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IMPORTANT NOTICE: Starting from April 4th, 2001, the new Web address for this page is http://www.alpertron.com.ar/ULAM.HTM. Please update your bookmarks, because this page will not be updated anymore.

Darío Alpern - Webmaster

Ulam's Spiral

Do you see any pattern in this graph? You will not believe at first glance that it is generated using prime numbers.

In order to generate it, the numbers are arranged in a spiral, as follows:

13 -- 12 -- 11 -- 10    25
|                 |     |
14    03 -- 02    09    24
|     |     |     |     |
15    04    01    08    23
|     |           |     |
16    05 -- 06 -- 07    22
|                       |
17 -- 18 -- 19 -- 20 -- 21

Then the prime numbers are marked. Note the abundance of diagonals.

In the applet above you can see the spiral made up to 1014. The prime numbers are marked in green.

Move the graph by clicking in the arrows. Also you can obtain more detail or see a larger area using the magnifying glass buttons.

You can also see the position (x, y) in the spiral and the number n of any point of the graph by moving the cursor to that point.

Move the center by typing a new number (up to 14 digits) in the input box.

Last updated November 10th, 2000.