publication . Article . 2016

Alternative analysis: the prime numbers theory and an extension of the real numbers set

Sukhotin A.; Zvyagin M.;
Open Access
  • Published: 15 Oct 2016 Journal: Bulletin of Science and Practice (issn: 2414-2948, Copyright policy)
Abstract
Here we consider the theory of prime numbers at a new methodology. The theory of prime numbers is one of the most ancient mathematical branches. We found an estimate of the all prime numbers sum using the notions of infinite lager numbers and infinitely small numbers, farther we estimated the value of the maximal prime number. We proved that Hardy–Littlewood Hypothesis has the positive decision too. The infinite small numbers define a new methodology of the well–known function o(x) application. We use the sets of the theory of prime numbers and infinitely small numbers with a linear function to formulate the alternative extension of the real numbers set.
Subjects
arXiv: Mathematics::Number Theory
free text keywords: First Euclidian theorem, the prime numbers, infinity large number, Hardy–Littlewood’s Hypothesis, the existence of maximal prime number, Mersenne’s prime numbers, the extension of the real numbers set
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Article . 2016
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