Number Theory: Unique Numbers

In summary, the conversation discusses the existence of a reference book that lists natural numbers with unique properties. While there are websites and books that mention certain numbers with interesting characteristics, a systematic reference work for all known unique numbers is difficult to find. It is also noted that labeling certain numbers as "interesting" can be subjective and may not necessarily reflect their true uniqueness. However, a book titled "The Penguin Dictionary of Curious and Interesting Numbers" is recommended as a potential resource for those interested in this topic.
  • #1
Islam Hassan
233
5
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
 
Mathematics news on Phys.org
  • #2
Wikipedia has such information: http://en.wikipedia.org/wiki/38_(number [Broken])
 
Last edited by a moderator:
  • #3
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
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.
 
  • #5
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
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.
 
  • #7
Yes, if course...silly me...
 
  • #8
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
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
 

1. What is number theory?

Number theory is a branch of mathematics that deals with the properties and relationships of integers, or whole numbers. It is also known as the study of unique numbers.

2. What are unique numbers in number theory?

Unique numbers, also known as prime numbers, are positive integers that are only divisible by 1 and themselves. They have exactly two positive divisors, making them distinct from other numbers.

3. How are unique numbers important in mathematics?

Unique numbers play a crucial role in various areas of mathematics, including cryptography, coding theory, and algebra. They are also important in understanding the distribution of prime numbers and solving complex mathematical problems.

4. How can I determine if a number is unique?

A number can be determined to be unique by checking if it is divisible only by 1 and itself. This can be done through trial and error or by using algorithms such as the Sieve of Eratosthenes or the AKS primality test.

5. Are there an infinite number of unique numbers?

Yes, there are an infinite number of unique numbers. This was first proven by the ancient Greek mathematician Euclid. The proof is known as Euclid's theorem, which states that there are infinitely many prime numbers.

Similar threads

Replies
4
Views
524
  • General Math
Replies
7
Views
1K
  • General Math
Replies
5
Views
1K
Replies
1
Views
1K
  • General Math
Replies
5
Views
982
  • General Math
Replies
12
Views
921
Replies
2
Views
1K
Replies
12
Views
3K
Replies
3
Views
1K
Replies
4
Views
285
Back
Top