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```Hallo conlangers!

On Friday 08 July 2011 13:00:20, R A Brown wrote:

> I can barely keep with this thread - but a few points:
>
> [PRIME-BASED SYSTEM]
> [...]
> On 07/07/2011 20:15, Jim Henry wrote:
>  > On Wed, Jul 6, 2011 at 11:15 AM, Alex
>  >
>  >> The original gjax-zym-byn system was prime-based; Jim
>  >> has told here a few times about finding it impractical
>  >> and therefore supplanting it with base systems.
>  >
>  > Yes; I still use the primes-based system for counting
>  > small numbers of things (up to around 31), including
>  > hours of the day (gzb uses a 24-hour clock).
>  >
>  > gzb nominally has root words for all the primes up to
>  > 113,
>
> Yes, that's the problem, it seems to me, in using a system
> based on primes? What happens after 113?
>
> In our system we can, in theory, express any number to
> infinity (and beyond?). Obviously, _in theory_ one could the
> same in a prime-based system *as long as one knew the full
> set of prime number* which, I guess, is also infinite   :)

There are indeed infinitely many prime numbers, which is easy
to prove.  Assume there were only finitely many primes.  Then
you can form the number (2*3*5*...*p)+1, wherein p is the
largest prime, and the product contains every prime number.
This number divides by none of the primes, it always leaves a
remainder of 1.  So it must either be a prime number itself,
or it must have other prime factors not on the list.  This
contradiction shows that there are infinitely many prime
numbers.

So in a prime-based number system, you can't just go by
multiplication, because for that you'd need infinitely many
basic numeral words.  (Of course, you can use a prime number
as a base the same way you could use 10, 12 or whatever, but
where is the point in that?)

> [snip]
>
>  > I think Joanna Russ had, in _And Chaos Died_, an implied
>  > conlang which, if it wasn't primes-based, at least had
>  > root words for every number up to a fairly largish prime.
>
> Yes, with an _implied_ conlang anything is possible.
> Certainly a theoretical prime-based system is fine
> for an implied conlang - but when it comes to actually
> putting it into practice it seems to me that, as Alex says
> above, one is likely to find it impractical.

It is.

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