Asymptotic Hcabdlog's conjecture

Let $b\geq 2$ be fixed. Define

$$\mathcal{R}_{1,1}(N):=\sum_{\substack{p_1,\overleftarrow{p_2}\leq N\N=p_1+\overleftarrow{p_2}\\(\overleftarrow{p_2},b^3-b)=1}}\log p_1\log p_2$$

and

$$\mathfrak{S}_2(N):=\prod_{\substack{p\mid b^3-b\p\mid N}}\left(1+\frac{1}{p-1}\right)\prod_{\substack{p\mid b^3-b\p\nmid N}}\left(1-\frac{1}{(p-1)^2}\right).$$

Also let $\#\mathfrak{B}(N)$ denote the number of admissible integer representations encoded by the source's set $\mathfrak{B}(N)$. Asymptotic Hcabdlog's conjecture. For fixed $b\geq 2$, every sufficiently large odd integer $N$ is representable as a prime plus a reversed prime, and, for any $A>0$,

$$\mathcal{R}_{1,1}(N)\sim\mathfrak{S}_2(N)\#\mathfrak{B}(N).$$

This is obtained from the major arcs of the circle method and is described as an asymptotic form of Hcabdlog's conjecture. The supplied text does not provide a full definition of $\mathfrak{B}(N)$.