Istituto di Scienza e Tecnologie dell'Informazione     
Romani F. Computations concerning primes and powers of two. In: Calcolo, vol. XX (III) pp. 320 - 336. Giardini, 1984.
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 2Δ31 and the results are 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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