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Prime number patterns

jasondavies.com

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Re: Prime number patterns

#71

Post by nessus42 »

ColinWright wrote: post #40
toomuchcoffee wrote: post #38

Earlier quoted context omitted.

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 fail…

Indeed the title did not stand. The title was recently changed, just as you asserted it "should" be.

Re: Prime number patterns

#72

Post by toast76 »

macspoofing wrote: post #50
JoeCortopassi wrote: post #48

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…

What are you talking about?

The title changed, and hence the topic. So no instead of a conversation about visualisations in JS, we'll have one about prime numbers.

If the OP thought the "prime number" aspect was interesting, he would have posted it as such.

Instead I'm sitting here looking at the OP thinking...this is not a very interesting visualisation of prime numbers.

Re: Prime number patterns

#73

Post by brianpan »

cturner wrote: post #70

It's interesting that the curve on the left passes through zero rather than one. I've always been inclined to think 1 x = x, and think of one as fundamental. But the pattern shows that rather than 1 x 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…

1. By definition

2. Because the math works out better

If it turns out that things that depend on prime numbers work in all cases except for 1, you might as well define 1 not to be a prime number.

http://en.wikipedia.org/wiki/Prime_number#Primality_of_one

Re: Prime number patterns

#74

Post by jjaredsimpson »

Retric wrote: post #66
thlt wrote: post #56

Earlier quoted context omitted.

how so ?

The number between them have a high number of small factors including 2 and 3. 2 * 3 = 6: 5 and 7 are prime. 2 * 3 * 2 = 12: 11 and 13 are prime 2 * 3 * 3 = 18: 17 and 19 are prime 2 * 3 * 5 = 30: 11 and 13 are prime 2 * 3 * 7 = 42: 41 and 43 are prime. However, 2 * 3 * 101 = 606 but 605 is not prime. But, 2 * 3 * 5 * 5 = 150 and 149 and 151 are prime. 2 * 3 * 2 * 3 * 5 = 180 and 179 and 181 are prime.

I don't see where the insight is. twin primes must be of the form (6k-1, 6k+1). So of course there will be a 2,3 at least.

Smaller numbers have multiples that are more densely distributed among the integers.

Re: Prime number patterns

#75

Post by dredmorbius »

darkstalker wrote: post #26
forinti wrote: post #15

I think he meant "El Padrón de los Números Primos". Patrón means "boss", not "pattern".

It's correct, "patrón" means both "boss" and "pattern" depending on context, but the word "jefe" is more widely used as "boss"

And of course, it turns out that the English "pattern" is derived from French, "patron", from the sense of "a model to be imitated".

http://www.etymonline.com/index.php?search=pattern

Re: Prime number patterns

#76

Post by jjaredsimpson »

jasondavies wrote: post #35

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).

Adding the fact that: perfect(x) -> abundant(nx) | n>=2

gives a proof why.

Re: Prime number patterns

#77

Post by cturner »

brianpan wrote: post #73
cturner wrote: post #70

It's interesting that the curve on the left passes through zero rather than one. I've always been inclined to think 1 x = x, and think of one as fundamental. But the pattern shows that rather than 1 x 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…

1. By definition 2. Because the math works out better If it turns out that things that depend on prime numbers work in all cases except for 1, you might as well define 1 not to be a prime number. http://en.wikipedia.org/wiki/Prime_number#Primality_of_one

"By definition" is a poor justification. I almost referenced the exact link you've given here. It gives poor justification for primality of one - resting on authority and lacking justification. The closest it comes (not very) is, "If 1 were admitted as a prime, these two presentations would be considered different factorizations of 15 into prime numbers, so the statement of that theorem would have to be modified." So what?

Re: Prime number patterns

#78

Post by jerf »

cturner wrote: post #77
brianpan wrote: post #73

Earlier quoted context omitted.

1. By definition 2. Because the math works out better If it turns out that things that depend on prime numbers work in all cases except for 1, you might as well define 1 not to be a prime number. http://en.wikipedia.org/wiki/Prime_number#Primality_of_one

"By definition" is a poor justification. I almost referenced the exact link you've given here. It gives poor justification for primality of one - resting on authority and lacking justification. The closest it comes (not very) is, "If 1 were admitted as a prime, these two presentations would be considered different factorizations of 15 into prime numbers, so the statement of that theorem would have to be modified." So…

"The closest it comes (not very) is, "If 1 were admitted as a prime, these two presentations would be considered different factorizations of 15 into prime numbers, so the statement of that theorem would have to be modified." So what?"

Many proofs depend on the unique factorization of primes, many directly and many many more indirectly. It is a trivial mechanical modification to them to deal with the non-uniqueness of a prime factorization if you admit 1 as a prime number by explicitly taking that case and saying it doesn't affect this case. So in that sense, no, it's not important.

Except... you've now taken numerous proofs and made them longer... and for what? There's no didactic advantage. There's no proof that is made easier by letting 1 be prime. What's the advantage of adding all these special cases? None.

And that's the real reason. In the end, "by definition" is the only justification, and the reason we choose the definition is that it works the best. Unlike 0 to the power of 0 where there's at least a bit of argument to be had (though the overwhelming preponderance is for it to be 1), there's no reason to put 1 in the set of prime numbers. Even if you don't personally consider it a "lot" of evidence, it's still entirely one sided.

Re: Prime number patterns

#79

Post by fauldsh »

JoeCortopassi wrote: post #48

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…

Was coming into this expecting an interesting piece about the distribution of prime numbers. Either a new approach to predicting them or a proof of why they're unpredictable. But no it's a visualisation of their distribution. Interesting but entirely not what was expected.
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