Is the number 1 a prime number?

[TwistedSystem]

Let the debate begin.

[fishki]

change the poll and put in a maybe

[gabrile23]

change the poll and put in a maybe

dam i wanted to put in mybe to late now.

[fishki]

change the poll and put in a maybe

dam i wanted to put in mybe to late now.

fixed...damn thats tuff if you do the research on primes

[TwistedSystem]

Well, that maybe just ruined this topic. I wanted to get an argument going but no, we had to do it the nice, peaceful way.

[gabrile23]

Thanks fish! three mybes so far. "The only absolute is there are no absolutes."

[fishki]

Well, that maybe just ruined this topic. I wanted to get an argument going but no, we had to do it the nice, peaceful way.

this will still end up as an arguement. but me and gab are on the same page with this prime stuff you started

[WHO_99]

Well I'm not surebif it's a prime number or not but I can tell you that

One is the lonlest number that you ever seen.....
(feel free to continue the song lol)

[King_Chile]

but 1 isnt prime nor composite its just 1 and if 1 was a prime number then the fundamental theorem of arithmetic would be all messed up and math would have to be rebooted and everything we ever learned would be wrong, imagine a world where 1+1 does not equal 2 instead it will equal like 11, thats the kind of world we'll be living in if 1 was a prime number

[fishki]

but 1 isnt prime nor composite its just 1 and if 1 was a prime number then the fundamental theorem of arithmetic would be all messed up and math would have to be rebooted and everything we ever learned would be wrong, imagine a world where 1+1 does not equal 2 instead it will equal like 11, thats the kind of world we'll be living in if 1 was a prime number

Until the 19th century, most mathematicians considered the number 1 a prime, with the definition being just that a prime is divisible only by 1 and itself but not requiring a specific number of distinct divisors. There is still a large body of mathematical work that is valid despite labelling 1 a prime, such as the work of Stern and Zeisel. Derrick Norman Lehmer's list of primes up to 10,006,721, reprinted as late as 1956,[2] started with 1 as its first prime.[3] Henri Lebesgue is said to be the last professional mathematician to call 1 prime.[citation needed] The change in label occurred so that the fundamental theorem of arithmetic, as stated, is valid, i.e., “each number has a unique factorization into primes.”[4][5] Furthermore, the prime numbers have several properties that the number 1 lacks, such as the relationship of the number to its corresponding value of Euler's totient function or the sum of divisors function.[6]



Ok, now the debate is on TS

[King_Chile]

so, we're going to google stuff and the copy n paste it here, sure i guess i can do that

[Noodlez]

omg...no...you just picked an argument with lil chile...this is gonna be fun

[King_Chile]

Answer One: By definition of prime!
The definition is as follows.

An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself.

Clearly one is left out, but this does not really address the question "why?"
Answer Two: Because of the purpose of primes.
The formal notion of primes was introduced by Euclid in his study of perfect numbers (in his "geometry" classic The Elements). Euclid needed to know when an integer n factored into a product of smaller integers (a nontrivially factorization), hence he was interested in those numbers which did not factor. Using the definition above he proved:

The Fundamental Theorem of Arithmetic
Every positive integer greater than one can be written uniquely as a product of primes, with the prime factors in the product written in order of nondecreasing size.

Here we find the most important use of primes: they are the unique building blocks of the multiplicative group of integers. In discussion of warfare you often hear the phrase "divide and conquer." The same principle holds in mathematics. Many of the properties of an integer can be traced back to the properties of its prime divisors, allowing us to divide the problem (literally) into smaller problems. The number one is useless in this regard because a = 1.a = 1.1.a = ... That is, divisibility by one fails to provide us any information about a.
Answer Three: Because one is a unit.
Don't go feeling sorry for one, it is part of an important class of numbers call the units (or divisors of unity). These are the elements (numbers) which have a multiplicative inverse. For example, in the usual integers there are two units {1, -1}. If we expand our purview to include the Gaussian integers {a+bi | a, b are integers}, then we have four units {1, -1, i, -i}. In some number systems there are infinitely many units.

So indeed there was a time that many folks defined one to be a prime, but it is the importance of units in modern mathematics that causes us to be much more careful with the number one (and with primes).
Answer Four: By the Generalized Definition of Prime.
(See also the technical note in The prime Glossary' definition).

There was a time that many folks defined one to be a prime, but it is the importance of units and primes in modern mathematics that causes us to be much more careful with the number one (and with primes). When we only consider the positive integers, the role of one as a unit is blurred with its role as an identity; however, as we look at other number rings (a technical term for systems in which we can add, subtract and multiply), we see that the class of units is of fundamental importance and they must be found before we can even define the notion of a prime. For example, here is how Borevich and Shafarevich define prime number in their classic text "Number Theory:"

An element p of the ring D, nonzero and not a unit, is called prime if it can not be decomposed into factors p=ab, neither of which is a unit in D.

Sometimes numbers with this property are called irreducible and then the name prime is reserved for those numbers which when they divide a product ab, must divide a or b (these classes are the same for the ordinary integers--but not always in more general systems). Nevertheless, the units are a necessary precursors to the primes, and one falls in the class of units, not primes.

See, for example, the section on factoring primes in A Brief Introduction to Adelic Algebraic Number Theory.

[fishki]

omg...no...you just picked an argument with lil chile...this is gonna be fun

no actually i voted maybe, since there is work out there that uses 1 as a prime and it is valid.

TS wanted a debate so we will make one for him.

But the fact remains that valid work has been done using 1 as a prime even tho it does not have two different factors.
And since 1 is neither prime nor composite, it is really the lonliest number.

[MichaelVash7886]

In a non-base 10 number system 1+1 could equal 11.....

[awentford]

a prime number has to have 2 factors... 1 only has one factor therefore it can't be prime.

whenever 1 is used as a prime number then it has to involve imaginery numbers, that's how studies are done with it.

[hippo999]

but 1 isnt prime nor composite its just 1 and if 1 was a prime number then the fundamental theorem of arithmetic would be all messed up and math would have to be rebooted and everything we ever learned would be wrong, imagine a world where 1+1 does not equal 2 instead it will equal like 11, thats the kind of world we'll be living in if 1 was a prime number

duh

[twistedblister]

anyone singing the sunday morning shoohouse rock stuff in thier head becase of this post besides me?

Damn Noodlez. your bro is a Wiz. wow. very impresvie post KC

[Noodlez]

yea...my bros a genius...i put him to read my college books wen hes on timeout :)

[stickcult]

Wow...amazing. I don't even tihnk I need to contribute now..

it's not.

[hippo999]

Wow...amazing. I don't even tihnk I need to contribute now..

it's not.

duh

[cloud945076]

What is No.

[hippo999]

What is No.

It means no.

[cloud945076]

lol. never seen Jeapordy?

[hippo999]

lol. never seen Jeapordy?

yep lol