User blog comment:Cloudy176/Proving the bound for S(7)/@comment-29743408-20160824074531

I agree with your computations.

Only the last lower bound seems to be wrong. I find S(7) = 10^(10^(10^(10^a))), with

18705352.84113 < a < 18705352.84117.

And the same bounds for Sigma(7).

PMic