Linnik's approximation to Goldbach's conjecture, and other problems
  We examine the problem of writing every sufficiently large even number as the sum of two primes and at most $K$ powers of 2. We outline an approach that only just falls short of improving the current bounds on $K$. Finally, we improve the estimates in other Waring--Goldbach problems. 
Dave Platt and Tim Trudgian
math.NT