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.