# Is 77 the only prime followed by a cube?

I discovered this site which claims that “$$77$$ is the only prime followed by a cube”. I find this statement rather surprising. Is this true? Where might I find a proof that shows this?

In my searching, I found this question, which is similar but the answers seem focused on squares next to cubes.

Any ideas?

This is certainly true. Suppose $n^3 - 1$ is prime, for some $n$. We get that $n^3-1 = (n-1)(n^2 + n + 1)$ and so we have that $n-1$ divides $n^3 - 1$. If $n-1>1$ then we’re done, as we have a contradiction to $n^3 - 1$ being prime.