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The set of primes: Towards an optimized algorithm, prime generation and validation, and asymptotic consequences

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  • Iovane, Gerardo

Abstract

Starting from the result that the prime distribution is deterministic, we show in its maximal reduced form, the set of prime numbers P. This set can be expressed in terms of two subsets of N using three specific selection rules, acting on two sets of prime candidates. The asymptotic behaviour is considered too. We go head towards an optimized algorithm to generate primes, whose computational complexity is C(n)∈O(n). In addition a pre-computed algorithm is also considered and its computational complexity C(n)∈O(1).

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  • 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.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1344-1352
    DOI: 10.1016/j.chaos.2008.04.060
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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. Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.
    2. 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.
    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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