Goldbach–Linnik type problems on cubes of primes

Abstract

In this paper, we will investigate three Goldbach–Linnik type problems on cubes of primes. For example, it was proved that, for $$k=1364,$$ every pair of sufficiently large even integers can be represented by a pair of eight prime cubes and k powers of 2. In this paper, we give the detailed proof for the first time and sharpen the value of k to 658.