Around 200 years ago, Legendre conjectured that there is always a prime between between consecutive squares $n^2$ and $(n+1)^2$ for all $n\geq 1$. This conjecture remains an open problem to this day. As progress towards this problem, much work has been done in finding successively smaller values of $m>2$ such that there is always a prime between $n^m$ and $(n+1)^m$. Historically, such results have only been for "sufficiently large" values of $n$. However, in the past 10 years there has been significant work in obtaining explicit results that hold for all $n\geq 1$. In this talk, we discuss the history of such explicit results, and suggest how one may lower this value of "m" even further.