Re: prime numbers and African artifact
Joseph Bret Wood (bretwood@cs.uoregon.edu)
13 Jul 1995 11:58:30 0700
In article <Pine.HPP.3.91.950713005613.12887I100000@weber.ucsd.edu>,
Daniel Kian Mc Kiernan <dmckiern@weber.ucsd.edu> wrote:
>On 12 Jul 1995, Peter Benie wrote:
>
>> Alistair J. R. Young <avatar@arkane.demon.co.uk> 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.)
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.
an example:
720 = 2 * 2 * 2 * 2 * 3 * 3 * 5
If 1 is considered to be a prime number, then the following are all prime
factorizations also:
720 = 1 * 2 * 2 * 2 * 2 * 3 * 3 * 5
720 = 1 * 1 * 2 * 2 * 2 * 2 * 3 * 3 * 5
720 = 1 * 1 * 1 * 2 * 2 * 2 * 2 * 3 * 3 * 5
720 = 1 * 1 * 1 * 1 * 2 * 2 * 2 * 2 * 3 * 3 * 5
etc.....
And that's why one isn't a prime number. (among other reasons.)
Bret Wood
bretwood@cs.uoegon.edu
