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Computations concerning primes and powers of two

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Abstract

The problem of representing odd integers as the sum of a prime and a power of two is investigated using numerical computations. The density of representable numbers is calculated up to 231 and the results are extrapolated in order to estimate the asymptotic density. A probabilistic model (suggested by Bombieri) is used to get an independent estimate for the asymptotic density. Either approach suggests 0.434... as a reasonable approximation for the asymptotic density.

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  1. Istituto di Elaborazione dell'Informazione, CNR Pisa, Via S. Maria 46, 56100, Pisa

    F. Romani

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  1. F. Romani
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Romani, F. Computations concerning primes and powers of two. Calcolo 20, 319–336 (1983). https://doi.org/10.1007/BF02576468

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  • DOI: https://doi.org/10.1007/BF02576468

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