Linnik proved in 1951 the existence of a constant K such that every sufficiently large even number is the sum of two primes and at most K powers of 2.
Roger Heath-Brown and Jan-Christoph Schlage-Puchta in 2002 found that K = 13 works. This was improved to K=8 by Pintz and Ruzsa in 2003.
In above approximation, is there anything special about "powers of 2" ? Is there any similar results for power of 3, or power of 5, etc ?
For example, can we say: every sufficiently large even number is the sum of two primes and at most K powers of 3 ?