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arXiv math/06097972006-09-28math.GM

自然数序列中素数分布的结构

Structure of the Prime Distribution within the Sequence of Natural Numbers

Andrei V. Vityazev, Galina V. Pechernikova

备注：: 10 pages, 4 figures, 2 tables

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摘要：

在研究素数在正整数中分布的混沌测度时，发现了N个拱形结构，本文简要地描述了正整数序列的精细结构，包括素数的分布。构造了一种新的非Eratostenian筛法，证明了正整数序列结构的多周期性。该筛表示一个无限三角形矩阵，我们称之为R-矩阵。利用该矩阵导出了素数和渐近主项的简单确定性方程。

英文摘要：

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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