# Status of a conjecture about powers of 2

I recently saw a conjecture on a blog ( http://blog.tanyakhovanova.com/?p=311 ) which the author refers to as the 86 conjecture. The conjecture claims that all powers of 2 greater than $2^{86}$ have a zero in their base 10 representation.

At first glance this seems like a numerical curiosity, and I wasn't sure that this was an interesting or deep mathematical question. I wanted to ask the community if they knew of any existing work that deals with either this type of question or something similar.

I tried searching for 86 conjecture on Google and didn't get anything useful.

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Richard Guy's Unsolved Problems in Number Theory, Problem F24, mentions only that Dan Hoey has verified this conjecture for $2^n$ up to $n = 2,500,000,000$. Guy tends to be fairly complete in his references. Since he doesn't give any others I doubt there's much more out there.