Why is 1 not considered a prime number?

[MathematicalPhysicist]

Primes are interesting precisely because 1 isn't a prime. 1 is a divisor of every number, therefore defining 1 as a prime dulls the main purpose of primes.

this is why god=1.

(god-> greatest omnipotent divisor).

a joke, which i hope that number theorists understand.

 

[matt grime]

Please tell me, why are primes interesting?
They are interesting because they are devisable by themself and 1 only and I see no reason why you should exclude 1 that definition. The official definition may say something else but until I find a good reason to exclude 1, I will keep it in my list of primes.

That isn't a very good definition of prime and *could* be interpreted to mean 1 isn't prime since 1 is not divisible by 1 *and* itself. Which is why some people prefer to say "exactly two factors" or to be more specific exacty two factors in N, or two positive factors in Z. However, the "real" reason that primes are interesting is that p is a prime if the ideal (p) is a prime ideal, that is p is not a unit and of p|ab then either p|a or p|b. We exclude 1 (and other units) since that special case is not interesting (and we do not allow the whole ring to be considered a prime ideal; prime ideals are proper, though the zero ideal, if prime as it is in a domain, is allowed as a prime ideal, at least in the things I've read recently). Anyway, go around with your different definition of prime then; the only person it will affect will be you.

 

[NewScientist]

a prime number is an integer which has exactly 2 distinct factors

 

[Zurtex]

a prime number is an integer which has exactly 2 distinct factors

Erm, yeah, you could define a prime number to be:

A prime number is an integer which has exactly 2 distinct positive factors

 

[WeeDie]

stick to it guys. the problem of duality will show up sooner or later. primes are very important.