Is it the largest known or is it proven its the largest?
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It can't be anything with 10 as base, as 10^n is n+1 digits long → the highest *base* is 9. With every power, you lose some of the way to the extra digit, and 21 is the largest before this loss turns into one less digit: 21: 109418989131512359209 22: 984770902183611232881
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sketch of a proof: we look for n and b such that 10^(n-1)<= b^n <10^n. The second inequality is satisfied with a<10. Then we take log of first inequality and get n-1 <= n log b n(1-log b)<= 1 n<= 1/(1-log b). for a=9, we get n<= 21.85... for a=1,2,3,...,8 we get much smaller n.
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In fact 9^n (where natural number n<22) is always n digit number. After 21 pattern breakspic.twitter.com/2Ei37ywUfX
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How does anyone find out these things?
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More than how, why??
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Has someone done this exercise across non-decimal bases? What are the results and is there a formula?
Thanks. Twitter will use this to make your timeline better. UndoUndo
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