Consider that $\mathcal{P}(x)$ represents the $x$-nth prime number.
Let let $y$ be a natural number and $p$ be the prime $\mathcal{P}(y).$ Then let $\mathcal{D}(p)$ the least $n \in \mathbb{N}^*$ which
$ \sum\limits_{i = y+1}^{n} \mathcal{P}(i) $
is a prime number. For example:
$\mathcal{D}(2) = 10$, because $\sum\limits_{i = 2}^{10} \mathcal{P}(i) = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 127$.
For every even number $m > 2$ there exists a prime number $q$ such that $\mathcal{D}(q) = m$?