About simultaneous representation of numbers by sum of primes

In this paper proved theorem
Theorema. If $X$ -it is enough big, $\delta$ ($0<\delta<1$) it is enough small real numbers, that fair estimation
$$ J(\overrightarrow{b})>\frac{\Bigl(\frac{1}{\sqrt{n}}3(n!)^{2}B^{(2n-1)}|\overrightarrow{b}|\Bigr)^{1-\frac{\delta}{10(n-1)}}}{\Bigl(\ln\Bigl(\frac{1}{\sqrt{n}}3(n!)^{2}B^{(2n-1)}|\overrightarrow{b}|\Bigr)\Bigr)^{n+1}}, $$
for all vector $\overrightarrow{b}\in U(X)$ with the exclusion of no more than
$$ E(X)<X^{n-\frac{\delta}{17n^{3}}} $$
the vector of them. Here $B=\max\{3|a_{ij}|\}$, $1\leq i \leq n$, $1\leq j \leq n+1$.