Legendre's Conjecture

Open Question
It is not known whether:
 * $\exists n \in \N_{>1}: \map \pi {n^2 + 2 n + 1} = \map \pi {n^2}$

where $\pi$ denotes the prime-counting function.

That is:
 * Is there always a prime number between consecutive squares?

Landau's Problems
This is the $3$rd of Landau's problems.