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-   -   Prime Constellations 2 (https://www.mersenneforum.org/showthread.php?t=20642)

 MattcAnderson 2015-11-07 16:37

Prime Constellations 2

Hi Math People

Many of you may not know what prime constellations are. They are a subset of the k-tuples. Please see this reference.

[URL]http://mathworld.wolfram.com/PrimeConstellation.html[/URL]

Also, I have written a webpage regarding Prime Constellations.

Additionally Tony forbes has written a webpage

[URL]http://primerecords.dk/constellations.htm[/URL]

Hurray for Dana. Dana has written a software that will find prime numbers in prime constellations.

He has made a list that is part of the Online Encyclopedia Of Integer Sequences (OEIS).

See for example [URL="http://oeis.org/A213601"][COLOR=#0066cc]http://oeis.org/A213601[/COLOR][/URL] a list of 12-tuplets.

The search software has been released. It is just not advertised the right way.

Can someone point me to a software that runs on windows64 and can list prime numbers that are in k-tuple patterns?

I want to augment the OEIS more.

Regards

Matt

 science_man_88 2015-11-07 16:40

[QUOTE=MattcAnderson;415295]Hi Math People

Many of you may not know what prime constellations are. They are a subset of the k-tuples. Please see this reference.

[URL]http://mathworld.wolfram.com/PrimeConstellation.html[/URL]

Also, I have written a webpage regarding Prime Constellations.

Additionally Tony forbes has written a webpage

[URL]http://primerecords.dk/constellations.htm[/URL]

Hurray for Dana. Dana has written a software that will find prime numbers in prime constellations.

He has made a list that is part of the Online Encyclopedia Of Integer Sequences (OEIS).

See for example [URL="http://oeis.org/A213601"][COLOR=#0066cc]http://oeis.org/A213601[/COLOR][/URL] a list of 12-tuplets.

The search software has been released. It is just not advertised the right way.

Can someone point me to a software that runs on windows64 and can list prime numbers that are in k-tuple patterns?

I want to augment the OEIS more.

Regards

Matt[/QUOTE]

if you input the pattern type you want you could make a 64 pari script.

 danaj 2015-11-07 17:26

[QUOTE=science_man_88;415297]if you input the pattern type you want you could make a 64 pari script.[/QUOTE]
This is all definitely possible in Pari/GP, but I don't think you'd use a one-liner such as the simple[FONT=Courier New] "isprime(n) && isprime(n+2) && isprime(n+6) && ...[/FONT]" That is quite slow.

Strawberry Perl plus download of latest code with the included cpan command suffices to use my software on Win64, including the threaded example script that will use all your cores. Alternately I could write a 20 line main() that read the parameters and called the function without using Perl -- I would just need something to compile as a static binary.

 science_man_88 2015-11-07 17:35

[QUOTE=danaj;415307]This is all definitely possible in Pari/GP, but I don't think you'd use a one-liner such as the simple[FONT=Courier New] "isprime(n) && isprime(n+2) && isprime(n+6) && ...[/FONT]" That is quite slow.

Strawberry Perl plus download of latest code with the included cpan command suffices to use my software on Win64, including the threaded example script that will use all your cores. Alternately I could write a 20 line main() that read the parameters and called the function without using Perl -- I would just need something to compile as a static binary.[/QUOTE]

with parallell computation it can be turned into one in theory 2.7.4, 64 bit has parapply, pareval, parselect, parfor, parforprime, parvector, and parsum, for example, sure the way they are written to make it more efficient and will likely [URL="http://pari.math.u-bordeaux.fr/dochtml/html/Parallel_programming.html"]change[/URL]. for example if enough primes can be generated and stored: parselect(r->r%2310==997,a) where a is the vector that stores the primes could be used to check the condition in the OEIS.

 danaj 2015-11-07 18:01

Using the 2310*i+997 to select and checking isprime for the constellation comes up at 6778 times slower than my program on a single thread. You need to expand your solution set from just "I can use parfor!". Bigger primorials will help, plus sieving. As for parselect, we don't want to generate all the primes and filter them. We'll be running to 1e23 or so at some point. The set of acceptable residues is much less dense than the primes.

 science_man_88 2015-11-07 18:08

[QUOTE=danaj;415311]Using the 2310*i+997 to select and checking isprime for the constellation comes up at 6778 times slower than my program on a single thread. You need to expand your solution set from just "I can use parfor!". Bigger primorials will help, plus sieving. As for parselect, we don't want to generate all the primes and filter them. We'll be running to 1e23 or so at some point. The set of acceptable residues is much less dense than the primes.[/QUOTE]

if CRG's assumptions about why my codes run slower with them it's because 1 thread = the same as using the non parallel instructions. looking at [URL="http://pari.math.u-bordeaux.fr/pub/pari/manuals/2.7.0/parallel.pdf"]this[/URL] [QUOTE]2.5 Load balancing.
If the parallel tasks require varying time to complete, it is preferable to perform the slower
ones first, when there are more tasks than available parallel threads. Instead of
parvector(36,i,bnfinit(’x^i-2).no)
doing
parvector(36,i,bnfinit(’x^(37-i)-2).no)
will be faster if you have fewer than 36 threads.[/QUOTE]

could also be at play.

 Batalov 2015-11-07 18:36

There is nothing more dangerous than little knowledge, sm88. A person can juggle jargon without understanding it for all day long (and even create a feeling in bystanders that a meaningful conversation is going on), but you should stop talking for a minute and listen to what DanaJ is saying. He is saying that thinking that simply calling parfor is a meaningless.

Saying that "I can use parfor!" is the same as the proverbial example of getting 40 virgins to produce a child in 1 week, or claiming that to build a house in 1 minute you only need 36 thousand hammers and strike them all at once.

 MattcAnderson 2015-11-07 21:05

Hi Math People

Thank you for your comments. I will repeat my request.

I would like an executable program that will be able to find prime constellations.

Private message me and I may be willing to pay money \$.

Regards

Matt

 Xyzzy 2015-11-07 21:36

[QUOTE=MattcAnderson;415341]…I may be willing to pay money \$.[/QUOTE][url]https://www.bountysource.com/[/url]

:mike:

 MattcAnderson 2015-11-07 23:56

BountySource name matt123

 MattcAnderson 2017-03-10 04:22

Matt's take at prime constellations redux

2 Attachment(s)
Hi Mersenneforum,

Attached are probably my last efforts on prime constellation mathematics.

Regards,

Matt

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