# Consequence of the Riemann Hypothesis

So I watched this video: http://m.youtube.com/watch?v=rGo2hsoJSbo

And it included the fact that a consequence of RH is that there will always be a prime number between consecutive cubic numbers. I havent heard of this consequence before so First off I was wondering if this result is true if and only if the Riemann hypothesis is true and secondly I was wondering where I could see the derivation of this result.

• This is also mentioned in the Wikipedia article on the upper bounds of prime gaps: An immediate consequence of Ingham's result is that there is always a prime number between $n^3$ and $(n+1)^3$, if n is sufficiently large. There's also a reference to a paper. – Lucian May 15 '14 at 1:10
• The analogous statement obtained by replacing cubes with squares is still widely open, even assuming RH. See en.wikipedia.org/wiki/Legendre%27s_conjecture. – lhf May 15 '14 at 1:41