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Subject: "Why isn't 1 a prime number."     Previous Topic | Next Topic
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Lida Mosiman
Charter Member
Oct-18-00, 09:40 PM (EST)
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"Why isn't 1 a prime number."
 
   Why isn't 1 a prime number? I am a 6th grade student and would like to understand why?

Justin Mosiman


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alexb
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672 posts
Oct-18-00, 09:53 PM (EST)
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1. "RE: Why isn't 1 a prime number."
In response to message #0
 
   It's all a matter of convenience. Under the current definition, every number has a unique factorization into powers of prime factors. For this teorem to hold, you would have to exclude 1 somehow if it were declared prime. Other theorems will also become less elegant. It's just cheaper not to declare 1 a prime to start with.

Mathematics is not cast in bronze. Like everyone else, mathematicians also learn what's good and what's not, what's covenient and what's cumbersome. It's a common concensus among mathematicians that calling 1 a prime just is not worth the trouble.

All the best,
Alexander Bogomolny


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Sam Kelly
Charter Member
Oct-19-00, 08:51 PM (EST)
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2. "RE: Why isn't 1 a prime number."
In response to message #0
 
   Well, I have always wondered this as well! I always considered 1 to be prime, but had no idea why others didn't. Well here's the reason that almost everybody (who considers 1 be not prime) uses to justify their reasoning.

There are two GENERAL "definitions" of a prime number circulating.

Most of the "1 is not prime" group say the definition of a prime number is this:

"A positive integer (natural number, or whole number) whose only divisors are 1 and itself."
They use the word "divisorS" to justify their reasoning, because it implies that the "divisors" are different. That means that 1 only has one positive divisor, 1, and no more...so it can't be prime according to that definition.

Now, the people that say that 1 IS prime usually use this definition for a prime number:

"A positive integer (natural number) that is divisible by only 1 and itself."
Using this definition, 1 is prime because:
it is "divisible" by itself (the number 1), and
it is "divisble" by 1 (in the definition!).

I believe that most people that express a strong opinion are those who haven't the need for the convenience that was mentioned by Alex.

By Sam Kelly


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Bandido1
guest
Oct-27-01, 04:46 PM (EST)
 
3. "RE: Why isn't 1 a prime number."
In response to message #0
 
   Let define an integer n >1. Then it can be prime or composite.
If it is composite it must be equal to the iterative sum of one or more primes.

For instance 9= 3+3+3

10=5+5=2+2+2+2+2.

Any number prime or composite is the iterative sum of 1

For instance

3 (prime)=1+1+1

4( composite)= 1+1+1+1

Therefore, in my opinion one is not a prime, because the iterative sum of a prime p+p....+p=p*n, instead the iterative sum of one not always is a composite.

Bandido 1.



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Rick Hindman
guest
Oct-29-01, 10:24 PM (EST)
 
4. "RE: Why isn't 1 a prime number."
In response to message #0
 
   There is a theorem that any positive integer can be written as the unique product of primes. For example:

10 = 5*2
99 = 11*3*3
1024 = 2*2*2*2*2*2*2*2*2*2 (ten '2's)
5 = 5 (being prime, it only has one factor, itself)

Being 'unique' means that there is only one way to write it (ignoring the order of the primes, of course). If we included '1' as a prime, then we could still write positive integers as products of prime numbers, but they would not be unique. For example

10 = 5*2 = 5*2*1 = 5*2*1*1 = 5*2*1*1*1*1*1*.........

That is one reason it is not a good idea to include '1' as a prime.

-Rick


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Minstrel
guest
Oct-29-01, 10:24 PM (EST)
 
5. "Why 1 isn't a prime number."
In response to message #0
 
   An alternate definition of a prime number would be that it could be made into a rectangle, so on graph paper it could be represented two ways:
examples:

333

or

3
3
3

ie. 3 is prime

999
999
999

999999999

9
9
9
9
9
9
9
9
9

that's three ways - 9 is not prime.

22

2
2

ok, 2 is prime...

1

But that's the only way you could show 1, so, because there's only one way to show it, it is not prime.


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