Goldbach Conjecture

[Lior]

I thought that maybe the most brilliant brains around here (Kedaman and Guv, of course ) might have an idea of how to start trying to prove (or refute) Goldbach's Conjecture.

As you all know (or maybe not), the conjecture says:

"Every even number bigger than 2, can be represented by the sum of 2 prime numbers"

For those who never heard of this hypothesis, it's one of the most difficult unsolved problems in the whole math!

I believe we (I mean, the humanity) don't know enough about the prime numbers.

For example, there is no formula which tells us the next prime number when we give it a certain prime number.

We cannot know exactly the amount of prime numbers below a given number.

Of course there are several theorems and facts we do know about the prime numbers, but it doesn't seem enough for solving Goldbach's conjecture.

Any suggestions/Comments?

P.S: Goldbach's conjecture was proved to be true up to 10^15, and counting...

[Gandalf_Grey_]

there must be a better way to prove something like that than just look at pythagoras theorum. how did he prove that? or is it still unproven?

[sunburnt]

There are about a billion ways to prove the pythagorean theory
(Ok, I exaggerate a bit.) We did a few of them freshman year in geometry; I dont remember them, but some involved drawing squares with the sides of the triangle, connecting midpoints, etc. Quite interesting actually. Now I might go back and look it up

EDIT: ah, here it is: http://www.nadn.navy.mil/MathDept/mdm/pyth.html

[Lior]

...Anything to the point of Goldbach's Conjecture, please?

[Lior]

Anything? Anyone?

[STT]

it's wrong...

[mendhak]

If Goldbach's Conjecture has been proven upto 10E15, that just about implies it's true for all numbers till infinity.

No no! don't jump on me yet. I was just applying a wee bit of logic.


I was just passing through, and I thought this was quite interesting. (comment. )

[mendhak]

Originally posted by STT
it's wrong...

proof...

[sql_lall]

Just a few comments:
1) "Every even number bigger than 2, can be represented by the sum of 2 prime numbers"
Can be re-written as:
"Every number bigger than 1 has two primes equi-distant from it"
i.e.
"For every number n bigger than 1 there exists another integer k (>0), where (n-k) and (n +k) are primes"
=> there may be a difference of squares applicable.

2) There is another theory similar, stating "Every even number greater than 5 can be written as the sum of 3 primes". This is apparantly easier to prove.

3) Has anyone else heard of Goedel's proof that in an ordered thing like Maths, there will always be things you can't prove. (He managed to prove this, how ironic )

[NotLKH]

Originally posted by Lior
For those who never heard of this hypothesis, it's one of the most difficult unsolved problems in the whole math!

Whats the easiest unsolved problem?

[SLH]

What's the most unsolved problem?

[DavidHooper]

http://www.mathsoft.com/asolve/

Any good?

[SLH]

[sql_lall]

Nice comments

Probably the most important unsolved problem would be he Reimann hypothesis, just for the sheer amount of other hypotheses that start 'If the Reimann Hypothesis is true, then...'

[Lior]

Originally posted by sql_lall

2) There is another theory similar, stating "Every even number greater than 5 can be written as the sum of 3 primes". This is apparantly easier to prove.

This is the SAME theory as Goldbach conjecture.

Actually this is exactly how Goldbach said the claim.
The version as I posted at first, was said by Euiler (spell?).

It's easy to prove, though.
because about the even numbers, if u say that they are consists of 3 primes, then one of the primes must be 2.
because the sum of 3 odd numbers are always odd.

This is why it is exactly the same to claim:
"every even number bigger than 2 can be represented as the sum of 2 primes"


And sorry for my bad english...

[DavidHooper]

Oh is that so? That's quite interesting. Euler by the way.

And sorry for my bad english...

Not to worry! You got the message across.

[sql_lall]

Sorry, i think it should be "Every ODD number greater than 5 can be written as the sum of three primes"

[Lior]

Nope, no need to add the "ODD" limitation.

The conjecture is true for all numbers greater than 5. (Of course we must not forget it is still a conjecture, and not a proved theorem).

for e.g: 6=2+2+2 (2 is the only even prime)

7=2+2+3
8=2+3+3
9=3+3+3
10=5+3+2

etc.....

Although this was found to be true up to 10^15 , yet a generic proof was found. (for about 3 centuries, if I'm not mistaken).

[STT]

I told you!

It's wrong

[Lior]

What's exactly wrong in here?

and if you mean you can refute the conjecture, post how.
(don't even try to find a sample with numbers, it's hopeless.
try the generic way to find some number X where the conjecture will not be true for.)

Bye.

[galway]

Actually if you are really interested in this topic John Konvalina of the University of Nebraska at Omaha has done a lot of work on this problem. He has already made more progress then anyone else towards proving it.

[STT]

proving it right or wrong?

[NotLKH]

Originally posted by STT
proving it right or wrong?

How can it be proven wrong, when it seems so axiometically right?

[sql_lall]

No matter how axiomatic something seems, it still has to be proven according to the axioms already set out. There may be some exception beyond the limit that time permits, until you prove it.

Also, what do you mean - "seems so axiomatically right"?

Oh, is there a good place to find out about Konvalina of the University of Nebraska at Omaha??
TY

[galway]

http://www.unomaha.edu/~wwwmath/facu...konvalina.html

There really isn't much on his website. You would probably have better luck searching math journals for more info. Last year he had a paper published in "The American Mathmatical Monthly"