Аннотация: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 Ed(X)=cardM. We obtain new a numerical sedate estimation for set Ed(X) and an estimation from below for number presentation n∉M in specified type. We prove estimations is revision and a generalization for arithmetical progression earlier got result by V.A. Plaksin.