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Hidden structure in the randomness of the prime number sequence?

Author

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  • Ares, S.
  • Castro, M.

Abstract

We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes, that would eventually appear in applications. Finally, our theory allows us to link with three different but important topics: the Hardy–Littlewood conjecture, the statistical mechanics of spin systems, and the celebrated Sierpinski fractal.

Suggested Citation

  • Ares, S. & Castro, M., 2006. "Hidden structure in the randomness of the prime number sequence?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 285-296.
    • Handle: RePEc:eee:phsmap:v:360:y:2006:i:2:p:285-296
    DOI: 10.1016/j.physa.2005.06.066
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    References listed on IDEAS

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    1. Dahmen, S.R & Prado, S.D & Stuermer-Daitx, T, 2001. "Similarity in the statistics of prime numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 523-528.
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    Cited by:

    1. Shaimaa said soltan, 2022. "Cubic and Quadratic Equations and Zeta Function Zeros," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(5), pages 1-8, November.
    2. Cattani, Carlo & Ciancio, Armando, 2016. "On the fractal distribution of primes and prime-indexed primes by the binary image analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 222-229.
    3. Alexei Kourbatov & Marek Wolf, 2019. "Predicting Maximal Gaps in Sets of Primes," Mathematics, MDPI, vol. 7(5), pages 1-28, May.

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