Structure of the Prime Distribution within the Sequence of Natural Numbers

Andrei V. Vityazev; Galina V. Pechernikova

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Structure of the Prime Distribution within the Sequence of Natural Numbers

Andrei V. Vityazev·Galina V. Pechernikova

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Abstract

In the course of studies of the measure of chaos for the distribution of the prime numbers among the positive integers N arched structures have been found. It is given a brief description of the fine structure of the positive integers sequence, including the distribution of the prime numbers. A new non-Eratostenian sieve was built to demonstrate the multi-periodicity in the structure of the positive integers sequence. This sieve presents an infinite triangular matrix, which is named by us as R-matrix (Russian matrix). The simple deterministic equations for prime numbers and the main term of asymptotic were derived with the use of this matrix.

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Andrei V. Vityazev, Galina V. Pechernikova. 2006-09-28. Structure of the Prime Distribution within the Sequence of Natural Numbers. https://arxiv.org/abs/math/0609797

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