I know that all the pure mathematitions are debating about it but what do you think.Is 1 prime or composite.
2006-10-22 07:29:38 · 9 answers · asked by emilyyy. 2 in Science & Mathematics ➔ Mathematics
So, to understand this, I need to explain a little bit of algebra to you:
Mathematicians have defined a prime element, p, as a non-unit in an integral domain, so that if p divides ab, then p divides a or p divides b.
What does that all mean?
First of all, and integral domain is a ring with identity, such that if ab=0, either a=0 or b=0. The integers, Z, form an integral domain. Since your question is about Z, I will start explaining the definition of a prime for the integers:
As stated, Z is an integral domain, so we may continue. What are the units of Z? Well, these are the numbers a, such that there exists a b with the property ab=1. It is easy to believe that the units of Z are simply {-1,1}. Therefore, by definitions 1 is not a prime element. From here on out, it is easy to prove that if the statement "p divides ab (written p|ab) implies p|a or p|b" is the same as the statement "|p| has exactly 2 positive divisors."
So, we can easily show that the set of prime elements of Z are {2,3,5,7, . . .} and {-2,-3,-5,-7, . . .}. We then define "prime number" to be a positive prime element of Z. Since 1 is not a prime element of Z, 1 is not a prime number.
2006-10-22 07:44:05 · answer #1 · answered by Eulercrosser 4 · 0⤊ 1⤋
There's no debate. BY CONVENTION, BY DEFINITION, 1 is NOT a prime. And the reason not to consider 1 as a prime number is quite practical and simple. If 1 was a prime, the fundamental theorem of arithmetic wouldn`t be true. For example, there would be 2 diferent forms to factor 6 as a product of primes, 1 X 2 X 3 and 2 X 3, and the diffrenece wouldn't be just the order of the factores.
Considering 1 as a prime would only bring about confusion and would be of no practical or usful purpouse.
2006-10-22 14:44:51 · answer #2 · answered by Steiner 7 · 0⤊ 0⤋
The definition of a prime number states that the integer may have no factors other than itself and 1 to be prime. Therefore, 1 is prime by definition. However, mathematicians may have decided not to make 1 prime to avoid complications in various applications. For example, when you do the prime factorization of a number, it would have infinately many factors of 1 since 1 to any power is still one.
There are a lot of instances in mathematics where people have "tweeked" definitions to make the system work out, and I believe this is one case.
2006-10-22 14:37:57 · answer #3 · answered by Charles M 1 · 0⤊ 1⤋
No, mathematicians are NOT debating about this, 1 is NOT prime by definition. It is just a convention but is has long been established that the smallest prime is 2.
2006-10-22 14:32:11 · answer #4 · answered by cmadame 3 · 1⤊ 0⤋
NO, prime means having exactly 2 positive whole number factors. Therefore, 2 is the smallest prime number.
2006-10-22 15:05:55 · answer #5 · answered by Kathy 2 · 0⤊ 1⤋
1 fits the definition, but it's not considered prime for the same reason Pluto isn't a planet any more. It makes things simpler.
2006-10-22 15:10:43 · answer #6 · answered by Nomadd 7 · 0⤊ 1⤋
1 is not prime or composite
Click on the URL below for additional information concerning prime and composite numbers.
primes.utm.edu/glossary/page.php?sort=Composite
2006-10-22 14:54:18 · answer #7 · answered by SAMUEL D 7 · 0⤊ 1⤋
1 is neither prime nor composite
2006-10-22 14:38:15 · answer #8 · answered by justme 3 · 0⤊ 1⤋
YES 1 IS PRIME BECAUSE NO NUMBER CAN BE MULTIPLIED OR DIDVIDED TO GET A POSTIVE 1!
2006-10-22 15:41:28 · answer #9 · answered by cutethang011 2 · 0⤊ 1⤋