From the Overview of the Royal Danish Sciences Institution's work and its members' work in the year 1882.
In the notes from a meeting on March 9th 1877, after discussing papers by Legendre, J. W. L. Glaisher, and Meissel, Oppermann stated:
At the same occasion, I made people aware of the not yet proven conjecture, that when $n$ is a whole number $>1$, at least one prime number lies between $n(n-1)$ and $n^2$ and also between $n^2$ and $n(n+1)$.
A solution to Oppermann's Conjecture leads to simple solutions to Legendre's, Brocard's, and Andrica's Conjectures.
