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      Maximal prime gaps bounds

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          Abstract

          This paper presents research results, pertinent to the maximal prime gaps bounds. Four distinct bounds are presented: Upper bound, Infimum, Supremum and finally the Lower bound. Although the Upper and Lower bounds incur a relatively high estimation error cost, the functions representing them are quite simple. This ensures, that the computation of those bounds will be straightforward and efficient.

          The Lower bound is essential, to address the issue of the value of the lower bound implicit constant C, in the work of Ford et al (Ford, 2016). The concluding Corollary in this paper shows, that the value of the constant C does diverge, although very slowly. The constant C, will eventually take any arbitrary value, providing that a large enough N (for p <= N) is considered.

          The Infimum/Supremum bounds on the other hand are computationally very demanding. Their evaluation entails computations at an extreme level of precision. In return however, we obtain bounds, which provide an extremely close approximation of the maximal prime gaps. The Infimum/Supremum estimation error gradually increases over the range of p and attains at p = 18361375334787046697 approximately the value of 0.03.

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          Author and article information

          Journal
          ScienceOpen Preprints
          ScienceOpen
          9 February 2021
          Affiliations
          [1 ] N. A.
          Article
          10.14293/S2199-1006.1.SOR-.PPWVKRR.v1

          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

          Maximal prime gaps bounds, Ford-Green-Konyagin-Maynard-Tao maximal gaps bound, Maximal prime gaps Infimum, Maximal prime gaps Supremum, Maximal prime gaps Lower bound, Maximal prime gaps Upper bound, Erdos-Rankin maximal gaps problem

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