Is There a Book Listing Natural Numbers with Unique Properties?

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Discussion Overview

The discussion revolves around the search for a reference work that lists natural numbers with unique properties. Participants explore the criteria for uniqueness and the existence of systematic compilations of such numbers, touching on examples and the subjective nature of defining "unique" properties.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant inquires about a reference work listing natural numbers with unique properties, citing 26 as an example.
  • Another participant mentions that Wikipedia contains information on unique numbers but does not fulfill the request for a systematic reference.
  • Some participants argue that the definition of "unique properties" is subjective, noting that every number has unique properties, though many may be considered trivial.
  • A participant questions whether certain uniqueness qualities can be defined as trivial, indicating a desire to understand the concept better.
  • Links to external resources are shared, including a brief compilation of numbers and a reference to the "Interesting number paradox," which highlights the subjective nature of labeling numbers as interesting.
  • Concerns are raised about the arbitrary nature of defining unique characteristics, with examples provided that illustrate the point that some properties may not be significant.
  • A suggestion for a specific book is made as a potential resource for further exploration of unique numbers.

Areas of Agreement / Disagreement

Participants express differing views on what constitutes a unique property and whether certain characteristics are trivial. There is no consensus on the existence of a comprehensive reference work, and the discussion remains unresolved regarding the criteria for uniqueness.

Contextual Notes

Participants acknowledge the subjective nature of defining unique properties and the limitations of existing compilations. The discussion highlights the variability in what may be considered interesting or unique among natural numbers.

Islam Hassan
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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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Wikipedia has such information: http://en.wikipedia.org/wiki/38_(number )
 
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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...
 
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.
 
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
 
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.
 
Yes, if course...silly me...
 
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
 
Thanx Curious, exactly the type of thing I was looking for, thanks a million...I kept repeating "unique" in all my Google searches, so there you go...a little variety is always good...IH
 
  • #10
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
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
 

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