Information Entropy and Correlations in Prime Numbers

Details Information Entropy and Correlations in Prime Numbers Information Entropy and Correlations in Prime Numbers

2003-03-06

arxiv.org/abs/cond-mat/0303110v4

Physics

Condensed Matter

Statistical Mechanics

6 pages, 2 figures

Scientific paper

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 $5\times 10^7$ 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.

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