[PD] prime numbers

[Claude Heiland-Allen]

Hi,

On 12/09/10 04:33, ydegoyon at gmail.com wrote:
>> Mathieu Bouchard wrote:
>>> On Sat, 11 Sep 2010, Kim Cascone wrote:
>>>
>>>> is there a Pd object for generating prime numbers?
>>>> currently I'm:
>>>> [1 2 3 5 7 9...97]
>>>
>>> 1 is not a prime number. (9 is not a prime number either)
>
> i just read '1 is not a prime number' of course 9 is not,
> ut a prime number can only be divided by 1 and itself,
> so why 1 can't be?

1 is special and unique, it has only 1 factor (itself).  I'd guess that 
0 has an infinite number of factors, but I'm not sure on this.  In any 
case it's probably special too.

Mathematicians almost all agree that 1 should not be classified as 
prime, because it does not have exactly 2 distinct factors.  The main 
reason is that if you leave out the number 1 from the set of prime 
numbers, you can prove nice uniqueness theorems about prime factorization:

http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic

The name shows just how important that property is considered to be. 
The uniqueness of prime factorization can be used to show some quite 
impressive things, see for example:

http://en.wikipedia.org/wiki/Goedel_numbering

used to prove that "you can't prove everything" (or something along 
those lines, I've not studied this maths in enough depth).


Claude
-- 
http://claudiusmaximus.goto10.org