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Prime number patterns

by dmarinoc on 7/17/12, 2:15 PM with 100 comments

  • by aaronharnly on 7/17/12, 5:28 PM

    Very, very lovely. You might (or might not) also be familiar with the Ulam Spiral[1] or the arguably more beautiful Sacks Spiral[2], which do reveal certain patterns in the distribution of the primes.

    I used the software from this site[3] to generate a large Sacks spiral graphic, which I had custom-printed on my shower curtain. To most folks who see it, it's just some pattern of dots, but knowing the order within gives me great joy.

    [1] https://en.wikipedia.org/wiki/Ulam_spiral

    [2] http://www.numberspiral.com

    [3] http://www.dcs.gla.ac.uk/~jhw/spirals/index.html

  • by mutagen on 7/17/12, 4:39 PM

    I'd like to add tone generation so you could hear the various harmonics being added and removed as you worked up through the numbers, occasionally hitting a pure sine wave as you hit a prime number.
  • by kevindication on 7/17/12, 2:41 PM

    Two things that were non-obvious to me but made me extremely happy when they worked: panning and zooming.
  • by alokm on 7/17/12, 3:35 PM

    Its beautiful. It has an interesting formation of an infinite coaxial cones. with semi vertical angles arctan(1/3), arctan(1/5), ... arctan(1/(2n-1))... (The even numbers slopes form the progression of circles on the top). Although that doesn't give the pattern of the primes, it is formed because every number has a multiple for each natural number.
  • by ColinWright on 7/17/12, 4:22 PM

    Interesting - exact same submission - exact same URL - submitted 12 days ago:

    http://news.ycombinator.com/item?id=4202198

    1 upvote, no discussion.

  • by toomuchcoffee on 7/17/12, 4:11 PM

    I find this app to be quite interesting, actually. Even though it's really more a visualization of compositeness rather than of primality per se.
  • by jasondavies on 7/17/12, 4:53 PM

    I hadn't realised this before making it, but one interesting pattern is that the number in between twin primes is always abundant, if greater than 6.

    It's reasonably simple to prove using the fact that every twin prime pair except (3, 5) is of the form (6n − 1, 6n + 1).

  • by supo on 7/17/12, 3:12 PM

    I didn't know that the Sieve of eratosthenes could look this good!
  • by cturner on 7/17/12, 8:54 PM

    It's interesting that the curve on the left passes through zero rather than one.

    I've always been inclined to think 1x = x, and think of one as fundamental. But the pattern shows that rather than 1x being fundamental, rather there is the issue of x exists or x doesn't exist. x doesn't exist => 0. I wonder if 1*x = x is really a distraction away from a better type of thinking around existence.

    Also, I've always been wary of the part of the rule that says that 1 is not a prime number. Why is that?.

  • by forinti on 7/17/12, 3:22 PM

    I think he meant "El Padrón de los Números Primos". Patrón means "boss", not "pattern".
  • by Bullislander05 on 7/17/12, 2:44 PM

    This is extremely neat! The visual semi-patterns here are very interesting.
  • by craig552uk on 7/17/12, 3:12 PM

    3^n sequence looks like fractal penguins
  • by guard-of-terra on 7/17/12, 3:09 PM

    It would look 2x nicer if they removed 0 ~ prime number branches and waves beginning from primes. Much easier to spot, less clutter.
  • by pehrlich on 7/17/12, 3:27 PM

    wow, that is very nice. Does anyone else think they notice that primes are near to highly divisible numbers?
  • by crisnoble on 7/17/12, 3:51 PM

    I had always liked the number 42. However, I must say n=48 looks a lot nicer.
  • by wildtype on 7/17/12, 8:02 PM

    Lets see how the explanation help me to solve ProjectEuler's problems.
  • by minikrob on 7/17/12, 7:41 PM

    Simply stunning, many thanks for the link !
  • by Zenst on 7/17/12, 2:58 PM

    Cute, though does appear to be limited by browser initialwindow size.

    Thing about prime numbers - ask yourself this question: Does the universe operate on base 10!

    Endless fun aint they.

  • by mayneack on 7/17/12, 8:43 PM

    This doesn't work in IE 8
  • by JoeCortopassi on 7/17/12, 5:57 PM

    Stop it, stop it, stop it, just stop. Once an article reaches the front page, it's title is no longer editable. It causes confusion and frustration, and is obviously an issue that a lot of people dislike. I don't care about prime numbers, this article was all about the visualization to me. Every time a title gets changed like this, you are telling your user base that you don't care about what they think. I feel like I'm back in Digg, waiting for something like Reddit to pop up so I don't have to deal with the 'power' users.

    /rant

  • by thlt on 7/17/12, 3:05 PM

    it can be eye catchy but says really nothing interesting about prime numbers nor their patterns