Re: prime numbers and African artifact
Ron Hunsinger (hnsngr@sirius.com)
Sat, 15 Jul 1995 00:23:34 -0700
In article <3u5qf7$64c@lyra.csx.cam.ac.uk>, M.J.Jennings@amtp.cam.ac.uk
(Michael Jennings) wrote:
> The reason that one is not a prime number is because virtually
> all theorems in mathematics based on prime numbers do not make sense
> if we include it. What's more, they _cannot_ be made to make sense
> if we include it.
They can be made to make sense. It's just that it's messy to have to keep
saying "prime bigger than one" everywhere instead of just "prime".
For an example of the alternatives, look at Euclid's Elements (which is
NOT all geometry, BTW. There are whole sections that are what we would
consider algebra and number theory. It's only the proofs that are
geometric.)
The Greeks did not considier 1 to be a number (prime or otherwise), so
Euclid frequently had to prove theorems twice - once for 1, and then again
for all the (other) numbers.
-Ron Hunsinger
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