IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v37y2008i1p23-42.html
   My bibliography  Save this article

The distribution of prime numbers: The solution comes from dynamical processes and genetic algorithms

Author

Listed:
  • Iovane, Gerardo

Abstract

In this work, we show that the set of primes can be obtained through dynamical processes. Indeed, we see that behind their generation there is an apparent stochastic process; this is obtained with the combination of two processes: a “zig-zag” between two classes of primes and an intermittent process (that is a selection rule to exclude some prime candidates of the classes). Although we start with a stochastic process, the knowledge of its inner properties in terms of zig-zagging and intermittent processes gives us a deterministic and analytic way to generate the distribution of prime numbers. Thanks to genetic algorithms and evolution systems, as we will see, we answer some of most relevant questions of the last two centuries, that is “How can we know a priori if a number is prime or not? Or similarly, does the generation of number primes follow a specific rule and if yes what is its form? Moreover, has it a deterministic or stochastic form?” To reach these results we start to analyze prime numbers by using binary representation and building a hierarchy among derivative classes.

Suggested Citation

  • Iovane, Gerardo, 2008. "The distribution of prime numbers: The solution comes from dynamical processes and genetic algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 23-42.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:1:p:23-42
    DOI: 10.1016/j.chaos.2007.10.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907008922
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.10.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. El Naschie, M.S., 2007. "From pointillism to E-infinity electromagnetism," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1377-1381.
    2. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
    3. El Naschie, M.S., 2008. "The fundamental algebraic equations of the constants of nature," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 320-322.
    4. Iovane, G., 2006. "Cantorian spacetime and Hilbert space: Part I—Foundations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 857-878.
    5. El Naschie, M.S., 2005. "A guide to the mathematics of E-infinity Cantorian spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 955-964.
    6. Wolf, Marek, 1998. "Random walk on the prime numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 335-344.
    7. El Naschie, M.S., 2008. "The Exceptional Lie symmetry groups hierarchy and the expected number of Higgs bosons," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 268-273.
    8. El Naschie, M.S., 2008. "Exceptional Lie groups hierarchy and some fundamental high energy physics equations," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 82-84.
    9. El Naschie, M.S., 2006. "Hilbert space, the number of Higgs particles and the quantum two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 9-13.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, Qingjiang & Liu, Baocang & Cao, Huaixin, 2009. "Construction of a sort of multiple pseudoframes for subspaces with filter banks," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 801-808.
    2. Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.
    3. Iovane, Gerardo, 2009. "The set of primes: Towards an optimized algorithm, prime generation and validation, and asymptotic consequences," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1344-1352.
    4. García-Sandoval, J.P., 2020. "Fractals and discrete dynamics associated to prime numbers," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Cecen, Songul & Demirer, R. Murat & Bayrak, Coskun, 2009. "A new hybrid nonlinear congruential number generator based on higher functional power of logistic maps," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 847-853.
    6. Iovane, Gerardo, 2008. "The set of prime numbers: Symmetries and supersymmetries of selection rules and asymptotic behaviours," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 950-961.
    7. Iovane, Gerardo, 2009. "The set of prime numbers: Multifractals and multiscale analysis," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1945-1958.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Iovane, Gerardo, 2008. "The set of prime numbers: Symmetries and supersymmetries of selection rules and asymptotic behaviours," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 950-961.
    2. Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.
    3. Iovane, Gerardo, 2009. "The set of prime numbers: Multifractals and multiscale analysis," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1945-1958.
    4. Chen, Qing-Jiang & Qu, Xiao-Gang, 2009. "Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1676-1683.
    5. Iovane, Gerardo & Giordano, Paola, 2007. "Wavelets and multiresolution analysis: Nature of ε(∞) Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 896-910.
    6. Wu, Guochang & Cheng, Zhengxing & Li, Dengfeng & Zhang, Fangjuan, 2008. "Parseval frame wavelets associated with A-FMRA," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1233-1243.
    7. Sun, Lei & Cheng, Zhengxing & Huang, Yongdong, 2007. "Construction of trivariate biorthogonal compactly supported wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1412-1420.
    8. Sun, Lei & Zhang, Xiaozhong, 2009. "A note on biorthogonality of the scaling functions with arbitrary matrix dilation factor," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 711-715.
    9. EL-Nabulsi, Ahmad Rami, 2009. "Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 52-61.
    10. Sun, Lei & Li, Gang, 2009. "Generalized orthogonal multiwavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2420-2424.
    11. Han, Jincang & Cheng, Zhengxing, 2009. "On the splitting trick and wavelets packets with arbitrary dilation matrix of L2(Rs)," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 130-137.
    12. Li, Rui & Wu, Guochang, 2009. "The orthogonal interpolating balanced multiwavelet with rational coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 892-899.
    13. El-Nabulsi, Rami Ahmad, 2009. "Fractional Dirac operators and deformed field theory on Clifford algebra," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2614-2622.
    14. Sun, Lei & Cheng, Zhengxing, 2007. "Construction of a class of compactly supported orthogonal vector-valued wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 253-261.
    15. Rami, El-Nabulsi Ahmad, 2009. "Fractional illusion theory of space: Fractional gravitational field with fractional extra-dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 377-384.
    16. Rami, El-Nabulsi Ahmad, 2009. "On the fractional minimal length Heisenberg–Weyl uncertainty relation from fractional Riccati generalized momentum operator," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 84-88.
    17. Liu, Zhanwei & Hu, Guoen & Wu, Guochang & Jiang, Bin, 2008. "Semi-orthogonal frame wavelets and Parseval frame wavelets associated with GMRA," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1449-1456.
    18. Iovane, G., 2007. "Hypersingular integral equations, Kähler manifolds and Thurston mirroring effect in ϵ(∞) Cantorian spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1041-1053.
    19. Liu, Zhanwei & Hu, Guoen & Wu, Guochang, 2009. "Frame scaling function sets and frame wavelet sets in Rd," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2483-2490.
    20. Chen, Qingjiang & Liu, Baocang & Cao, Huaixin, 2009. "Construction of a sort of multiple pseudoframes for subspaces with filter banks," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 801-808.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:37:y:2008:i:1:p:23-42. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.