval, namely between the twin primes. This has been done in order to establish the bounds, on the smallest number of primes within that interval. The research objective was not only to provide a true/false answer, but to clarify some aspects of the distribution of prime numbers within this interval as well.

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            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            21 February 2021
            Affiliations
            [1 ] N. A.
            Article
            10.14293/S2199-1006.1.SOR-.PPIH4LV.v1
            5faa8db6-7d55-42da-a581-c81b6a3d41ba

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .


            The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
            Mathematics
            Brocard conjecture,Maximal prime gaps bound,Prime Number Theorem,Twin primes,Least number of primes in Brocard's interval

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