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The set of prime numbers: Multifractals and multiscale analysis

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  • Iovane, Gerardo

Abstract

In this work we show that the prime numbers can be seen as the sides or angles of a multifractal polygon based on a hexagon. This also means that primes follow a multiscale distribution and can be generated in a beautiful deterministic fashion.

Suggested Citation

  • Iovane, Gerardo, 2009. "The set of prime numbers: Multifractals and multiscale analysis," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1945-1958.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:1945-1958
    DOI: 10.1016/j.chaos.2009.03.203
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    References listed on IDEAS

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    1. El Naschie, M.S., 2007. "From pointillism to E-infinity electromagnetism," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1377-1381.
    2. 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.
    3. El Naschie, M.S., 2008. "On a major exceptional Lie symmetry groups hierarchy and quantum gravity," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 42-44.
    4. El Naschie, M.S., 2008. "The fundamental algebraic equations of the constants of nature," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 320-322.
    5. Wolf, Marek, 1998. "Random walk on the prime numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 335-344.
    6. 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.
    7. 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.
    8. Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.
    9. 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.
    10. 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.
    11. 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.
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    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. García-Sandoval, J.P., 2020. "Fractals and discrete dynamics associated to prime numbers," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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