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Largest power of 2 which doesn't contain 0?

What is the largest power of \(2\) which doesn't contain \(0\)?

I tried a variety of methods to tackle this problem including programming and I even got the answer as \(86\) but I couldn't prove that there exists no larger power of \(2\) which doesn't contain \(0\).

Note: I tried brute forcing for integers up to \({2}^{100000}\) but with no luck. So for \({2}^{n}\), the \(n\) must be greater than \(100000\). Inspiration (Calvin Lin's comment).

Note by Arulx Z
2 years ago

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If you've tried up to \(2^{100000},\) which has in excess of \(30000\) digits, then the probability that any given power of two greater than this not including a \(0\) would be less than \(10^{-1378}.\) While this is not a proof, it seems pretty certain that no greater power than \(2^{100000}\) will be devoid of a \(0.\) So perhaps \(86\) is indeed the solution that you are looking for.

Edit: This is in fact the conjectured greatest power with this property, but a proof remains an open problem. Brian Charlesworth · 2 years ago

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Relevant. Pi Han Goh · 1 year, 8 months ago

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99999999999999999999998 Rushikesh Jyoti · 1 year, 11 months ago

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@Rushikesh Jyoti Prove it. Arulx Z · 1 year, 10 months ago

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