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 December 3rd, 2007, 03:05 PM #1 Senior Member   Joined: Nov 2007 Posts: 258 Thanks: 0 Goldbach conjecture Show how the statement "The product p1(n-p1)p2(n-p2)...pπ(n)(n-pπ(n)) does not divide n! for every even n" implies that every even n is the sum of two primes.
 December 5th, 2007, 08:21 AM #2 Senior Member   Joined: Nov 2007 Posts: 258 Thanks: 0 I forgot to say that n must be >2π(n). The product divides n! for n=4,6, but these cases may be verified easily to be the sum of two primes. Is this obvious to anyone?
 February 16th, 2009, 09:24 AM #3 Senior Member   Joined: Dec 2008 Posts: 206 Thanks: 0 Re: Goldbach conjecture Has goldbach conjecture been solved??
February 16th, 2009, 10:19 AM   #4
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Re: Goldbach conjecture

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 Originally Posted by kaushiks.nitt Has goldbach conjecture been solved??
No. Goldbach's weak (ternary) conjecture is close to resolution, with only finitely many cases left to check. (It's still far to many to check by computer.) Goldbach's strong (binary) conjecture has a long way to go.

 February 17th, 2009, 05:28 AM #5 Senior Member   Joined: Dec 2008 Posts: 160 Thanks: 0 Re: Goldbach conjecture I was able to show that these two statements are equivalent if second statement is : every even number is a sum of two different primes. Consider that if N = p + q, and p > q, then in our product p appear twice: as p and as n - q = p; n is not divisible by p, and in n! - p is only once, since 2p > n, so our product does not divide factorial. Backwards is similar. If n is sum of 2 equal primes - I do not know so far how to show it.
 February 17th, 2009, 07:57 AM #6 Senior Member   Joined: Dec 2008 Posts: 206 Thanks: 0 Re: Goldbach conjecture So if i prove the conjecture is true for all even numbers which are divisible by 6 then is it a good attempt . I mean would my work be recognized.
February 17th, 2009, 10:15 AM   #7
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Re: Goldbach conjecture

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 Originally Posted by kaushiks.nitt So if i prove the conjecture is true for all even numbers which are divisible by 6 then is it a good attempt . I mean would my work be recognized.
I'm not familiar with the literature -- I don't know if that result would be new. It would be new to me.

But if you want to prove a major special case of a famous conjecture, you'd probably do well to first read the relevant papers.

 February 17th, 2009, 11:40 PM #8 Senior Member   Joined: Dec 2008 Posts: 206 Thanks: 0 Re: Goldbach conjecture Would i able to know all the literature survey if i google Goldbach Conjecture.
February 18th, 2009, 07:10 AM   #9
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Re: Goldbach conjecture

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 Originally Posted by kaushiks.nitt Would i able to know all the literature survey if i google Goldbach Conjecture.
Surely not, but it's a start. Ideally you'd find a good survey paper on the topic which will point you to relevant developments.

 February 18th, 2009, 11:35 PM #10 Senior Member   Joined: Dec 2008 Posts: 206 Thanks: 0 Re: Goldbach conjecture Thanks I have a statement regarding the prime gaps i know it's true via my observation . But as of now i don't know to prove it. So can i state it as a conjecture or lemma . As well am i allowed to use such a statement in any of my proofs

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