Re: [PrimeNumbers] Explicit calculation of prime positive integers

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• Hi ! ... hmmmm it looks like... some sort of folded sieve, it reminds me of stack-based algorithms, and your vector is a bit like a stack... quite clever :-) a
Message 1 of 2 , Aug 2 5:01 PM
Hi !

Kermit Rose wrote:
> Kermit says:
> One could construct the following vector sequence that would make clear
> what it is that makes a prime a prime.
>
> To make the next entry,
> Just add 1 to each number in the vector.
>
> Each time you cross a prime, you add another entry for that prime.
>
> Each time you reach 2 in the 2's place, start over, so that the next
> entry in the 2's place is a 1.
> Each time you reach 3 in the 3's place, start over so that the next
> entry in the 3's place is a 1.
> etc
hmmmm it looks like... some sort of folded sieve,
it reminds me of stack-based algorithms,
and your vector is a bit like a stack... quite clever :-)
a stack of counter in fact...
but this method needs to scan all numbers.
it does not jump from one prime number to the other :-/

> 2 = [2] First prime.
> 3 = [1] Prime because 2 is not in the 2's place.
> 4 = [2,1] Not prime because in the 2's place is a 2.
> 5 = [1,2] Prime because in the 2's place is not a 2, and in the 3's
> place is not a 3.
> 6 = [2,3,1] Not prime because in the 2's place is a 2. Also not prime
> because in the 3's place is a 3.
> 7 = [1,1,2] Prime because in the 2's place is not a 2, and in the 3's
> place is not a 3, and in the 5's place is not a 5.
<snip>
> etc
I'll think carefully about the method you show.
does it have a name, where is it used, how can it be found or referenced ?

> Kermit says:
> Yann, in order to answer your question, we need to know details of your
> method.
I have just put some example code online at http://ygdes.com/sources/premiers.html
The algo is in JavaScript inside the page (very handy).
I'm not (yet ?) used to the tools that many contributors here use
(pari ?), it could change when I get a better idea about it.

The algorithm is explained in an article that will soon be published.
The original is there : http://ygdes.com/sources/misc-prems.html
(sorry, french only). It's a newcomer-level article but some
interesting stuff is at the end.

> Kermit says:
> Hmmmm...... Why versus how.
> I think that maybe I have never understood the meaning of "why?".
> For me, answering how things happen does answer all my questions.
> I myself see no difference in meaning for "why?" and "how?".
maybe my "why" is the "how" of the "how" ?

anyway i'm too tired to dissert about it now.

thank you very much for your insight,
> Kermit Rose
yg
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