The Prime Debate: Is 1 prime?

[Enigma_Nova]

...
I believe that it is NOT.
G_Slacker will fill you in with the chatlog

[GePap]

And now, for the award of "possibly most boring thread topic", the nominee's are:

The Prime Debate: Is 1 prime?
.......
.......
.......

[geeslaka]

Posted directly in because it's only 161 lines.

19:28 < G_Slacker> Programmers Proof that all odd numbers are prime: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 will be fixed by the next patch, 11 is prime...
19:28 < WIA_working_AFK> Catch you later...
19:29 < Enigma_Nova> I'll be in here
19:29 -!- WIA_working_AFK [~mrwhereit@131.203.9.136] has left #apolyton []
19:29 < Enigma_Nova> 1 is not prime you ditz
19:29 < G_Slacker> Yes it is.
19:29 < G_Slacker> Define prime.
19:29 < Enigma_Nova> Fundamental theorem of Arithmetic: All numbers can be divided into prime factors
19:29 < Enigma_Nova> If One is prime, all numbers have an infinite number of factors
19:30 < Enigma_Nova> As you can keep multiplying on One
19:30 < G_Slacker> And the problem with that?
19:30 < Enigma_Nova> Euler's Theorem stuffs up - and so does cryptography - and the internet packet transmission system -
19:30 < Enigma_Nova> 1 is not prime
19:30 < G_Slacker> I can't remember Euler's Theorem right now.
19:31 < Elias> what math are you people taking
19:31 < Enigma_Nova> 3rd year
19:31 < Elias> of what
19:31 < Enigma_Nova> Math
19:31 < G_Slacker> But those are systems that should only count one once, and not as many times as they can divide it out.
19:31 < Enigma_Nova> At university
19:31 < Elias> ??
19:31 < Elias> your 17 right
19:32 < Enigma_Nova> Actually, if you count One once, then you can't count 2 Twice.
19:32 < Enigma_Nova> Factor 4
19:32 < Enigma_Nova> Yes I'm 17
19:32 < Elias> Algebra claclus geomotry what??
19:32 < Enigma_Nova> Start my 3rd year in a few months
19:32 < Elias> 2
19:32 < Elias> 1
19:32 < Enigma_Nova> Got all HDs (A) and Ds (B)
19:32 < G_Slacker> What? How does that follow logically from what I said?
19:32 < G_Slacker> Elias: BC Calc for me.
19:32 < Enigma_Nova> If you can only count One once... then You can't count any other number more than once, by your hypothesis
19:33 < Enigma_Nova> Else why not count one as many times as it divides?
19:33 < Enigma_Nova> Which is of course infinitely many times
19:33 < Elias> 1
19:33 < Elias> 1
19:33 < Elias> 1
19:33 < Elias> 1
19:33 < Elias> 1
19:33 < Elias> 1
19:33 < G_Slacker> One is a special case, thus there are things that should be applied to it that should not be applied to other numbers.
19:33 < Elias> 1
19:33 < Elias> 1
19:33 < Elias> 1
19:33 < Elias> 1
19:33 < Elias> 1
19:33 < Elias> etc etc etc
19:33 < Enigma_Nova> 12 = 3*2*2, not 3*2*2*1*1*1*1*1*1*1...
19:34 < G_Slacker> Those two factor sets are equivalent.
19:34 < Enigma_Nova> Primes IIRC are defined that they have no factors except themselves
19:34 < G_Slacker> The only reason you only put one or zero ones is to save reading time.
19:34 < Elias> ahh i think i understand now
19:34 < Enigma_Nova> Of course - They both multiply to 12
19:35 < Elias> enought talk about math this is not school
19:35 < Enigma_Nova> But a prime number cannot have an infinite number of factors.
19:35 < G_Slacker> Elias: Why do you think school subject's shouldn't be discussed outside of school?
19:35 < Enigma_Nova> If you're talking about NON-ONE factors, then 1 falls out of the Fundamental Theorem of Arithmetic as not being prime
19:35 < G_Slacker> Why not?
19:36 < G_Slacker> To the infinite factors statement.
19:36 < Enigma_Nova> A prime number IIRC has a finite number of factors - Namely itself
19:36 < Elias> you spend all day listening about there why do it at home too ?
19:36 < G_Slacker> Here, I do it willingly.
19:36 < Enigma_Nova> I believe the term is modality - 17 has modality 1
19:36 < Elias> actually im just very confused.
19:36 < Enigma_Nova> When all numbers have an infinite number of factors then there is no way of determining which ones are prime
19:37 < G_Slacker> The definition I've always heard for prime numbers is that their only factors are one and themselves.
19:37 < Enigma_Nova> That's a corrupt definition
19:37 < Enigma_Nova> Actually, all mathematicians believe 2 is the first prime
19:37 < Enigma_Nova> (well first positive prime)
19:37 < G_Slacker> You can still determine which ones are prime, it depends on your determination algorithm.
19:38 < Enigma_Nova> Go by Non-one factors, then by the definition of the Fundamental Theory of Arithmetic, One is not prime
19:38 < Enigma_Nova> By definition of a number being the product of its prime factors
19:38 < Elias> maby we should get a 3rd opnion
19:38 < Enigma_Nova> If you disregard One as a factor...
19:38 < Enigma_Nova> .
19:38 < Enigma_Nova> Okay you do that.
19:39 < Enigma_Nova> Find me a Math professor
19:39 < Enigma_Nova> Or a Math Postgraduate
19:39 < Elias> i can e-mail mine
19:39 < Elias> well he is just a high school teacher
19:39 < Enigma_Nova> Sounds good
19:39 < Enigma_Nova> Teachers are Postgraduates.
19:39 < Enigma_Nova> That counts
19:40 < G_Slacker> What you stated as the Fundamental Theory of Arithmetic said nothing to define what makes a number prime.
19:40 < Enigma_Nova> Anyone ever heard of a prime number tree?
19:40 < Enigma_Nova> 12
19:40 < Enigma_Nova> 4 3
19:40 < Enigma_Nova> 2 2 3
19:40 < Elias> I got a 3rd opnion my dad thinks 1 is prime
19:40 < Enigma_Nova> Now if one were prime I could extend that tree down ad infinitum
19:40 < Enigma_Nova> Well your dad is wrong
19:41 < G_Slacker> And what is your problem with that tree branching infinitely?
19:41 < Enigma_Nova> 1 is not officially prime
19:41 < Aidun> I'm going offline, catching sleep in the left hours
19:41 < Enigma_Nova> I'm off to see a mathematical website to bloody SOURCE my validity...
19:41 < G_Slacker> What is the reason for this perverse avoidance of infinity?
19:43 < Enigma_Nova> So the set is Countable and Finite
19:43 < Enigma_Nova> Stuff is easier to work with if you define it like that
19:44 < Enigma_Nova> http://teachers.net/mentors/math/top....14.45.17.html
19:44 < Enigma_Nova> See it for yourselves
19:45 < Enigma_Nova> http://teachers.net/mentors/math/top....22.08.38.html
19:45 < Enigma_Nova> That one mentions the Fundamental Theorem of Arithmetic
19:45 < Enigma_Nova> Just what I've been going on about
19:46 -!- Aidun [Aidun@xs195-241-31-18.dial.12move.nl] has quit [Quit: sleeping, again thanks to Chieftess!]
19:47 < G_Slacker> I talked to my brother, who went rather far into math, and he says that most college level books will say 1 is prime, and most research mathematticians make the decision based on how it affects the problem they are working on.
19:47 < G_Slacker> Reading links now.
19:48 < Enigma_Nova> Fundamental Theorem of Arithmetic fails if One is considered prime...
19:48 < Enigma_Nova> If the problem you are working on negates the FTA then so be it
19:48 < Enigma_Nova> But I wouldn't deny myself such a useful theory
19:48 < Elias> the only use for knowing if a number is prime is so you can tell some one else it is prime
19:48 < Enigma_Nova> ... Actually 1 is neither Prime nor Composite.
19:49 < Enigma_Nova> You ignorant fool! Primes are used quite heavily in Cryptography
19:49 < Elias> 1 and 0 always have execptions
19:49 < Enigma_Nova> Bloody 0
19:49 < Elias> is 0 prime
19:49 < Elias> no
19:49 < Enigma_Nova> x / x = 1 Unless x = 0
19:49 < Elias> is it composite
19:49 < G_Slacker> "there would be no
19:49 < G_Slacker> unique prime factorization"
19:50 < Enigma_Nova> 0 is neither prime nor composite...
19:50 < G_Slacker> Garbage.
19:50 < G_Slacker> To what I quoted.
19:50 < Enigma_Nova> Let me prove it.
19:50 < Enigma_Nova> 2 = 2
19:50 < Enigma_Nova> 2 = 2 * 1
19:50 < Elias> why is 0 considerd positive?
19:50 < Enigma_Nova> There. different.
19:50 < Enigma_Nova> It isnt
19:50 < G_Slacker> 0 is neither positive or negative.
19:50 < Enigma_Nova> It's that midway point
19:51 < G_Slacker> But some braindead teachers try to claim it's positive.
19:51 < Enigma_Nova> Prolly the same ones that violate the FTA
19:51 < Enigma_Nova> ...I wonder what they do about negative numbers...
19:51 < G_Slacker> Enigma_Nova: How is that factorization not unique?
19:51 < Enigma_Nova> The set containing: 2
19:51 < Enigma_Nova> Differs from the set containing: 2, 1
19:52 < Enigma_Nova> *sigh* If I have a red marble and a green marble... that's not the same as having only a red marble, even if the green marble has no value
19:52 < Enigma_Nova> 2 = 2, and 2 = 2*1
19:52 < Enigma_Nova> Both are factorisations
19:52 < G_Slacker> Both of which are incomplete if 1 is considered prime.
19:52 < Enigma_Nova> But only one is the PRIME factorisations.
19:53 < Enigma_Nova> If 1 is considered prime than any number of multiplications can be done.
19:53 < G_Slacker> To your analogy: You simply aren't counting the things you have 0 of for convenience.
19:53 < Enigma_Nova> Quite true
19:54 < Enigma_Nova> 12 = 2^2 * 3^1 * 5^0 * 7^0 * ... 1^Anything.
19:54 < Elias> 4th and 5th opnion my college bro thinks its prime but my twin bro thinks its not
19:54 < G_Slacker> Thus, the only reason 1 could be considered non prime is purely for matters of convenience.
19:54 < Enigma_Nova> Or why it would be would be for convenience
19:54 < Enigma_Nova> Namely, the FTA
19:54 < G_Slacker> Leaving out matters of convenience, 1 is prime.
19:55 < Elias> I agree with G
19:55 < Enigma_Nova> Ignore an important mathematical theorem and it becomes true
19:55 < Enigma_Nova> Sure... ignore what makes it false and everything becomes true
19:55 * Enigma_Nova is darn well posting this in the OT forum
19:55 < Elias> lol
19:55 < Elias> im gonna have to see that
19:56 < G_Slacker> I'm still looking for an exact stating of the FTA.
19:56 < Enigma_Nova> The Great Prime Debate

[geeslaka]

Thanks Gepap.

[Inverse Icarus]

one is prime.

the simplest definition of prime is any number that is only divisible by itself and one (note, 2 factors, not infinate amount of ones), and one fits into that description.

btw, funny:

19:31 < Elias> what math are you people taking
19:31 < Enigma_Nova> 3rd year
19:31 < Elias> of what
19:31 < Enigma_Nova> Math

[GePap]

Just thanks to the chatlog it should win without question.

[geeslaka]

Found a statement of the FTA in Enigma_Nova's link.

The
FDA states that every positive integer greater than one can be
expressed uniquely as a product of primes, apart from the
rearrangement of terms.

http://teachers.net/mentors/math/topic3635/9.22.03.10.03.55.html

One being prime does not void the FTA because all the factorisations stated as being different but for the same number are incomplete. Any factorisation that does not include 1^infinity is incomplete.

[Enigma_Nova]

The FTA mentions nothing about complete factorisations.
It mentions unique prime factorisations.
Which if 1 is prime would make these not unique.

A factorisation is a factorisation if it multiplies to give the desired number.

[SnowFire]

1^infinity is whatever the heck you want it to be. So that seems dangerous to stick in a factorization.

Anyway, as noted before, having unique factorizations is a Good Thing, among other reasons.

[geeslaka]

The FTA mentions nothing about complete factorisations.
It mentions unique prime factorisations.
Which if 1 is prime would make these not unique.

To determine uniqueness, the whole must be considered. If the whole is not considered, then there is still doubt about the uniqueness. The factorisations cited as proof are not whole, and thus cannot be compared for uniqueness.

A factorisation is a factorisation if it multiplies to give the desired number.

True.

[geeslaka]

1^infinity is whatever the heck you want it to be. So that seems dangerous to stick in a factorization.

When evaluated, 1^infinity is not "whatever the heck you want it to be", it is 1.

Anyway, as noted before, having unique factorizations is a Good Thing, among other reasons.

1 being prime does not eliminate unique factorizations.

[Urban Ranger]

Originally posted by geeslaka
When evaluated, 1^infinity is not "whatever the heck you want it to be", it is 1.

Therefore, 1^Infinity is meaningless.

[geeslaka]

Therefore, 1^Infinity is meaningless.

It is not meaningless, it is a statement that the complete factorisation is being used.

[Urban Ranger]

Originally posted by geeslaka

Therefore, 1^Infinity is meaningless.

It is not meaningless, it is a statement that the complete factorisation is being used.

Of course it is, because 1^Infinity evaluates to 1, nothing more.

Do not forget 1 is unity in multiplication, therefore it can be safely removed from all multiplications and divisions. Of course, you can also introduce terms that evaluates to 1, and that's one of the tricks in algebra.

[geeslaka]

Originally posted by Urban Ranger
Of course it is, because 1^Infinity evaluates to 1, nothing more.

Factorisation is the process of finding the complete set of numbers that when multiplied together, will evaluate to the number being factored.
Thus, evaluating part of the factorisation defeats the purpose.

Do not forget 1 is unity in multiplication, therefore it can be safely removed from all multiplications and divisions. Of course, you can also introduce terms that evaluates to 1, and that's one of the tricks in algebra.

]
Exactly my point, the only reason 1^infinity is not included everywhere, is convenience. When it's needed, it's put in, when it's not, it's taken out.

Edit:
As I stated before:

19:54 < G_Slacker> Thus, the only reason 1 could be considered non prime is purely for matters of convenience.
19:54 < Enigma_Nova> Or why it would be would be for convenience
19:54 < Enigma_Nova> Namely, the FTA
19:54 < G_Slacker> Leaving out matters of convenience, 1 is prime.