Good_Burning_Plastic comments on Talking Snakes: A Cautionary Tale - Less Wrong

107 Post author: Yvain 13 March 2009 01:41AM

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Comment author: CCC 06 May 2016 09:53:42AM *  1 point [-]

There is a fairly trivial proof^ that every prime number except 3 can be written such that it ends in a 2 if the base in which it it written is correctly chosen.

For example, 11 (base 10) in base 3 is 102. 37 (base 10) in base 7 is 52. 101 (base 10) in base 3 is 10202.

Of course, the base has to always be odd.


^ Deliberately left as an exercise for the reader. It really is trivial, but it seems so obvious once it's known that I'm honestly curious how obvious it is (or isn't?) when it's not already known.

Comment author: Good_Burning_Plastic 06 May 2016 05:15:01PM *  2 points [-]

Deliberately left as an exercise for the reader. It really is trivial, but it seems so obvious once it's known that I'm honestly curious how obvious it is (or isn't?) when it's not already known.

Took me several minutes, and I'm still not 100% sure my proof is correct.

Edit: The one I was thinking of was more complicated than needed. Nal vagrtre a terngre guna sbhe raqf jvgu gjb jura jevggra va onfr a zvahf gjb.

Comment author: g_pepper 06 May 2016 05:35:36PM *  1 point [-]

Nal vagrtre a terngre guna sbhe raqf jvgu gjb jura jevggra va onfr a zvahf gjb

That was the proof that I thought of as well.

Comment author: CCC 09 May 2016 08:57:54AM 0 points [-]

Yep, that's what I had.

More generally: Sbe nal vagrtre a terngre guna gjb gvzrf k, cvpx gur onfr (a zvahf k) gb jevgr a fhpu gung vg raqf va gur qvtvg k.