Hardy–Littlewood Goldbach representation conjecture

Let $R(n)$ denote the number of ordered pairs of odd primes $(p,q)$ satisfying $p+q=n$, and let

$$C_2= \prod_{p>2}\left(1-\frac{1}{(p-1)^2}\right)$$

be the twin-prime constant. Hardy–Littlewood's conjecture. As $n$ tends to infinity,

$$R(2n)\sim 2C_2\frac{n}{\log^2 n}\prod_{\substack{p\mid n \\ p>2}}\frac{p-1}{p-2}.$$

This is the classical quantitative conjecture for the number of Goldbach representations; the paper uses it as an assumption for asymptotic results concerning the sequence $a(m)$ and its summatory function.