J Andrew Lipscomb wrote:
The definition as I (also a math major) was taught is this: Primes have two divisors, themself (so to speak) and 1. Composites have more than two. 1 has exactly one, so it's neither.
MathWorld[1] (I suspect we'd all consider this authoritative) would agree with your conclusion:
The number 1 is a special case which is considered neither prime nor composite (Wells 1986, p. 31). Although the number 1 used to be considered a prime (Goldbach 1742; Lehmer 1909; Lehmer 1914; Hardy and Wright 1979, p. 11; Gardner 1984, pp. 86-87; Sloane and Plouffe 1995, p. 33; Hardy 1999, p. 46), it requires special treatment in so many definitions and applications involving primes greater than or equal to 2 that it is usually placed into a class of its own. A good reason not to call 1 a prime number is that if 1 were prime, then the statement of the fundamental theorem of arithmetic would have to be modified since "in exactly one way" would be false because any n==n.1. In other words, unique factorization into a product of primes would fail if the primes included 1. A slightly less illuminating but mathematically correct reason is noted by Tietze (1965, p. 2), who states "Why is the number 1 made an exception? This is a problem that schoolboys often argue about, but since it is a question of definition, it is not arguable." As more simply noted by Derbyshire (2004, p. 33), "2 pays its way [as a prime] on balance; 1 doesn't."
So I think we can put this discussion to bed, jp [1] http://mathworld.wolfram.com/PrimeNumber.html _______________________________________________ Unsubscribe or switch delivery mode: <http://www.realsoftware.com/support/listmanager/> Search the archives of this list here: <http://support.realsoftware.com/listarchives/lists.html>
