Are negative numbers prime or what?

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0 looks like a composite number (since it has many different factors, with the added restriction that at least one factor must be 0 itself). 1 is none of the above (which I've always found odd - I used to think it was a prime number).

But what about negative numbers?

-1 looks prime, as -1 * 1 = -1 and those are the only factors you will ever find that fit.

But look at -2. -2 * 1 = -2 and 2 * -1 = 2 ! !

So it doesn't look prime, but if it is composite then you have the problem of -2 * -1 = 2 as factors for 2.

I'm pretty sure the official answer is going be something like "you can't classify negative numbers as prime or composite, only positive ones" but if we tried, how would we do it?

Perhaps we could take the easy way out and just say that the primeness of a negative number is defined the primeness of its absolute value....

I don't know.

I'm no math whiz (ask anyone who knows me), but I'd say that whether or not a negative number could be considered "prime" would be based on its absolute value. Or perhaps they don't have that trait. Zero is neither prime nor composite.

Well, I like your inquiry, but I think the answer is rather brief and rather legalistic.

The definition of a prime number is it has no proper factors and thus is only divisible by 1 and itself. By itself does refer to absolute value (this is what I was originally taught, and I cannot find anything in my texts to the contrary). So if you divide a negative number against its absolute value, you don't get 1. You get -1. Therefore it's not a prime number, by the definition of a prime number. It seems to suggest negative numbers are composite (but I can't confirm that either from my texts). Very legalistic, but hey.

I'm not saying this is all to be said about this. I've thumbed through my copy of Prime Obsession and can't find anything to contradict the basic definition of a prime number, or stating otherwise a prime number can be negative. But I think one could take this discussiona little further by discussing what exactly is the distinction between 1 and -1, and if that is a valid enough distinction to exclude negative negative from the primes.

OK, I found this when I googled it: http://mathforum.org/library/drmath/view/55940.html

Don't know if that helps. Granted,he gives a historical explanation for this, but it's still more legalistic than rational.

OK, that makes sense. So no negative numbers are primes.

Does that mean they are composites? Or are they excluded from that as well?

OK, so Dr Math mentions that allowing negative primes would complicate things. Also, Prime Obsession mentions in passing a few times that negative numbers make things more complicated too. Yet exactly how is not explained (or at least I can't find that section in my book - the author says he'll explain it later at one point, but I can't locate it ).

Suffice to say, "more complicated" is not the same as "impossible." So it would appear that the distinction between 1 and-1 doesn't really matter and that negative primes can exist. It's just it's be messy and the mathamaticans don't want to deal with that. How's that for an answer? LOL.

http://en.wikipedia.org/wiki/Prime_numbers

phew! glad that's sorted.

what a great question!

Glad we figured that one out!

*wanders back off into her nonmathematical world where prime refers to "rib"*