> These patterns are certainly beautiful, but they don't have a hidden, divine message about primes.
As far as we know, for now.
Why do prime numbers make these spirals? (2019)
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Re: Why do prime numbers make these spirals? (2019)
#12Bit of a let down when they reveal that plotting integers in general results in the same spiral pattern as primes. So naturally primes as a subset of integers also produce spirals. Seems the title is a bit misleading!
A bit misleading I agree. I suppose since prime numbers DO make these spirals, it's not inaccurate.
We expect patterns from quotidian integers. The seeming chaos of primes, in contrast, brings the intrigue.
Re: Why do prime numbers make these spirals? (2019)
#13What's the commentary on prime numbers currently? Is it expected that there is some unfound pattern to them? Or will they always remain elusive?
No.
Re: Why do prime numbers make these spirals? (2019)
#14I can also make all integers look like sine waves sin(x)
Better divide x by something or you get a pretty crummy sine.
Or multiply by 19.
Re: Why do prime numbers make these spirals? (2019)
#15It could use a (2019) in the title. Interesting, but not recent.
Does it matter for math articles? It’s not like the math has changed in 4 years.
Re: Why do prime numbers make these spirals? (2019)
#16Bit of a let down when they reveal that plotting integers in general results in the same spiral pattern as primes. So naturally primes as a subset of integers also produce spirals. Seems the title is a bit misleading!
I don't know, for me the fact that this gives you a visualization of a totient is really interesting.
Another really interesting idea is to deliberately change the thing which you are rationally approximating; you don't have to rationally approximate π if you don't want to, that's just if you make steps of 1 radian. Make steps of q radians and you get the denominators for rational approximations of q/π.
This is used in the golden spiral algorithm[1] to evenly-ish distribute points on a sphere, we choose the most irrational number q/π = φ, the golden ratio. Since all of its rational approximations suck, the spirals are as inoffensive as they can be.
1. https://stackoverflow.com/questions/9600801/evenly-distribut...
Re: Why do prime numbers make these spirals? (2019)
#17What's the commentary on prime numbers currently? Is it expected that there is some unfound pattern to them? Or will they always remain elusive?
Maybe.
Re: Why do prime numbers make these spirals? (2019)
#18I can also make all integers look like sine waves sin(x)
y = (-1)**x
-1 is a circle, brah!
Re: Why do prime numbers make these spirals? (2019)
#19a factor, plus one. maybe? so it’s the pair of primes in that short sequence
Re: Why do prime numbers make these spirals? (2019)
#20I’m hardly a math genius, but isn’t this basically because he’s using polar coordinates, where nearly any trend is going to look like curves and spirals?