Information Entropy and Correlations in Prime Numbers

Information Entropy and Correlations in Prime Numbers
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信息熵和素数的相关性

DOI：
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发表时间：
2003
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通讯作者：
H. Stanley
H. Stanley
中科院分区：
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文献类型：
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作者：
Pradeep Kumar;Plamen Ch.Ivanov;H. Stanley

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两个连续素数之间的差称为素数之间的距离。我们研究了由前$5乘以10^7$素数组成的序列的距离及其增量（两个连续距离之间的差值）的统计性质。我们发现增量的直方图遵循指数分布，具有周期3的叠加周期行为，类似于先前报道的距离的周期6振荡。
The difference between two consecutive prime numbers is called the distance between the primes. We study the statistical properties of the distances and their increments (the difference between two consecutive distances) for a sequence comprising the first $5 imes 10^7$ prime numbers. We find that the histogram of the increments follows an exponential distribution with superposed periodic behavior of period three, similar to previously-reported period six oscillations for the distances.