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Comments (226)
Every base is base 10.
(There is no prime number ending with a 2 in binary. Other than that, you're fine.)
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.
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.
That was the proof that I thought of as well.
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.
To me: about three seconds' thought after reading your statement. But I'm an actual mathematician and therefore not necessarily typical.
Took me about 30 seconds, but I'm only an ex-mathematician and I'm not as clever as g!
Noted. Thanks, this tells me that to someone with some knowledge of mathematics it really is as obvious as it looked.
In my case, at least, essentially all the time taken to solve the problem was "decoding" it -- working out what it was really saying. That is: fnlvat gung jura lbh jevgr n ahzore va onfr o vg raqf va n gjb vf rknpgyl gur fnzr guvat nf fnlvat gung gur ahzore rdhnyf gjb zbqhyb o, naq (vs lbh'er hfrq gb guvf fghss) gb fnl gung vf gb frr gur fbyhgvba.
Never underestimate the utility of properly describing a problem. I've found that it's really amazing how often, by the time you've figured out what question you really want to ask to solve the problem, you're already most of the way to the answer...
I think this is the basis of good Business Analysis. A field I'm intending to move into.
It's the very essence of "Hold off on proposing solutions".
Yes, I very much agree.