The irrelevance of the location of Riemann's zeros to the disposition of the prime numbers

William Fidler

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Academic Paper from the year 2022 in the subject Mathematics - Analysis, grade: 2.2, , language: English, abstract: It is shown t...

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Academic Paper from the year 2022 in the subject Mathematics - Analysis, grade: 2.2, , language: English, abstract: It is shown that there is a direct connection between the Riemann zeros, the counting numbers, and hence the prime numbers, but not in the so-called Critical Strip. A mathematical structure is developed in which the articulation of the numerical location of a Riemann zero in the sequence of zeros is sufficient to determine the counting number with which it is associated, its location, Im(s) on the line of symmetry and, the Gauss/Legendre prime number counting function. It is concluded that the disposition of the prime numbers within the system of counting numbers is solely an intrinsic characteristic of that system and is totally unrelated to the distribution of the Riemann zeros.