Quote:
Originally Posted by Jens
Quote:
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Originally Posted by Jeff Root
It is clear to me that the number 'one' is a prime number (since it is
not the product of other integers), but for convenience in certain cases
in number theory, an ad hoc addition was made to the definition to
specify that it is 'not a prime'. By nature, it is prime. By definition,
it is not prime.
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But I think there are two reasonable ways to define a prime. One is a
number that can only be divided by 1 and itself. The other definition
could be a number that can be divided by exactly two numbers, 1 and
itself. By the first definition, 1 is in, in the second definition, it is out. |
To me it is obvious that the natural definition is "A positive integer
which cannot be evenly divided by any other integers."
Following your argument, a "second" would be "A number that can
be divided by exactly three numbers." A 'tertiary" must be "A number
that can be divided by exactly four numbers." And so forth.
The essential idea of "prime numbers" is not that they ARE divisible
by a limited set of numbers, but that they are NOT divisible into
other integers. It is their indivisibility which makes them prime.
-- Jeff, in Minneapolis
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