23/05/2018

A mathematical problem has puzzled humanity for 276 years.

Reproduction of Marcelo Viana's column in Folha de S. Paulo.

On June 7, 1742, the German mathematician Christian Goldbach (1690-1764) wrote to his Swiss colleague Leonhard Euler proposing the following conjecture: every even number greater than 2 is the sum of two prime numbers. For example, 18 is the sum of 7 and 11, both prime numbers.

Euler replied on the 30th of the same month: “That every even integer is the sum of two primes I consider a completely certain theorem, although I cannot prove it.” No one has succeeded to this day: despite many attempts, there is still no proof accepted by the mathematical community as correct.

With the help of computers, it is not difficult to verify whether a statement is true or false for a given number, although it can be time-consuming if the number is large. Thus, we know that every even integer with fewer than 19 digits is the sum of two prime numbers. The challenge is to mathematically prove that the same holds true in all cases.

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