Legendre's conjecture

Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between $n^{2}$ and $(n+1)^{2}$ for every positive integer $n$ . The conjecture is one of Landau's problems (1912) on prime numbers; as of 2023, the conjecture has neither been proved nor disproved.

Unsolved problem in mathematics:

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

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