In the case of $\dfrac{1}{7^{800}}$ it's easy, to find the $2^{2020}$ decimal, but what about the simplest of the irrational numbers.

Question:Do we know how to determine the $2^{2020}$ decimal of $\sqrt{2}$?

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In the case of $\dfrac{1}{7^{800}}$ it's easy, to find the $2^{2020}$ decimal, but what about the simplest of the irrational numbers.

Question:Do we know how to determine the $2^{2020}$ decimal of $\sqrt{2}$?

withoutcomputing all the preceding ones and that may be quite tricky since there is no obvious pattern in the digit sequence. I would say the answer is "no" but there is no proof of that either. $\endgroup$ – fedja Feb 23 '20 at 21:58