Exotic number representations

[GMarco]

Hi

I was just browsing around, searching for exotic number representations, and was suprised to find only really few different ways to represent numbers.

1. widely used integer and floating point.
2. Roman or Babylonian ( like MCXXV)
3. Double base Number systems
4. Residue Number Systems.

each has different advantages and disadvantages.

I did not find something based on prime numbers like
(1)=2
(1,0)=3
(1,0,0)=5
(1,0,1)=10
(1,1,0)=15
(2,1,0)=75
...
(x,y,z)=5^x*3^y*2^z


Does anybody know the prime numbers - number representation, what keyword can I search for?
Does anybody know other exotic number representations?


GMarco

[BioPhysEngr]

You may be interested in Godel Numbering: http://en.wikipedia.org/wiki/G%C3%B6del_numbering

[Juliusbk]

Well it is not very smart to use prime numbers, since it is NP-hard to find the prime factors. Search for prime factorization for more information.

Other ways to represent numbers is by using an surjective function. Of course this still uses some base number reprsentation, but each number is mapped into its true form.

[Eri523]

Well it is not very smart to use prime numbers, since it is NP-hard to find the prime factors.

It may not be efficient when used as a general-purpose numbering system. But maybe it is useful for specific applications. For instance, many years ago I used a CAS that employed prime factors to represent a set of "bit flags" stored in a single numeric variable independent of any number base. I.e., if the number was divisible by the prime specific for the flag, the flag was set, otherwise not. I found that a really elegant solution.

[nuzzle]

I was just browsing around, searching for exotic number representations, and was suprised to find only really few different ways to represent numbers.

You have the complex numbers and their more exotic relatives the quarternions and the octonions.