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I know using Euler's Totient function, it's easy to find the last $n$ digits of Graham's number (or any large repeating power tower), but is there any known way to find the first $n$ digits of Graham's Number? How about in binary? Or in any base besides a power of 3?

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    $\begingroup$ Can anyone think of any other good tags for this problem? big-numbers was all I could find $\endgroup$ – dspyz Apr 17 '13 at 21:55
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    $\begingroup$ Finding the first $n$ digits is a completely different and much harder problem. Take a base-$10$ logarithm and you'll see that the problem boils down to computing the fractional part of the logarithm... $\endgroup$ – Qiaochu Yuan Apr 17 '13 at 22:03
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    $\begingroup$ Related: mathoverflow.net/questions/20765/… $\endgroup$ – Lord Soth Apr 17 '13 at 22:10
  • $\begingroup$ It will even be hopeless to calculate the FIRST digit of graham's number. $\endgroup$ – Peter Jan 12 '16 at 20:20

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