Let $\Pi$ be the twin prime constant and $\pi_2(n)$ the twin prime counting function. Define $$ t(n) = | \pi_2(n) - 2 \Pi \int_2^n \frac{dx}{\ln(x)^2} | $$ Is it consistent with current data that for $n > 100 $ we have : $$ t(n) < \ln(n+2)^2 \sqrt (n+2) $$ ?? Is there a stronger plausible boundary for $t(n)$ ?