Question

Prove that every positive even integer greater than or equal to 4 can be expressed as the sum of two primes.

Answer 1

You prove it.

Answer 2

I cant even prove that even integers exist :)

Answer 3

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

Answer 4

Am I right Pasi?

Answer 5

You are ignorant

Answer 6

No that is how the problem is presented word to word.

Answer 7

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]"

Answer 8

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

Answer 9

The name of this problem is strong Goldbach conjecture in my book.

Answer 10

Yes, just as I said

Answer 11

Then it is wrong, given there, as I know the statement which gave is the right statement

Answer 12

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.

Answer 13

I meant the statement, that I gave is the right (sorry for the typos)

Answer 14

Whatever it may be, it is a conjecture

Answer 15

You seem familiar with this here is some more detalied information from Wolfram mathworld:

http://mathworld.wolfram.com/GoldbachConjecture.html

Answer 16

Whatever it may be its a conjecture

Answer 17

I woudn't have been sitting here if I would been able to prove a conjecture

Answer 18

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.

Answer 19

But Pasi, its a conjecture, it means it is yet not proven by anyone

Answer 20

How can you expect it to be proved by some one here

Answer 21

Your lecturer is perhaps playing a little joke with you

Answer 22

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.

Answer 23

You will find something here http://en.wikipedia.org/wiki/Goldbach's_conjecture

Answer 24

Hope thats helpful

Answer 25

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.