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The interesting question is: are there real numbers whose N-th digit provably cant be calculated in O(N)?
I don't know of any with practical use, but you can fairly easily define a contrived one: cmeacham98's constant: a number where the `n`th digit is the `2^n`th digit of pi
Earlier quoted context omitted.
I don't know of any with practical use, but you can fairly easily define a contrived one: cmeacham98's constant: a number where the `n`th digit is the `2^n`th digit of pi
You're assuming that the N-th digit of pi can't be computed in sub-linear time, no?
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This sounds like a lot of work, when the physical limit of how many decimal places you need in our universe given the Planck length is only 63 or so.
What do you mean that we βonly needβ 63 decimal places? A computer can calculate and hold a lot more than 63 digits. So I guess my question is more like: if the universe was just one big computer dedicated only to calculating (and storing) digits of pi, how many digits could it get to calculate, max?