December 3rd, 2007, 02:05 PM  #1 
Senior Member Joined: Nov 2007 Posts: 258 Thanks: 0  Goldbach conjecture
Show how the statement "The product p1(np1)p2(np2)...pπ(n)(npπ(n)) does not divide n! for every even n" implies that every even n is the sum of two primes. 
December 5th, 2007, 07:21 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, 08:24 AM  #3 
Senior Member Joined: Dec 2008 Posts: 206 Thanks: 0  Re: Goldbach conjecture
Has goldbach conjecture been solved??

February 16th, 2009, 09:19 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Goldbach conjecture Quote:
 
February 17th, 2009, 04:28 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, 06:57 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, 09:15 AM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Goldbach conjecture Quote:
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, 10:40 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, 06:10 AM  #9  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Goldbach conjecture Quote:
 
February 18th, 2009, 10:35 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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