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.

Computations Concerning Primes and Powers of Two

ROMANI, FRANCESCO
1983

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.
Romani, Francesco
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/3696
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