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The webpage Visualizing Prime Numbers [] does exactly that. It contains a number of consecutive visualization experiments titled "Maps of Factors". Each "map" reveals the factors for each number, so that when only 2 circles intersect the horizontal axis at their right quadrants, a prime number is revealed (highlighted by green vertical lines in the graphs). Since factors in general are geometrically chaotic in nature, prime numbers are also geometrically chaotic in nature, as the resulting image seem dependent from initial conditions (much like "atoms in Quantum Mechanics").

If I understand this correctly, in an interesting twist, the author attempts to find large prime numbers in a more efficient way through analyzing and predicting the resulting visualizations, instead of working the other way around, that is to visually represent prime numbers which were derived purely algorithmically.

See also:
- The Visualization of Randomness
- Data Signals (also of prime numbers)
- Symmetrical Mathematics
- Ulam Prime Numbers Spiral
- Prime Number Spiral




Another visualization approach is Mario Klingemann's Wheel of Primes. The discussion with Dave Bollinger and others on Flickr ("This is so beautiful, it must be true") is compelling and interesting.

Fri 11 Dec 2009 at 1:57 AM

I've done work with integer factorization and spent some time producing a visualization of my method; You can find the work here.

Fri 11 Dec 2009 at 2:24 AM

I fail to see how this is at all useful. The location of primes does not seem to be indicated in any way by the visualization.

Fri 11 Dec 2009 at 4:06 AM

Josh, you'd have to see the site in the link to better understand how the prime numbers are visualized.

Fri 11 Dec 2009 at 4:52 AM

you can't see all prime numbers as they were not all discovered yet

start donating your unused computer powerto calcualte prime numbers now:

and get yourself awarded;)

Fri 11 Dec 2009 at 7:00 AM

This visualisation is a demonstration of one of the oldest methods for finding primes called the Sieve of Eratosthenes. Nothing revolutionary but a interesting visualisation nonetheless.

Fri 11 Dec 2009 at 5:32 PM
Stephen O'Hora

I was thinking the same thing as Stephen. It is almost certainly the Sieve of Eratosthenes. I hope the following doesn't come off as condescending as I don't mean it that way.(Anyway, I'm not a mathematician) You get very interesting results like this when amateurs approach a mature field of expect study. They re-reason things that great minds of many generations past came up with, but using entirely different approaches. You don't see this sort of thing in people who were taught these results rather than discovering them. Over years, teaching seems to have settled on a fairly limited range of methods for communicating these ideas. To me, this is most interesting insofar as it informs us about humans discover new ideas and assimilate/digest them into their base of knowledge.

Sat 12 Dec 2009 at 1:11 PM
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