Goldbach's conjecture is an unsolved question dating back to 1742. The conjecture states that every even number greater than 2 can be expressed as the sum of two (not necessarily distinct) prime numbers.
For example,
4=2+2
6=3+3
8=3+5
10=3+7=5+5
12=5+7
14=3+11=7+7
In studying the Goldbach conjecture, it is useful to define the so-called Goldbach function, g(n), which gives the number of different ways that 2n can be expressed as the sum of two primes. For example, since 22 can be written as 3+19, 5+17 and 11+11, it follows that g(11) = 3. In terms of this function, the conjecture can be restated as: for all n > 1, g(n) > 0.
The scatterplot known as Goldbach's comet is simply a plot of the Goldbach function.