Legendre's conjecture

Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between ${\displaystyle n^{2}}$ and ${\displaystyle (n+1)^{2}}$ for every positive integer ${\displaystyle n}$. The conjecture is one of Landau's problems (1912) on prime numbers, and is one of many open problems on the spacing of prime numbers.

Unsolved problem in mathematics

Does there always exist at least one prime between ${\displaystyle n^{2}}$ and ${\displaystyle (n+1)^{2}}$?

More unsolved problems in mathematics