Possible Duplicate:

How does $ \sum_{p\lt x} p^{-s} $ grow asymptotically for $ \mathrm{Re}(s) \lt 1 $?

from the prime number theorem is it possible to have

$$ \sum_{p \le x}\: x^{m} = \frac{ \text{Li}\: (x^{m+1})}{m+1} $$ ?

here 'Li' is the logarithmic integral $ \int_{2}^{\infty} \frac{dt}{logt} $

valid for m > -1 in the case m=0 we recover the usual prime number theorem.