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Number Theory: Unique Numbers 
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#1
May1714, 07:31 AM

P: 149

Does anyone know of a reference work that lists natural numbers with unique properties? Like 26, for example, being the only natural number sandwiched between a square (25) and a cube (27). Does such a reference book exist?
IH 


#2
May1714, 07:56 AM

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P: 18,099

Wikipedia has such information: http://en.wikipedia.org/wiki/38_(number)



#3
May1714, 08:01 AM

P: 149

Thanx Micro, I was aware of certain Wikipedia articles; what I specifically am looking for though, is a systematic reference work of all know unique numbers. I could not find something resembling this on the net...



#4
May1714, 10:01 AM

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P: 11,631

Number Theory: Unique Numbers
It depends a lot on the things you consider as unique properties. Every number has unique properties, but most of them are boring ("is the only number x where x23 and x24 are primes" is another one for 26). Random collections are the best things you can find.



#5
May1714, 10:10 AM

P: 149

Hmm...is that a trivial uniqueness quality that you just mentioned for 26? Doesn't seem so to me but then I am the layman here...
Can one somehow 'define' mathematical triviality for such unique qualities I wonder... IH 


#6
May1714, 10:14 AM

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P: 11,631

It is trivial in the way that "x23 prime and x24 prime" requires two primes with a difference of just 1, and 2 and 3 are the only primes that satisfy this.
You can set this up for every integer. 


#7
May1714, 10:30 AM

P: 149

Yes, if course...silly me...



#8
May1814, 02:18 AM

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P: 2,943

A very brief effort on google gave me this: http://www2.stetson.edu/~efriedma/numbers.html
Of course, when you start labelling particular natural numbers as "interesting" based on arbitrary criteria, you will encounter this paradox: http://en.wikipedia.org/wiki/Interesting_number_paradox 


#9
May1814, 02:22 AM

P: 149

Thanx Curious, exactly the type of thing I was looking for, thanx a million...I kept repeating "unique" in all my Google searches, so there you go...a little variety is always good...
IH 


#10
May1814, 06:42 AM

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P: 11,631

Note that not all those entries are unique, and some of them just reflect our limited knowledge. And some are... pointless.
"151 is a palindromic prime."  true, but there are 7 smaller palindromic primes and probably infinitely more larger ones. "146 = 222 in base 8."  so what? 


#11
May1914, 10:03 AM

P: 149

Thanx for the clarification mob...funny I would have thought that a compendium of numbers with unique characteristics would be a given in number theory...quite surprised that it's so difficult to find...
IH 


#12
May2114, 03:50 AM

P: 10




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