# 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, 11 months 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.

- 2 years, 11 months ago

- 2 years, 7 months ago

99999999999999999999998

- 2 years, 10 months ago

Prove it.

- 2 years, 9 months ago