# 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?

## Source of Name

This entry was named for Adrien-Marie Legendre.

## Landau's Problems

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