素数k元组的渐近密度及Hardy和Littlewood的一个猜想

computational methods in science and technology Pub Date : 2019-10-07 DOI:10.12921/cmst.2019.0000033

L. T'oth

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引用次数: 3

摘要

1922年Hardy和Littlewood提出了一个关于容许素数k元组的渐近密度的猜想。2011年，Wolf计算了双素数的“偏数”，即第一个出现Hardy-Littlewood不等式反转的素数。在本文中，我们找到了另外8个素数k元组的“偏数”，并提供了支持Hardy-Littlewood猜想的数值数据。此外，我们还提出了几种计算这些数字的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Asymptotic Density of Prime k-tuples and a Conjecture of Hardy and Littlewood

In 1922 Hardy and Littlewood proposed a conjecture on the asymptotic density of admissible prime k-tuples. In 2011 Wolf computed the "Skewes number" for twin primes, i.e., the first prime at which a reversal of the Hardy-Littlewood inequality occurs. In this paper, we find "Skewes numbers" for 8 more prime k-tuples and provide numerical data in support of the Hardy-Littlewood conjecture. Moreover, we present several algorithms to compute such numbers.

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computational methods in science and technology

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