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: |
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| Numbers on the marked curve are of the form |  | x2 + x + 41, | | | the famous prime-generating formula discovered by Euler in 1772. |
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If we continue winding for a while and zoom out a bit, the result looks like this: |
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| 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: |
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| Let’s try making the primes darker than the non-primes: |
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| 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.) | |
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| It looks as though primes tend to concentrate in certain curves |
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