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Joshua_Blaine comments on New Monthly Thread: Bragging - Less Wrong
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I solved the last 8 digits of 3^^^3 (they're ...64,195,387). Take that ultrafinitists!
I.. just.. WHAT? The last digits are the easiest, of course, BUT STILL. What was your methodology? (because I can't be bothered to think of how to do it myself)
I started with some iterated powers of 3 and tried to find patterns. For instance, 3 to an odd (natural number) power is always 3 mod 4, and 3 to the power of (a natural number that's 3 mod 4) always has a 7 in the one's place.