On the exceptional set of the sum of a prime number and a fixed degree of a prime number

Let $X$ be an enough big real number and let $M$ denote the set natural numbers not exceeding $X$ which cannot be written as a sum a prime and fixed degree of a prime number from arithmetical progression with a difference $d$. Let $E_d (X)=\mathrm{card}\, M.$ We obtain new a numerical sedate estimation for set $E_d (X)$ and an estimation from below for number presentation $n\notin M$ in specified type. We prove estimations is revision and a generalization for arithmetical progression earlier got result by V.A. Plaksin.