Apparently the negation of RH is enough to state that there needs to be infinitely many numbers such that d(n)&lt;=0. That would imply that you can find arbitrarily large n such that d(n)&lt;=0, but I don&#x27;t think that&#x27;s enough to claim that &quot;lim sup (n-&gt;infinity) (d(n)) &lt;= 0&quot;.<p>I think it&#x27;s enough to claim &quot;lim inf (n-&gt;infinity) (d(n)) &lt;= 0&quot; though, but for some reason they proved that in a different way, that I don&#x27;t quite understand yet.