Is 77 the only prime followed by a cube?

I discovered this site which claims that “7 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 n31 is prime, for some n. We get that n31=(n1)(n2+n+1) and so we have that n1 divides n31. If n1>1 then we’re done, as we have a contradiction to n31 being prime.

Source : Link , Question Author : David Starkey , Answer Author : Community

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