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The set of prime numbers: Multiscale analysis and numeric accelerators

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  • Iovane, Gerardo

Abstract

In this work, we show that the prime numbers follow a multiscale distribution. Indeed they can be classified thanks to tree structures, which are expressed in terms of two maximal subsets of N and using multilayer selection rules, acting on these sets of prime candidates. Consequently, the prime numbers follow a specific deterministic rules. Indeed, a numeric accelerator for generating primes can be realized in terms of the above mentioned specific rules. From the comparison with the Fibonacci numbers a beautiful harmony comes in terms of the Golden Mean which is relevant to high energy physics and E-Infinity theory too.

Suggested Citation

  • Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1953-1965
    DOI: 10.1016/j.chaos.2008.07.047
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    References listed on IDEAS

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    1. 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.
    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. 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., 2008. "The Exceptional Lie symmetry groups hierarchy and the expected number of Higgs bosons," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 268-273.
    6. 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.
    7. 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.
    8. 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.
    9. El Naschie, M.S., 2007. "From pointillism to E-infinity electromagnetism," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1377-1381.
    10. 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.
    11. 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.
    12. 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.
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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).
    3. Iovane, Gerardo, 2009. "The set of prime numbers: Multifractals and multiscale analysis," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1945-1958.

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