By ET
Came across the fascinating website: Prime Number Spiral
|
Number spirals are very simple. To make one, we just write the non-negative integers on a ribbon and roll it up with zero at the center.
The trick is to arrange the spiral so all the perfect squares (1, 4, 9, 16, etc.) line up in a row on the right side:
|
 |
| Figure 1 |
| If we continue winding for a while and zoom out a bit, the result looks like this: |
|
 |
|
| If we zoom out even further and remove everything except the dots that indicate the locations of integers, we get the next illustration. It shows 2026 dots: |
|
|
|
|
 |
|
|
| Figure 3 |
|
|
| Let’s try making the primes darker than the non-primes: |
|
|
|
|
| The primes seem to cluster along certain curves. Let’s zoom out even further to get a better look. The following number spiral shows all the primes that occur within the first 46,656 non-negative integers. (For clarity, non-primes have been left out.) |
|
|
|
|
 |
|
|
| Figure 5 |
|
|
It looks as though primes tend to concentrate in certain curves that swoop away to the northwest and southwest, like the curve marked by the blue arrow.
On the next few pages of this website, we’ll investigate these patterns and try to make sense out of them.
By ET This entry was posted
on Friday, April 20th, 2007 at 8:54 pm and is filed under General, Play, Research.
You can follow any responses to this entry through the RSS 2.0 feed.
You can skip to the end and leave a response. Pinging is currently not allowed.
