User blog comment:Vel!/Hyperfactorial digits/@comment-10429372-20150430191353

You might be able to reduce it a bit by noting that H(9) is quite a bit more than 36*H(8).

So I believe there are no solutions between 2*10^27 and 2*10^34.

Further, there are no solutions between 10^20 and 5*10^25.

That can save a bit, but I don't think it will help much.