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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?

Martin Sleziak
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dspyz
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    Can anyone think of any other good tags for this problem? big-numbers was all I could find – dspyz Apr 17 '13 at 21:55
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    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... – Qiaochu Yuan Apr 17 '13 at 22:03
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    Related: http://mathoverflow.net/questions/20765/the-problem-of-finding-the-first-digit-in-grahams-number – Lord Soth Apr 17 '13 at 22:10
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    It will even be hopeless to calculate the FIRST digit of graham's number. – Peter Jan 12 '16 at 20:20
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    just the start number is already over $10^{10^{12}}$ – Roddy MacPhee Apr 28 '21 at 14:45

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