 Posers and Puzzles

1. 16 Aug '06 14:44
This is a thought that I've had for a time.

Every prime is odd. Odd, isn't it?
And I can prove it. Does anyone know how?
2. 16 Aug '06 14:491 edit
Originally posted by FabianFnas
This is a thought that I've had for a time.

Every prime is odd. Odd, isn't it?
And I can prove it. Does anyone know how?
Yes, you must first prove that 2 is odd. And the rest is easy.
3. 16 Aug '06 14:55
Originally posted by ThudanBlunder
Yes, you must first prove that 2 is odd. And the rest is easy.
Well, 2 is prime and even, thats a fact. The proof that every prime is odd doesn't take that into consideration. Just a minor detail... ;-)

Does anyone know the proof?
4. 16 Aug '06 15:21
Because all even numbers are divisable by 2....
5. 16 Aug '06 15:26
If you mean "odd" as in "unusual", it's quite easy to prove.
6. 16 Aug '06 17:20
Nono, unusual is odd enough but here I mean odd as not being even as matematicians do.

thespacemonkey says:
"Because all even numbers are divisable by 2...."

Well, either you give a glimpse that you know the proof or you're not. This I have to think over.

(*think, think, think*) What about two itself? (*think, think, think*)

Yes, you are right. The statement of yours that "all even nubers are evenly divisable with two" has the same kind of proof that the statement "all primes are odd" has. Well done.
7. 16 Aug '06 17:29
The proof that you are even odder is contained within this very thread.
8. 16 Aug '06 17:30
Well as the definition of an even number is a number that is divisible by 2, and the definition of a prime number is a number only divisible by 1 and itself, if a number is not 2 (as you decided to take it out of the prime numbers for some reason) it has to be odd to be prime.
9. 16 Aug '06 17:341 edit
I didn't think far enough here, sorry for that.

"All even numbers are divisable by 2 and still gives an even result"
then the proof of this would be very like the proof of that every prime is odd.

Please forgive me of this lapsus.

Let's stick to the statement that all primes are odd.
10. 16 Aug '06 19:55
Originally posted by FabianFnas
Let's stick to the statement that all primes are odd.
...unless they are even.
11. 16 Aug '06 20:40
Originally posted by FabianFnas
I didn't think far enough here, sorry for that.

"All even numbers are divisable by 2 and still gives an even result"
then the proof of this would be very like the proof of that every prime is odd.

Please forgive me of this lapsus.

Let's stick to the statement that all primes are odd.
Equally, no primes are divisible by 3 either.
12. 16 Aug '06 23:54
Maybe it's because it's early in the morning, maybe it's because I am missing something, maybe it's because I am thick as pig excriment. I don't get exactly what you are asking to be proved.
13. 17 Aug '06 00:241 edit
Originally posted by iamatiger
Equally, no primes are divisible by 3 either.
And now by induction I will expand this proof.

A prime P will not be divisible by any n where n != 1 or p.
Already it has been shown for n=2 and n=3. Therefore all I have to show is that if the nth case is true then the n+1th case is true.

So if no A exists such that n*A = p then then no B must exist such that (n+1)*B = P. Utilizing the properties of primes we can show that no B exists that divides P except P and 1.

Therefore the n+1th case is true.

Therefore by induction we have shown that a prime number is only divisible by 1 and itself.

(Seriously what's going on in this thread?)
14. 17 Aug '06 07:28
The first 10 primes is as follows: 2, 3, 5, 7, 11, 13, 17, 23, 29,31.
Of theese 10 first primes only one is even, the rest is odd. Right?
The ratio of odd primes of the ten first is 9/10=90%. Right?

Do anyone se what I'm aiming at?
15. 17 Aug '06 07:48
Originally posted by FabianFnas
The first 10 primes is as follows: 2, 3, 5, 7, 11, 13, 17, 23, 29,31.
Of theese 10 first primes only one is even, the rest is odd. Right?
The ratio of odd primes of the ten first is 9/10=90%. Right?

Do anyone se what I'm aiming at?
A proof that 100% of primes are odd is not the same as proof that all primes are odd.