# Goldbach conjecture

Goldbach's latter to Euler dated June 6, 1742.

The Goldbach conjecture is one of the oldest and easiest-to-understand hypotheses in mathematics that
remains unproven. In its original form, now known as the **weak Goldbach
conjecture**, it was put forward by the Prussian amateur mathematician
and historian Christian Goldbach (1690–1764) in a letter dated June 7, 1742,
to Leonhard Euler. In this guise it says that
every whole number greater than 5 is the sum of three prime
numbers. Euler restated this, in an equivalent form, as what is now
called the **strong Goldbach conjecture** or, simply, the Goldbach
conjecture: every even number greater than 2 is the sum of two primes. Thus,
4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 3 + 7, ..., 100 = 53 + 47, ...

In fact René Descartes knew about
the two-prime version of Goldbach's conjecture before either Goldbach or
Euler did. So, is it misnamed? Paul Erdös said, "It is better that the conjecture be named after Goldbach because,
mathematically speaking, Descartes was infinitely rich and Goldbach was
very poor." In any event, there is a much more important question, namely,
is the conjecture true? The general assumption is that it is, but no one
knows for sure. The most significant step toward a proof came in 1966 when
the Chinese mathematician Chen Jing-Run showed that every sufficiently large
even integer is the sum of a prime and a number that has at most two prime
factors. Using powerful computers, the Goldbach conjecture has been checked
out to about 400 trillion. But there is no great optimism among mathematicians
that a final breakthrough is on the horizon. Even a reward of $1 million
dollars for a proof offered by the publishing house Faber & Faber in 2000,
to help publicize the novel *Uncle Petros and Goldbach's Conjecture* by the Greek mathematician and author Apostolos Doxiadis, went unclaimed.^{1}

### Reference

1. Doxiadis, Apostolos K. *Uncle Petros and Goldbach's Conjecture*.
New York: Bloomsbury, 2000.