Article citationsMore>>

Matomäki, K. and Merikoski, J. (2021) Siegel Zeros, Twin Primes, Goldbach’s Conjecture, and Primes in Short Intervals. arXiv, arXiv:2112.11412.
https://doi.org/10.48550/arXiv.2112.11412

has been cited by the following article:

• TITLE: The Symmetric Series of Multiples of Primes

  AUTHORS: Pal Doroszlai, Horacio Keller

  KEYWORDS: Twin Primes, Prime Gaps, Goldbach’s Conjecture

  JOURNAL NAME: Advances in Pure Mathematics, Vol.12 No.3, March 18, 2022

  ABSTRACT: The union of the straight and over the point of reflection—reflected series of the arithmetic progression of primes results in the double density of occupation of integer positions. It is shown that the number of free positions left by the double density of occupation has a lower limit function, which is growing to infinity. The free positions represent equidistant primes to the point of reflection: in case the point of reflection is an even number, they satisfy Goldbach’s conjecture. The double density allows proving as well that at any distance from the origin large enough—the distance between primes is smaller, than the square root of the distance to the origin. Therefore, the series of primes represent a continuum and may be integrated. Furthermore, it allows proving that the largest gap between primes is growing to infinity with the distance and that the number of any two primes, with a given even number as the distance between them, is unlimited. Thus, the number of twin primes is unlimited as well.