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Goldbach's original conjecture written in a June 7, 1742 letter to Euler , states "at least it seems that every number that is greater than 2 is the sum of three primes". Note that here Goldbach considered the number 1 to be a prime, a convention that is no longer followed. As re-expressed by Euler, an equivalent form of this conjecture (called the "strong" or "binary" Goldbach conjecture) asserts that all positive even integers can be expressed as the sum of two primes. Two primes such that for a positive integer are sometimes called a Goldbach partition.

According to Hardy "It is comparatively easy to make clever guesses; indeed there are theorems, like 'Goldbach's Theorem,' which have never been proved and which any fool could have guessed." Faber and Faber offered a prize to anyone who proved Goldbach's conjecture between March 20, 2000 and March 20, 2002, but the prize went unclaimed and the conjecture remains open.

Schnirelman (1939) proved that every even number can be written as the sum of not more than 300000 primes, which seems a rather far cry from a proof for two primes! Pogorzelski (1977) claimed to have proven the Goldbach conjecture, but his proof is not generally accepted.

As of this date, the Goldbach conjecture is accepted as likely true, but has not been proven.

2006-10-13 12:27:03 · answer #1 · answered by Puzzling 7 · 2 1

The Goldbach Conjecture and its new extensions are no longer conjectures:they are theorems directly derived from the Riemann Hypothesis confirmation*. Let us mention the new extensions conjectures/theorems (july 2016)**: 1- Any even number is the difference of two odd prime numbers.
2- Any odd number is a prime number, or a sum or a difference of an odd prime number and the even prime number 2.
*The Riemann Zeta function of a non-trivial-zero-noted s may be expressed as the parametric quadratic function (s(1-s) - p), where p = p(s) is a parameter. From this view, the RH is directly confirmed (Re(s) = 1/2). The RH is indirectly validated through a Hilbert-Polya approach by demonstrating that the quadratic equation related to the above parametric function implies the existence of an adhoc positive self-adjoint hermitian operator.
The new Goldbach conjecture extensions are direct outcomes of the above RH
conjecture validation approach.
**to follow up.

2016-07-30 05:35:26 · answer #2 · answered by Tony G. 1 · 0 0

goldbach's conjecture

as far as i know nobody has claimed the prize yet

2006-10-13 19:50:24 · answer #3 · answered by Anonymous · 0 0

But they aren't....try to do it for 2...or be more precise in your description.


And it's Goldbach.

2006-10-13 12:26:42 · answer #4 · answered by Mr Glenn 5 · 0 0

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