mathistopheles

If it is of any relevance, I am the original poster and I have no objection to Richard Green's article being the one referenced. He has clearly credited me as his source, and very few people would have seen my piece if he hadn't written his. Also his piece is clearly much more digestible in summarising the points of interest, while mine was more of a puzzle (the solution page is the one being referenced) followed by a loose account of my investigation into the problem.

I'm just pleased that it seems to have captured the imagination in the way it has.

The expectations are not independent though. There can be no more solutions for b=6 than there are for b=5. Given what we already know, we should calculate those sums, not from i=2, but from i=10^2184 or so, because we there are no solutions below that. The theoretical expected number of solutions for b=6 is therefore vanishingly small.