What is the Goldbach conjecture?
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The Goldbach conjecture is one of the oldest and best-known unsolved problems in number theory. It states that every even integer greater than 2 can be expressed as the sum of two prime numbers. In other words, for every even integer n > 2, there exist two prime numbers p1 and p2 such that n = p1Read more
The Goldbach conjecture is one of the oldest and best-known unsolved problems in number theory. It states that every even integer greater than 2 can be expressed as the sum of two prime numbers. In other words, for every even integer n > 2, there exist two prime numbers p1 and p2 such that n = p1 + p2. For example, 4 can be written as 2+2, 6 as 3+3 or 5+1, 8 as 3+5 or 7+1, and so on.
The conjecture was first proposed by Christian Goldbach in a letter to Leonhard Euler in 1742. Despite centuries of effort by some of the greatest mathematicians in history, no one has been able to prove the conjecture definitively. However, the conjecture has been verified for all even integers up to 4 × 10^18.
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