On Apr 11, 2006, at 11:42 AM, Mark O'Neill wrote:
Hi Charles,
On 11 Apr 2006, at 16:36, Charles Yeomans wrote:
Actually, 1 is not a prime.
I thought the definition of a Prime is:
"A number only divisible by 1 and itself"?
If that's the case, 1 is a Prime, no?
No, because implicit in that definition is the additional condition
that the number be a non-unit. Furthermore, this definition only
works in the presence of unique factorization.
Here is a more general definition of a prime.
p is prime if for any a, b without common factors, p | ab implies
either p | a or p | b.
This definition excludes units, and it makes sense in number systems
without unique factorization.
Charles Yeomans
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