anonymous
  • anonymous
Prove that every positive even integer greater than or equal to 4 can be expressed as the sum of two primes.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
You prove it.
amistre64
  • amistre64
I cant even prove that even integers exist :)
anonymous
  • anonymous
Actually I think the question is mistaken, it should have been Every positive even integer greater than 2 can be expressed as the sum of two primes

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anonymous
  • anonymous
Am I right Pasi?
anonymous
  • anonymous
You are ignorant
anonymous
  • anonymous
No that is how the problem is presented word to word.
anonymous
  • anonymous
Googling: ignorant was kinda' right Also: "In 1930, Lev Schnirelmann proved that every even number n ≥ 4 can be written as the sum of at most 20 primes. This result was subsequently improved by many authors; currently, the best known result is due to Olivier Ramaré, who in 1995 showed that every even number n ≥ 4 is in fact the sum of at most six primes. In fact, resolving the weak Goldbach conjecture will also directly imply that every even number n ≥ 4 is the sum of at most four primes.[13] Leszek Kaniecki showed every odd integer is a sum of at most five primes, under Riemann Hypothesis. [14]"
anonymous
  • anonymous
Then I don't have idea. For a moment I thought may be you were talking about Goldbach's conjecture. The statement I provided is Goldbach's conjecture. And it is not yet proved. If you don't mind, may I know the book, the problem is from
anonymous
  • anonymous
The name of this problem is strong Goldbach conjecture in my book.
anonymous
  • anonymous
Yes, just as I said
anonymous
  • anonymous
Then it is wrong, given there, as I know the statement which gave is the right statement
anonymous
  • anonymous
I believe you are talking about the prolem in which number '1' is regarded as a prime. This convention is not used anymore in this version of the prolem.
anonymous
  • anonymous
I meant the statement, that I gave is the right (sorry for the typos)
anonymous
  • anonymous
Whatever it may be, it is a conjecture
anonymous
  • anonymous
You seem familiar with this here is some more detalied information from Wolfram mathworld: http://mathworld.wolfram.com/GoldbachConjecture.html
anonymous
  • anonymous
Whatever it may be its a conjecture
anonymous
  • anonymous
I woudn't have been sitting here if I would been able to prove a conjecture
anonymous
  • anonymous
Bit odd of our lecturer to have this task included in our course paper. If someone here gets a spark to solve this it would be good though.
anonymous
  • anonymous
But Pasi, its a conjecture, it means it is yet not proven by anyone
anonymous
  • anonymous
How can you expect it to be proved by some one here
anonymous
  • anonymous
Your lecturer is perhaps playing a little joke with you
anonymous
  • anonymous
I don't really expect, but it cant do any harm either. I agree with the joke part now that I familiarized my self with the conjecture.
anonymous
  • anonymous
You will find something here http://en.wikipedia.org/wiki/Goldbach's_conjecture
anonymous
  • anonymous
Hope thats helpful
anonymous
  • anonymous
Considerable efforts seem to have been made to prove this conjeture and I'm sure someday it will be proved. Thank you for the link. Here is another one full of unsolved problems: http://garden.irmacs.sfu.ca/ This types of problems sure seem intriguing.

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