2 problems

Let $R(n)$ denote the number of representations of $n$ as a sum of two primes, and let $\varphi(n)$ be Euler's totient function. For sufficiently large $x$ and $q\leq x/4$, weighte…

Let $R(n)$ denote the number of representations of $n$ as a sum of two primes. For sufficiently large $x$ and $q\leq x/4$, exceptional-interval Goldbach conjecture. There is an abs…