  It is shown that every sufficiently large even integer is a sum of two primes
and exactly 13 powers of 2. Under the Generalized Rieman Hypothesis one can
replace 13 by 7. Unlike previous work on this problem, the proof avoids
numerical calculations with explicit zero-free regions of Dirichlet
L-functions. The argument uses a new technique to bound the measure of the set
on which the exponential sum formed from powers of 2 is large.
