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.
Prime number patterns
31–40 of 105 posts
Re: Prime number patterns
#32it can be eye catchy but says really nothing interesting about prime numbers nor their patterns
Oh? And what insights do you have share with us about prime numbers? Do tell.
Number theory is a big field and prime numbers are its core. There are tons of discoveries about prime numbers in the history and now people are quite focusing on Zeta function and the Riemann hypothesis, check out this chart http://upload.wikimedia.org/wikipedia/commons/3/30/Riemann_z.... Read more at http://en.wikipedia.org/wiki/Prime_number
Re: Prime number patterns
#33it can be eye catchy but says really nothing interesting about prime numbers nor their patterns
I don't know much about number theory, but I think this visualization probably provides significant intuition as to why number theory, which contains only theorems about integers, uses tons of math that is about a lot more than integers. Edit : Why would anyone down-vote this comment. Barbarians at the gates, I tell you! The only possible explanation is that the down-voters thinks that the relationship between number…
this chart basically includes a set of periodic curves, even though it looks nice but what does it tell you about prime numbers ? Intersected by only two curves 1 and itself ??? well, everyone knows this, no need to make a chart.
Re: Prime number patterns
#34Earlier quoted context omitted.
I don't know much about number theory, but I think this visualization probably provides significant intuition as to why number theory, which contains only theorems about integers, uses tons of math that is about a lot more than integers. Edit : Why would anyone down-vote this comment. Barbarians at the gates, I tell you! The only possible explanation is that the down-voters thinks that the relationship between number…
this chart basically includes a set of periodic curves, even though it looks nice but what does it tell you about prime numbers ? Intersected by only two curves 1 and itself ??? well, everyone knows this, no need to make a chart.
It tells you that prime numbers and periodic curves might be related more than you might have thought at first blush. I.e., if you can mathematically describe and analyze this set of periodic curves, then you have also described and can analyze the prime numbers.
As I mentioned, I don't know much about number theory, but I do know that it uses a lot of math that is counterintuitive at first blush. Perhaps this visualization gives us a clue as to why that is the case.
Re: Prime number patterns
#35I 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).
Re: Prime number patterns
#36I find this app to be quite interesting, actually. Even though it's really more a visualization of compositeness rather than of primality per se.
Yeah, it took me a while to sadly realize this visualization tells us nothing useful about primes. otoh, it does tell us a lot about composites. Hover on 29. The pattern is completely useless - you get one wave of period 29, and the other wave of period unity. However, hover on 28. Now you get 6 waves - of periods 1,2,4,7,14,28 - these being the divisors of 28. The intersection of these 6 waves produces those interes…
That's just the thing. Does anyone understand the primes, really?
We know a lot about number fields, multiplication and sieving... but the primes themselves (the "holes" left in the wake of the sieving process) are something of an epiphenomenon to all of this.
Re: Prime number patterns
#37I had always liked the number 42. However, I must say n=48 looks a lot nicer.
Try touching down some place strongly composite, like 720.
Re: Prime number patterns
#38Interesting - exact same submission - exact same URL - submitted 12 days ago: http://news.ycombinator.com/item?id=4202198 1 upvote, no discussion.
But the title was much less descriptive.
Re: Prime number patterns
#39Two things that were non-obvious to me but made me extremely happy when they worked: panning and zooming.
That is a very nice touch. Good catch. It does seem to break a bit if you resize the browser after the initial render. A refresh will fix it though.
Thanks, it should handle resizing better now.
Re: Prime number patterns
#40Interesting - exact same submission - exact same URL - submitted 12 days ago: http://news.ycombinator.com/item?id=4202198 1 upvote, no discussion.
But the title was much less descriptive.
Agreed, but if you use a descriptive title it's likely to get changed by the mods to something less useful, simply because that's what's on the article.
Indeed, this title shouldn't be allowed to stand, it should be changed to the title on the page itself, based on moderators' recent behavior.
Added in edit: Oh look - downvotes for pointing out that the current HN system of finding interesting items occasionally fails.