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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
            97deccbd-db11-4a0e-a55c-ec97fa313ad9

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

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