Number Theory: Unique Numbers

by Islam Hassan
Tags: number, numbers, theory, unique
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 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
 Mentor P: 18,346 Wikipedia has such information: http://en.wikipedia.org/wiki/38_(number)
 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...
 Mentor 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.
 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
 Mentor 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.
 P: 149 Yes, if course...silly me...
 HW Helper P: 2,954 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
 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
 Mentor 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?
 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
 P: 13 You could try this book: http://www.amazon.com/Penguin-Book-C...509318-8526260

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