Re: prime numbers and African artifact

Daniel Kian Mc Kiernan (
Sun, 16 Jul 1995 21:04:51 -0700

On 13 Jul 1995, Joseph Bret Wood wrote:

] Daniel Kian Mc Kiernan <> wrote:
]> On 12 Jul 1995, Peter Benie wrote:
]>> Alistair J. R. Young <> wrote:
]>>> Rick Hawkins writes:
]>>>> But only half-credit, since it's the wrong answer. 1 is not prime.
]>>> Correct me if I'm wrong but if a prime number is only divisible by itself
]>>> and 1, 1 is prime.
]>> A prime number is a number that has two positive factors.
]> Do we want to play Battling References here?
] Since prime numbers are a concept which was invented to be useful for certain
] things, it's important that our choice of including or excluding the number 1
] is constant with our uses for primes. (Just like the definition of 0! is 1,
] because it makes the equations work out, not because of some metaphysical
] argument.)

Boy, I am genuinely surprised with the confusion here between the
=word= "prime", and the various meanings that may be attached to
that word. We are arguing about =which= concept is to be associated
with "prime", not about which concept is which concept.

All three of the various concepts to which someone has here pointed
were created because someone found them useful.

] It is well known that every counting number ( 0 < n < infinity ; n is integer )
] has a unique prime factorization. If one is a prime number, then the counting
] numbers would all have an infinite number of prime factorizations.

<Illustration of the factorization theorem deleted.>

] And that's why one isn't a prime number. (among other reasons.)

As I have stated elsewhere, the factorization theorem can be
expressed with "prime" defined in a way that includes 1, the
expression merely has to be different than that when "prime" is
defined to exclude 1. This is a trivial exercise, but I can show
you how to do it if you need help.

As I've said elsewhere, the matter of what shall be meant by prime
is purely a matter of felicity of expression. Certainly, in one
context it is very useful to exclude 1, but in other contexts it
makes sense to include 1, and the original poster deserves =full=
credit (rather than half-credit), as does Mr Young.

It's always Dark. Light only hides the Darkness.

Daniel Kian Mc Kiernan (619) 535 - 0546 <75013,676>