**Conjecture**. For every natural number $n \in \Bbb{N}$, there exists a finite set of consecutive numbers $C\subset \Bbb{N}$ containing $n$ such that $\sum\limits_{c\in C} c$ is a prime power.

A list of the first few numbers in $\Bbb{N}$ has several different covers by such consecutive number sets.

One such is:

```
3 7 5 13 8 19 11 25 29 16 37 41 49 53
___ ___ _ ___ _ ____ __ _____ _____ __ __ _____ _____ _____ _____ __
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
___ ___ _____ _____ __ ________
11 17 31 43 81
59 71 3^5
___ __ _____ _________________
30 31 32 33 34 35 36 37 38 39 40 41 42 43 .....
_____ _____ _____
61 67 73
```

Has this been proved already?