The Goldbach’s Comet

Every even integer greater than 2 can be expressed as the sum of two primes (Christian Goldbach, 1742)

The point cloud known as Goldbach’s Comet represents the amount of different ways (y axis) an even number (x axis) can be writen as sum of two prime numbers. In this plot, x axis is between 2 and 50.000 (stars are just ornaments):


Mathematicians are still waiting for a proof of this conjecture. This is the code for drawing this plot:

data(primlist)[primlist>2 & primlist<n-2], 2)))
primes2=count(primes, "V3")
stars=cbind(runif(50, min=-n*0.05, max=n), runif(200, min=-n*0.001, max=max(primes2$freq)))
par(mai = rep(0, 4), bg = "gray12")
plot(NA,type="n", xlim=c(-n*0.05,n), xaxs="i", ylim=c(-n*0.001,max(primes2$freq)))
points(stars, col = "blue4", cex=.7, pch=16)
points(stars, col = "blue", cex=.3, pch=16)
points(stars, col = "gray75", cex=.1, pch=16)
apply(primes2, 1, function(x) points(x=x[1],y=x[2], col = if (runif(1)&gt;x[1]/n) {"white"} else {sample(colours(),1)}, cex=.1, pch=16))

One thought on “The Goldbach’s Comet

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s