Re: what makes it true?


"odin" <ragnarok@xxxxxxxxx> wrote in message
news:zP2dnZ2dnZ1D9IesnZ2dnSc9hd6dnZ2dRVn-zp2dnZ0@xxxxxxxxxxxxxxxxx
>> 1 is prime. Your statement is false.
>
> Nope.
>
> Today, the standard definition of a prime number is any positive integer
> greater than 1 which has no divisors other than 1 and itself. This is good
> because it makes the Fundamental Theorem of Arithmetic work out nicely.
> You often need to multiple primes, which kind of sucks if you are
> multiplying by 1. In Gauss's time, 1 was included as a prime. But they
> eventually decided to drop the unit from the club. But hey... its just a
> definition. Nothing to get worked up about.
>

Ok we are both right, in a way ---

http://mathworld.wolfram.com/PrimeNumber.html

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."


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