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)