question and answer thread.

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Originally posted by souldog
Ok here is a question. Are there an infinite number of prime numbers p such that p+2 is also prime.

e.g. 5 and 7 :o

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I heard this in my class some time ago...:)

when we were introduced about properties of Primes and

Diophantine equations...:p , Moreover,

your question I assume is taken from one of many FAMOUS open problems relating to Prime Number Theorem...:o :p
Yeah.... Hometown is Nina, Nani is Nina....Yes.
And another thing to pay back is...

cut that out!

In case I am allowed to make a question now to Souldog, I would like to ask you to prove:[lim(n*log(n))]/pn=1 Knowing that n->inf, p is prime.
:)

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Originally posted by SeventhStar
cut that out!

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Seventh Star...
I am trying to solve that problem, I thought that you would agree to tell me whether my answer to that question was correct or not, which is also what I am expecting from you now....
I think that your answer to that question was just like you were finishing only half of your little loaf of bread, and what I posted was the other half but because you asked me to stop, so I deleted it, I hope you wont remember any word of it....
:confused: :confused: But I am still :cool:

Souldog willnot get angry at me Okay ? And SeventhStar willnot either, hah.....
:) :):)

Here's one:

Prove that every integer n > 5 is the sum of three primes. :D

Fierytycoon

Quote:

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Originally posted by hometown
Souldog willnot get angry at me Okay ? And SeventhStar willnot either, hah.....

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False.
That's what you get for posting that in the Question and Answer thread! ;):D

It's been a while with all this proof stuff but here goes. Here's a proof by induction.

I can show this works for
6 = 3+2+1
7 = 3+3+1
8 = 5+2+1
9 = 5+3+1

Now let x be a number that's the sum of three primes. If I can show that x+1 will be the sum of three primes then I'm done.

Assume x is even. Then one of the three numbers in the sum must be 2 because 2 is the only even prime and to add three numbers together and get an even number you can either add three even numbers or two odd numbers and one even. Since we can't do three even numbers then one of three numbers has to be 2 ( 2+2+2 will work but that's as high as it will go). So x can be written like
x = a + b + 2 where a and b are odd primes.
Change the 2 to 3 and there we go.
x + 1 = a + b + 3.

That's if x is even. What about if x is odd? Well it's not quite as clear but here goes.

Assume x = a + b + c and x is an odd number and a,b,c are primes. Since x+1 is an even number we know x+1 = r + s + t where r,s,t are primes. One of them must be 2 from the argument above. Let's say t=2 so x+1 = r + s + 2.
That means x = r + s + 1.

And we are done. Let me know if you find any problems with this proof or have any questions. It might seem a little backwards but I think it works.

-Ben

Quote:

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Originally posted by bmacri
6 = 3+2+1
7 = 3+3+1
8 = 5+2+1
9 = 5+3+1

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1 is not prime. You can do it like this, though:
6 = 2 + 2 + 2
7 = 3 + 2 + 2
8 = 3 + 3 + 2
9 = 3 + 3 + 3

Quote:

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Assume x = a + b + c and x is an odd number and a,b,c are primes. Since x+1 is an even number we know x+1 = r + s + t where r,s,t are primes. One of them must be 2 from the argument above. Let's say t=2 so x+1 = r + s + 2.
That means x = r + s + 1.

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You're using what you're supposed to prove to prove what you're supposed to prove.

You're on the right track though. But who am I to criticize when I myself am too lazy to do it? ;):rolleyes:

Your right 1 isn't a prime numnber. So much for that.

quote:
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You're using what you're supposed to prove to prove what you're supposed to prove.
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Not really although it seems like that. I had shown at that point that any even number could be written as the sum of three primes. So from that point forward I could use that information. It seems wierd and a think it can be better written but at that point I think I can use that piece of information. I don't have time now to redo the proof with out using 1 but I'll try to put something up tomorrow.

bmacri,

Nice try, but even the mathemeticians who have studied this topic have not been able to prove it. Here is a link concerning this topic:

http://www.utm.edu/research/primes/notes/conjectures/

- Kevin

P.S. Can we have some riddles which are not impossible (or virtually impossible) to solve?

Thanks Kevin. At least I won't waste anymore time trying to do it. If only one was a prime number then it just might be possible to prove.

So any possible questions out there?

-Ben