Re: prime numbers and African artifact
SEELIGER (jes7123@omega)
15 Jul 1995 18:41:57 GMT
Joseph Bret Wood (bretwood@cs.uoregon.edu) wrote:
: In article <Pine.HPP.3.91.950713005613.12887I-100000@weber.ucsd.edu>,
: 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.)
Not only that but we identify prime number as having only one prime
factor. For 2 it is 2. A composite number is the product of two or
more primes: i.e. 4=2*2. If one were a prime number then numbers like
2,3, 5,7, etc. couldn't be prime. They would be composite. In fact one
would be composite too since it would be 1*1 and would therefore have at
least two factors.
--
John Seeliger Nutritional Information
jes7123@omega.uta.edu Cholesterol..90 Sodium..5 Copper.........3
jes7123@utarlg.uta.edu Fiber .......12 Iron....1 Calcium........7
seeliger@utahep.uta.edu Fat.........200 Zinc....4 Einstienium..<10^-14
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