Legendre's Conjecture

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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.