Kindly comments on New Monthly Thread: Bragging - Less Wrong

30 Post author: Joshua_Blaine 11 August 2013 05:50PM

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Comment author: Kindly 12 August 2013 11:47:43AM *  16 points [-]

...62535796399618993967905496638003222348723967018485186439059104575627262464195387.

Boo-yah.

Edit: obviously this was not done by hand. I used Mathematica. Code:

TowerMod[base_, m_] := If[m == 1, 0, PowerMod[base, TowerMod[base, EulerPhi[m]], m]];

TowerMod[3, 10^80]

Edit: this was all done to make up for my distress at only having an Erdos number of 3.

Comment author: answer 12 August 2013 06:31:49PM *  5 points [-]

Impressive, I didn't think it could be automatized (and even if it could, that it could go so many digits before hitting a computational threshold for large exponentials). My only regret is that I have but 1 upvote to give.

Comment author: Luke_A_Somers 12 August 2013 03:21:01PM 2 points [-]

It is not clear to me why the above code works. In particular, the 10^80 part.

Comment author: [deleted] 12 August 2013 04:03:31PM *  4 points [-]

A number mod 10^n yields the last n digits of the number.

Comment author: Luke_A_Somers 12 August 2013 04:13:54PM *  1 point [-]

Aaah. it was just saying how much to output. Phew. I was trying to figure out what 10^80 could have to do with 3^^^3 and failing, hard. So, it's a great relief that the answer is, 'nothing'.

Comment author: Kindly 12 August 2013 04:37:59PM 0 points [-]

Technically, I have not used the fact that the number in question is 3^^^3 -- I am treating it as 3^^X, where X is very large. So for huge numbers of digits, this will not give the correct answer, but I don't think it's practical to compute that many digits, in any case.

Should I explain how everything else works?

Comment author: Luke_A_Somers 12 August 2013 06:08:54PM 0 points [-]

Nah, I just figured that the named functions were something relevant, and I'm satisfied with that level of knowledge at this point.