Odd-prime sum counting beyond exp260

Let $r(s)$ count representations of $s$ by two odd primes, using the shared campaign definitions, and write $R(n)=\#\{0\le s\le n:r(s)>0\}$. For every natural number $n\ge e^{260}$,

This lowers the large-range threshold of the previously proved estimate from $e^{410}$ to $e^{260}$. It is a supporting counting estimate, not a complete19-prime campaign endpoint.