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Number Theory: Unique Numbers

by Islam Hassan
Tags: number, numbers, theory, unique
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Islam Hassan
#1
May17-14, 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
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micromass
#2
May17-14, 07:56 AM
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Wikipedia has such information: http://en.wikipedia.org/wiki/38_(number)
Islam Hassan
#3
May17-14, 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...

mfb
#4
May17-14, 10:01 AM
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P: 12,037
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 x-23 and x-24 are primes" is another one for 26). Random collections are the best things you can find.
Islam Hassan
#5
May17-14, 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
mfb
#6
May17-14, 10:14 AM
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P: 12,037
It is trivial in the way that "x-23 prime and x-24 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.
Islam Hassan
#7
May17-14, 10:30 AM
P: 149
Yes, if course...silly me...
Curious3141
#8
May18-14, 02:18 AM
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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
Islam Hassan
#9
May18-14, 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
mfb
#10
May18-14, 06:42 AM
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P: 12,037
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?
Islam Hassan
#11
May19-14, 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
kjhskj75
#12
May21-14, 03:50 AM
P: 13
You could try this book:

http://www.amazon.com/Penguin-Book-C...509318-8526260


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