I have a rather simple question of number theory which I can't seem to be able to find a good reference for. I am not a specialist and I don't really know where to look. I would like to show that the following sequence 


$$ \frac{1}{N^2}\sum\_{p \leq N \ p \ \mathrm{prime }}{p^2} $$ goes to infinity. Numerical computation indicates that it is true. 


Thank you very much for your attention :)



Asymptotic of the sum of squared primes
[This question appeared on Math.stackexhange](https://math.stackexchange.com/questions/49383/how-does-sum-px-p-s-grow-asymptotically-for-textres-1/49434#49434). The answer linked above uses partial summation to show that for $k>-1$ we have
$$\sum\_{p\leq x}p^{k}=\text{li}\left(x^{k+1}\right)+O\left(x^{k+1}e^{-c\sqrt{\log x}}\right).$$


