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• ## Re: Formula that couples each composite number to one prime only

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• ... I had been thinking of patterns along these lines and tried to post earlier but the formatting was off so I deleted post. Here is a link to my website to
Message 1 of 22 , Jul 21, 2010
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--- In primenumbers@yahoogroups.com, "reijkersz" <vic@...> wrote:
>
> or in other words a way to make a sieve in which every composite number is "crossed out" only once. and no cases occur where for example 45 is crossed out by 3 and by 5. every prime crosses out a number of composite numbers, so that eventually all composite numbers are crossed out, and only crossed out by 1 prime.
>
> is this anything new under the sun? or is it already out there?
>
> i posted the whole story here:
>
>
> any feedback from primes enthousiasts is more then welcome!
>
> thank you,
> Vic
>

I had been thinking of patterns along these lines and tried to post earlier but the formatting was off so I deleted post. Here is a link to my website to explain my thinking on patterns.

Tell me what you think.
• Hi Steve, For starters i want to say i am pleasantly surprised to find somebody else on our planet who s looking at prime numbers in the same way. Its a
Message 2 of 22 , Jul 22, 2010
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Hi Steve,

For starters i want to say i am pleasantly surprised to find somebody else on our planet who's looking at prime numbers in the same way. Its a small world after all :)

However you did follow a slightly different approach then i did. I gotta feeling your approach works however. If i find some time the comming days i can run it through a computer simulation and see if it holds up. actually i see now reason why it should not.

It might seems a slow technique if you look at it as finding the next prime, but actually you are not only finding the next prime, you are finding an enormous ammount of primes because the pattern is exactly equal to the prime gap distribution.

translating to 3 pattern finds 1 new prime
translating to 5 pattern finds 2 new prime
translating to 7 pattern finds 7 new primes
translating to 11 pattern finds +-42 new primes
translating to 13 pattern finds +-341 new primes
etc...

best regards,
Vic

>
>
>
>
> --- In primenumbers@yahoogroups.com, "reijkersz" <vic@> wrote:
> >
> > or in other words a way to make a sieve in which every composite number is "crossed out" only once. and no cases occur where for example 45 is crossed out by 3 and by 5. every prime crosses out a number of composite numbers, so that eventually all composite numbers are crossed out, and only crossed out by 1 prime.
> >
> > is this anything new under the sun? or is it already out there?
> >
> > i posted the whole story here:
> >
> >
> > any feedback from primes enthousiasts is more then welcome!
> >
> > thank you,
> > Vic
> >
>
> I had been thinking of patterns along these lines and tried to post earlier but the formatting was off so I deleted post. Here is a link to my website to explain my thinking on patterns.
>
>
> Tell me what you think.
>
• hi ! ... that is what this list is for :-) ... Have a look at this JavaScript code : http://ygdes.com/sources/premiers.html It is a bit similar but uses a
Message 3 of 22 , Jul 22, 2010
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hi !

Le jeu 22/07/10 19:29 , "Victor Reijkersz" a écrit::
>Hi Steve,
>
>For starters i want to say i am pleasantly surprised to find somebody else on our planet who's looking at prime numbers in the same way. Its a small world after all :)
that is what this list is for :-)

>However you did follow a slightly different approach then i did. I gotta feeling your approach works however. If i find some time the comming days i can run it through a computer simulation and see if it holds up. actually i see now reason why it should not.
Have a look at this JavaScript code :
http://ygdes.com/sources/premiers.html
It is a bit similar but uses a slightly different method (more crude) for collapsing consecutive deltas.

>It might seems a slow technique if you look at it as finding the next prime, but actually you are not only finding the next prime, you are finding an enormous ammount of primes because the pattern is exactly equal to the prime gap distribution.
More precisely, it is not finding an "enormous amount of primes", but of pseudoprimes (candidates for further sieving).

>best regards,
_o/

>Vic
yg
• ... Nope... its finding only and all next real primes. seriously. the pattern of 7 as steve writes it is [6,4,2,4,2,4,6,2] or as i write is
Message 4 of 22 , Jul 23, 2010
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> More precisely, it is not finding an "enormous amount of primes", but >of pseudoprimes (candidates for further sieving).

Nope... its finding only and all next real primes. seriously. the pattern of 7 as steve writes it is [6,4,2,4,2,4,6,2] or as i write is
[4,2,4,2,4,6,2,6]... in my case being
7+4=11
11+2=13
13+4=17
17+2=19
19+4=23
23+6=29
29+2=31
31+6=37
or again: the pattern of 7 returns 8 primes.
pattern of 11 returns 48 primes
pattern of 13 returns 480 primes
etc..

of course my algorithm and also steve maddox his algorithm cannot be used to find the next biggest prime because both need to at least keep an ammount of numbers in memory equal to all primes that have been discovered so far.

but still... both give enormous insight in the spreading of the primes and composite numbers.

best,
vic
• Hi ! ... I ll have to examine this further. I have probably spoken too fast. ... I agree completely here ! ... _o/ ... yg
Message 5 of 22 , Jul 23, 2010
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Hi !

>Le ven 23/07/10 08:53 , "Victor Reijkersz" a écrit::
>> More precisely, it is not finding an "enormous amount of primes", but >of pseudoprimes (candidates for further sieving).
>Nope... its finding only and all next real primes. seriously. the pattern of 7 as steve writes it is [6,4,2,4,2,4,6,2] or as i write is
>[4,2,4,2,4,6,2,6]... in my case being
>7+4=11
>11+2=13
<snip>

I'll have to examine this further. I have probably spoken too fast.

>but still... both give enormous insight in the spreading of the primes and composite numbers.

I agree completely here !

>best,
_o/

>vic
yg
• Hi Yann/stmaddox, Whats actually going on is that each pattern predicts the next primes up to the pattern slot where the total of pattern numbers is larger
Message 6 of 22 , Jul 26, 2010
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Whats actually going on is that each pattern predicts the next primes up to the pattern slot where the total of pattern numbers is larger then the patterns prime square.

So the 5 and 7 patterns are all primes... but the 11 pattern is the first pattern who's sum (210) is larger then the square of the prime of the pattern (121)

however thats still a substantial number of primes that get predicted.

best regards,
Vic

--- In primenumbers@yahoogroups.com, Yann GUIDON <whygee@...> wrote:
>
> Hi !
>
> >Le ven 23/07/10 08:53 , "Victor Reijkersz" a Ã©crit::
> >> More precisely, it is not finding an "enormous amount of primes", but >of pseudoprimes (candidates for further sieving).
> >Nope... its finding only and all next real primes. seriously. the pattern of 7 as steve writes it is [6,4,2,4,2,4,6,2] or as i write is
> >[4,2,4,2,4,6,2,6]... in my case being
> >7+4=11
> >11+2=13
> <snip>
>
> I'll have to examine this further. I have probably spoken too fast.
>
> >but still... both give enormous insight in the spreading of the primes and composite numbers.
>
> I agree completely here !
>
> >best,
> _o/
>
> >vic
> yg
>
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