  Legendre's conjecture states that there exists a prime between $n^2$ and
$(n+1)^2$, for every positive integer $n$. Here I prove that for sufficiently
large $n$, there is a prime number between $n^2$ and $(n+1)^2$. The proof
relies on the idea of counting the maximum power, $o_p(n)$ of a prime $p\leq n$
such that $p^{o_p(n)}||n$.
