After a short investigation I
have observed that:

A) The sum of consecutive primes
could be a perfect power.

Example: 3^13 = 5821+5827+…+7879

B) If the sum of consecutive
squared primes is a perfect power, then it is a perfect square.

Example: 586^2 = 41^2+43^2+…+173^2

C) Not observed a perfect power
being the sum of consecutive powered primes to a power higher than
two.

I thus conjecture that:

**For the equality:
***x*^{s}=p(n)^{r}+p(n+1)^{r}+p(n+2)^{r}+…+p(m)^{r}

**if r and s have following
relationship**

** r=1 then s>0**

** r=2 then 0<s<=2**

** r>2 then s=1 **

**Q:
Find counter examples**