Quote:
Originally Posted by Jeff Root
I think that my definition, that a prime number is a positive integer which is not the product of other integers, captures the intended meaning of "prime number". This definition, primitive and not the currently universally-used definition, includes 'one' as a prime.
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Part of
why the currently used definition of prime numbers excludes 1 is that it is
even "deeper" than the 'the intended meaning of "prime number"'. 1 and -1 are "units" in the set of integers. You could argue that being a unit shouldn't preclude it also being called a prime, but that would still ignore the other reasons not to consider 1 a prime.
Quote:
Originally Posted by Jeff Root
It departs from the essential meaning of what a prime number is.
It adds an artificial restriction to make certain theorems simpler. 'One' clearly would be considered the quintessential prime number if not for the desire to simplify those theorems. 'One' is a positive integer which is not the product of other integers.
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I'm still not convinced by your "essential meaning" of what a prime is. That a prime number can only be produced by multiplying 1 and the number itself is a very specific thing. Multiplying 1 by itself seems very much the odd or trivial case; the exception.
That 5, 7 or 2
43112609-1 are prime is quite different to "1 is a prime".
Quote:
Originally Posted by Jeff Root
It is the prime prime number in every way except by the modern definition.
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...it's a "unit". (insert smiley)