In English, please.
Goldbach's original conjecture (sometimes called the "ternary" Goldbach 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" (Goldbach 1742; Dickson 1957, p。 421)。 Note that here Goldbach considere...全部
Goldbach's original conjecture (sometimes called the "ternary" Goldbach 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" (Goldbach 1742; Dickson 1957, p。
421)。 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 (p, q) such that for n a positive integer are sometimes called a Goldbach partition (Oliveira e Silva)。
According to Hardy (1999, p。 19), "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 primes (Dunham 1990), 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 (Shanks 1993)。
The following table summarizes bounds n such that the strong Goldbach conjecture has been shown to be true for numbers 。
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