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 CRGreathouse 2017-07-12 21:27

Prime constellations?

What's the best software for searching for prime constellations? I have constellations of the form kn + {k0, k1, ..., kj} for constants k, k0, ..., kj, where k0, ..., kj are all small (in my case, k = 23# and 1 = k0 < ... < kj < 100).

I seem to remember PFGW had a feature to do something like this, but maybe there is something more specialized? Any suggestions?

 Cybertronic 2017-07-13 00:40

APSieve can do that or write a own sieve. APSieve is not the fastest. What is the exact term ?

 CRGreathouse 2017-07-13 01:45

Incidentally what I meant above was that kj - k0 is small, not that (say) kj is small.

[QUOTE=Cybertronic;463294]APSieve can do that or write a own sieve. APSieve is not the fastest. What is the exact term ?[/QUOTE]

Well, I actually have ~200 constellations. For example,

223092870n + 217153 + {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76, 84, 88, 94, 96}

 Cybertronic 2017-07-13 05:55

"223092870n + 217153 + {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76, 84, 88, 94, 96}"

Is it an AP project ?

 Cybertronic 2017-07-13 10:51

Okay, looks like a tuplet project, but a 23 -tuplet have d=94, not 96 ?!

23 94 : 0 4 6 10 12 16 24 30 34 40 42 46 52 54 60 66 70 72 76 82 84 90 94
23 94 : 0 4 10 12 18 22 24 28 34 40 42 48 52 54 60 64 70 78 82 84 88 90 94

( ktpatt.txt at T.Forbes site )

I wrote for my 15 tuplet a sieve.
To find an example is not easy. Maybe n up to 10^30 one case.
I wrote a test sieve for a 18-tuplet. No chance. All primes up to 10M into the sieve, maybe 10 n's left for PRPing in an 100 billion -n-block.
BTW ,are you Mr. Stocker ?

 CRGreathouse 2017-07-13 16:58

[QUOTE=Cybertronic;463303]Is it an AP project ?[/QUOTE]

It's just something I'm doing on my own.

OK, great!

[QUOTE=Cybertronic;463312]Okay, looks like a tuplet project, but a 23 -tuplet have d=94, not 96 ?!

23 94 : 0 4 6 10 12 16 24 30 34 40 42 46 52 54 60 66 70 72 76 82 84 90 94
23 94 : 0 4 10 12 18 22 24 28 34 40 42 48 52 54 60 64 70 78 82 84 88 90 94[/QUOTE]

Yes, it's a little different from those. I have other constraints that give me a slightly larger final term (hence my collection is not a prime 23-tuplet by the standard definition).

[QUOTE=Cybertronic;463312]To find an example is not easy. Maybe n up to 10^30 one case.[/QUOTE]

I only need one case between all 200, so 0.01 or 0.02 solutions on average would be OK. But without specialized sieving software I can't even get that high (it took 8 hours for my naive GP script to search all forms up to 3e16).

[QUOTE=Cybertronic;463312]BTW ,are you Mr. Stocker ?[/QUOTE]

No, I'm [url=https://oeis.org/wiki/User:Charles_R_Greathouse_IV]some other guy[/url].

 Cybertronic 2017-07-13 17:21

[url]https://www.sendspace.com/file/idqrzc[/url]

Problems, ask me. There are some bugs in APSieve....

Best

 CRGreathouse 2017-07-13 18:16

Well, I'm running it now with
[code]apsieve -v -npb -ex23# -b23,217153,217157,217159,217163,217169,217171,217177,217181,217183,217187,217193,217199,217201,217207,217211,217213,217219,217223,217229,217237,217241,217247,217249 -k100000000 -K4000000000[/code]
but it's a pity that it's limited to 4 billion.

 CRGreathouse 2017-07-13 18:35

Oh wait, this is better because it PRPs as well:
[code]apsieve -v 134473145 4000000000 23# 23 217153 217157 217159 217163 217169 217171 217177 217181 217183 217187 217193 217199 217201 217207 217211 217213 217219 217223 217229 217237 217241 217247 217249 1000000000[/code]

 Cybertronic 2017-07-13 19:50

Can you find a command - line for this ?

for n=1000000 to n=10000000 , 1009# with 2 b's 16061 , 16063 and stop maxP=100000000 without PRP-Test -> so left n write APSieve in output.txt automatic

Never I found a solution for this with P<2^31 . Program ever crashed. Better, reload an output.txt file , set maxP <2^31

...and yes, 4 billion is maximum but 40 x 100 Million in order is faster via bat file

 Cybertronic 2017-07-14 09:45

Found a way:

apsieve -npb -k1000000000 -K5000000000 -ex1200# -b4,16061,16063,16067,16069 -mP100000000

Stop at 100M without PRP -> write the output.txt file

PRPing with PFGW is twice faster totay, so its better to start pfgwxx -f0 output.txt after sieving

But reload an output.txt and set maxP < 2^31 is not possible.

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