Earlier quoted context omitted.
Hence, the video...
Hence the video what? It's polar coordinates making the spiral, not prime numbers.
This is pointed out in the video
Why do prime numbers make these spirals? (2019)
41–50 of 141 posts
Re: Why do prime numbers make these spirals? (2019)
#42Earlier quoted context omitted.
Does it matter for math articles? It’s not like the math has changed in 4 years.
It has less to do with math, and more to do with the conventions of posting to HN where people expect dates for non-recent links. There's nothing wrong with them otherwise.
The convention exists because for most articles, publication year is an important piece of context. I'm not sure we have to blindly follow the convention when it isn't.
Re: Why do prime numbers make these spirals? (2019)
#43Earlier quoted context omitted.
Does it matter for math articles? It’s not like the math has changed in 4 years.
> Does it matter for math articles It matters for all the articles, so yes.
But, why does it matter for all articles? Is it just a blind rule, or can we apply it just when it actually makes sense?
Re: Why do prime numbers make these spirals? (2019)
#44[dead]
Re: Why do prime numbers make these spirals? (2019)
#45Earlier quoted context omitted.
> Does it matter for math articles It matters for all the articles, so yes.
But, why does it matter for all articles? Is it just a blind rule, or can we apply it just when it actually makes sense?
The year in the title means: it is so good, it is worth reposting here.
Re: Why do prime numbers make these spirals? (2019)
#46Re: Why do prime numbers make these spirals? (2019)
#47Re: Why do prime numbers make these spirals? (2019)
#48One of the thrills of studying the primes is the discovery that all primes greater than 3 are of the form 6k+1 or 6k-1. And for primes greater than 2, all primes are of the form 4k+1 or 4k-1. It is something that is commonly rediscovered by students, and that new independent finding was quite exciting for me. The reasoning, which is in the article here, is that you can make any whole number you wish if the number is…
This is neat and I never noticed this. For 5, I guess the linear component would be (2*3*5)k, but it isn't as interesting or useful because the constant component would be +/- 1, 7, 11, or 13. This method feels like it's basically a "higher order prime sieve".
[append] Oh, and because this pattern (of 1 always being one of the constants) carries out for arbitrarily large linear coefficients, that also explains the "twin prime" phenomenon: https://www.youtube.com/watch?v=QKHKD8bRAro
Re: Why do prime numbers make these spirals? (2019)
#49One of the thrills of studying the primes is the discovery that all primes greater than 3 are of the form 6k+1 or 6k-1. And for primes greater than 2, all primes are of the form 4k+1 or 4k-1. It is something that is commonly rediscovered by students, and that new independent finding was quite exciting for me. The reasoning, which is in the article here, is that you can make any whole number you wish if the number is…
Isn't 4k+1/4k-1 rule trivial though?
If we take any number K=N*4 divisible by 4 and >2, that'd be an even number by definition. The two closest odd numbers on either side would be (K-3), (K-1), (K+1), (K+3). As it happens (K+3) is the same as K(-1) for the next N, and (K-3) is the same as (K+1) for the previous N. So _all_ odd numbers follow this rule.
What "4k+1 or 4k-1" says in a roundabout way is that all prime numbers (>2) are odd, which isn't much of a surprise.
Re: Why do prime numbers make these spirals? (2019)
#50One of the thrills of studying the primes is the discovery that all primes greater than 3 are of the form 6k+1 or 6k-1. And for primes greater than 2, all primes are of the form 4k+1 or 4k-1. It is something that is commonly rediscovered by students, and that new independent finding was quite exciting for me. The reasoning, which is in the article here, is that you can make any whole number you wish if the number is…
Somehow I find 30k +/- 1, 7, 11, 13 more pleasing. It's 8 numbers and the primality of each "group" can be encoded in a byte.