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I have something to check. It is about prime constant (I don't know if it is officially so called), but it is created on following way. We start with binary point number represenation. Zero followed by point and then if the number is prime we write an one if not we write a zero and so on filling the empty places this way. Now when we have this array of a bigger length we can transform it in simple black white bitmap. We open the file in hex-editor changing the hex values of zeros and ones to 00 and FF to form bitmap. In my case I have the array of length 10000 it is divisable by four and needs no paddings in bitmap file. The header of bitmap file is created in gimp with an empty file bmp with 100x100px . The results are surprising , and that is the question to the forum: First to check if there isn't an error in this process of bitmap creation and secondly if not to interpret the results. I will attach the bitmap file and also the bitmap file from binary representation of Pi just to compare created in same manner. I personally expected great randomness as by Pi bitmap but in prime constant bitmap there are great regularities. Any explanation or simply an error?

PS: I am not able to post pictures due to reputation. Is there another way to show what is all about?

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closed as off-topic by Joonas Ilmavirta, Marco Golla, Lucia, Yemon Choi, Boris Bukh Aug 19 '15 at 15:27

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If I understand correctly, here is sage code to play with (one can run in a browser in the cloud).

n=300;M=Matrix(QQ,n,n,[int(is_prime(k)) for k in xrange(1,n^2+1)]);pl=M.plot();pl.save("/tmp/primes300.png")

Here is the plot for $n=213$:

enter image description here

And for $n=300$:

enter image description here

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  • $\begingroup$ I think that's it. For 100x100 is similar with 300x300 and I thought this regularities shouldn't be. Do you know where they come from (in your example 300x300)? As we see in 213x213 picture it looks more random. $\endgroup$ – F. P. Aug 19 '15 at 10:04
  • $\begingroup$ @F.P. Don't know. But expect the pattern heavily to depend on $n$. $\endgroup$ – joro Aug 19 '15 at 14:41

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