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I was plotting the Ulam spiral (https://en.wikipedia.org/wiki/Ulam_spiral), and decided to isolate twin/cousin/sexy primes on the Ulam spiral.

Although plotting twin primes offered no obvious lines, isolating cousin primes seemed to yield distinctly prime-rich lines (and not always on 45 degree angles, as are common in the Ulam spiral). How do you feel? Do you think these lines are significant? Look under the orange dotted lines.

Cousin primes on the Ulam spiral (from 1 - 500000) Cousin primes on the Ulam spiral (from 1 - 500000)

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  • $\begingroup$ If someone could just let me know if these lines seem non-random, I would appreciate that information. Make sure I'm not just seeing things. $\endgroup$ – Dashiell Shulman Dec 17 '15 at 22:02
  • $\begingroup$ Anyone see anything here? Didn't get any responses originally. $\endgroup$ – Dashiell Shulman Mar 2 '16 at 18:13
  • $\begingroup$ it is difficult to see the dot lines you try to show in your plotting.In general, there are a lot of interesting observations about the behavior of the primes inside the Ulam spiral; e.g. some time ago I noticed something regarding the numbers of an Ulam spiral (starting at 0 in the center) in which the shape of the spiral is exactly a rectangle. It might give you ideas about which type of observations, calculations you can try, so just in case (the conjecture is written in the comments block): oeis.org/A024206 $\endgroup$ – iadvd Jul 7 '16 at 6:26
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    $\begingroup$ Thanks for your reply, iadvd. Sorry I missed it. I do suppose some of the lines are harder to see than others; I haven't run this program in some time but I could get it back up and running for some more detailed lines. $\endgroup$ – Dashiell Shulman Dec 2 '16 at 16:31

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