I am certain it is greater.  BB(n) grows super-exponentially.<p>In fact I would be willing to bet serious money that BB(n+1)&#x2F;BB(n) is greater than BB(n) if 3 &lt; n.<p>(This is, of course, assuming that one assumes that BB(n) is well-defined.  That is an interesting point of philosophy given the existence of Turing machines which can&#x27;t be proven to not halt.)