For an application in statistical group theory, we need explicit upper and lower bounds that an expert in number theory (I am not one) may know how to prove.

**Question 1:** What are "good" bounds $f_1(x)<\displaystyle\sum_{p>x}\frac{1}{p^2}<f_2(x)$ where $p>x$ is prime?

For our application, sharper bounds than the following $f_1(x),f_2(x)$ are desirable: $$ \frac{1}{12\left(\frac{x}{\log(x)-4}+1\right)^4}<\sum_{p>x}\frac{1}{p^2}<\frac{1}{x-1}.$$ The lower bound can hold for $x>x_1$ and the upper bound for $x>x_2$ provided $x_1,x_2$ are "small".

**Question 2:** Is there a function $f(x)$ and *explicit* positive constants $c_1,c_2$ such that
$$c_1f(x)<\sum_{p>x}\frac{1}{p^2}<c_2f(x)?$$