Goldbach Conjecture: Closer To Solved?

mikejuk writes "The Goldbach conjecture is not the sort of thing that relates to practical applications, but they used to say the same thing about electricity. The Goldbach conjecture is reasonably well known: every integer can be expressed as the sum of two primes. Very easy to state, but it seems very difficult to prove. Terence Tao, a Fields medalist, has published a paper that proves that every odd number greater than 1 is the sum of at most five primes. This may not sound like much of an advance, but notice that there is no stipulation for the integer to be greater than some bound. This is a complete proof of a slightly lesser conjecture, and might point the way to getting the number of primes needed down from at most five to at most 2. Notice that no computers were involved in the proof — this is classical mathematical proof involving logical deductions rather than exhaustive search."

Comments

Re:and here is the proof for every even number

[Smurf]

I hereby prove that every even number is a sum of no more than six primes, one of those is 1.

Psst, 1 isn't prime. Or composite. It's neither.

True, but you can change the GP's proof to "every even number n (where n > 4) is a sum of no more than six primes, because m = n - 3 is an odd number".

Re:Every Integer?

[jejones]

7 + 2 = 9

Is this progress?

[spaceyhackerlady]

Sorry, but I can't accept this being progress toward a proof.

Consider Fermat's Last Theorem. Proving it for any particular exponent is doable. Mathematicians had proved it for various sets of exponents (Sophie Germain, Wieferich, etc.). But the proof for all exponents was based on completely different mathematics (Elliptic curves/modular forms, Taniyama-Shimura, Wiles) and didn't look like anything that had come before.

...laura