%0 Journal Article %T Linnik's approximation to Goldbach's conjecture, and other problems %A Dave Platt %A Tim Trudgian %J Mathematics %D 2014 %I arXiv %X 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. %U http://arxiv.org/abs/1404.5669v2