Computations concerning primes and powers of two

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 2?31 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.