The proposition P states: There exists an $n\in \mathbb{N}$ such that $2^n > 1000$. This means there is a natural number $n$ for which $2^n > 1000$ holds true.

To negate this proposition, we want to state that there is no natural number $n$ for which $2^n > 1000$. In other words, for any natural number $n$, the inequality $2^n \leq 1000$ will hold.

Therefore, the negation $¬P$ can be expressed as: For all $n \in \mathbb{N}$, $2^n \leq 1000$.

Thus, the negation $¬P$ is $\boxed{\forall n \in \mathbb{N}, 2^n \leq 1000}$.