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Goldbach conjecture


In mathematics, a conjecture is a proposition that many mathematicians believe to be true, based on assumptions, evidence, forebodings, hypotheses, but have not yet proved it.

Goldbach's famous conjecture is one of the oldest unresolved problems in mathematics. It was proposed on June 7, 1742 by Prussian mathematician Christian Goldbach, in a letter written to Leonhard Euler.


Letter written by Christian Goldbach on June 7, 1742

The conjecture reads as follows:

Any even number greater than 2 can be represented by the sum of two prime numbers.

For example:

4 = 2+2
6 = 3+3
8 = 3+5
10 = 3+7 = 5+5
12 = 5+7
14 = 7+7
16 = 5+11
18 = 7+11
20 = 7+13

This proposition seems very simple, right? But the fact is that until today nobody has been able to demonstrate it! Several computer checks have already confirmed Goldbach's conjecture for the most varied numbers. However, the mathematical demonstration never occurred.

In 1995, French mathematician Olivier Ramaré arrived at the closest result so far, proving that every even number is the sum of at most six prime numbers.

There is a variation called Goldbach's "weak" conjecture, which reads as follows:

All odd numbers greater than 7 are the sum of three odd cousins.

It is called "weak" because the original (known as Goldbach's "strong" conjecture), if demonstrated, would automatically demonstrate Goldbach's weak conjecture. While Goldbach's weak conjecture appears to have been proved in 2013 by Peruvian mathematician Harald Helfgott, the strongest conjecture remains unsolved.