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Look ma, I've solved the Prime Numbers! ;.)

Hum. I either broke the matrix or I've stumbled across nature's secret morse code.

 

In any case this looks very interesting I must say. Again what we see here is the outcome of my playing with the Ulam Prime Number Spiral concept. In my variation I have arranged the prime numbers up to 1000000 in a fermat spiral using an angle increase of 2.41379035550925 (henceforth called the "Klingemann Constant" ;-))

 

As usual I probably did not do my homework properly and others have come across this pattern before. Only neither on Wikipedia nor on Mathworld Wolfram I could find any traces of it. Also google image search did not turn up anything except the usual ones. If you know of any prior sightings please leave a link in the comments.

 

My next step will be to try to find the formulas for those rays, since if my totally unscientific hunch holds true that any prime number must lie on one of those rays one could devise a simple test for primality.

 

[UPDATE 19:30]

Holy Crap, something is at work here... Now guess what this is:

41

2441

12041

13241

15641

18041

20441

32441

33641

34841

40841

45641

50441

57641

60041

66041

70841

[...]

792041

800441

801641

805241

811241

814841

823241

830441

832841

841241

844841

853241

855641

856841

860441

867641

868841

872441

873641

876041

883241

884441

890441

892841

895241

903641

908441

915641

916841

918041

920441

924041

925241

931241

932441

937241

942041

948041

949241

951641

957641

961241

962441

966041

969641

978041

982841

992441

 

These are all prime numbers that lie on a single ray of this diagram.

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Uploaded on August 3, 2009