Definition talk:Composite Number

Bad. Negative numbers are composite as well. --prime mover 14:24, 9 March 2011 (CST)

For what its worth, Wolfram and Wikipedia both specify that composite numbers are positive integers. Of course, you could define it either way, but the way you had it before is at least as iffy since it would make -2, -3, -5, etc composite numbers, which is a little misleading IMO. I would actually vote to define it as "A composite number $c$ is a positive integer that has more than two positive divisors; that is it is a positive integer that is neither $1$ nor prime." That would just leave negative numbers classified neither as prime nor composite. What was your reasoning for having it the way you did? --Alec (talk) 10:34, 10 March 2011 (CST)

We have on the prime number page the suggestion that prime numbers can be extended to negative numbers by insisting that a prime integer is one which has exactly four divisors. IIRC I had to fight for the right to let that paragraph join the party.

This definition is consistent with the course on number theory that I did for a degree, and also it's consistent with the treatment by Helmut Hasse in his Zahlentheorie, which takes the subject to a more abstract footing.

I believe it may not be profitable to use Wikipedia as an authority (although can be a useful resource on occasion), and sorry, but Mathworld is not completely infallible itself. This is an area which is so frequently glossed over "because everyone knows what a prime number is" that the subtle points of units, primes, composites etc. in the context of a general integral domain, division ring, field etc. get mislaid.

But no matter. If Wolframkipedia trumps weighty Springer-Verlag tomes, then maybe I'm too old for this game. --prime mover 15:36, 10 March 2011 (CST)

To add my tuppen'orth, negative numbers should be prime/composite for algebraic reasons: $p \in \Z$ is prime iff $(p) \subseteq \Z$ is a prime ideal. This is speaking as an algebraist of course. --Linus44 17:04, 10 March 2011 (CST)

Actually thinking about it it's sometimes important that distinct primes are coprime. Perhaps a prime $p$ should be a representative of an equivalence class $ [p] \in \Z / \{\pm 1\} $, and $p \neq q \in [p]$ is considered to be the same prime? --Linus44 06:53, 11 March 2011 (CST)

If it is important that distinct primes are coprime, we would make sure that from the context only positive primes are under consideration. --prime mover 13:31, 11 March 2011 (CST)

I put in the edit summary that I wasn't finished...I was going to make the negative number extension a separate section so it corresponds to the prime number page JamesMazur2 16:07, 10 March 2011 (CST)

This page is fine. --prime mover 13:31, 11 March 2011 (CST)