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2019-05-01, 16:31   #12
danaj

"Dana Jacobsen"
Feb 2011
Bangkok, TH

2·3·151 Posts

Quote:
 Originally Posted by henryzz I was correct about this taking a while. I have searched 11#*x + 1451 with x upto 1e14 in about 3 hours with no results(best was upto 48). Started a run upto 1e15. I think I am being a victim here of the numbers getting larger and less likely to be prime as I search deeper.
Code:
$perl -Mntheory=:all -E 'prime_set_config(verbose=>2); say for sieve_prime_cluster(0,1e14,2,6,8,18,20,30,32,36,38,48,50,60,62,78,80);' cluster sieve found 1 residues mod 30 cluster sieve found 1 residues mod 210 cluster sieve using 0 residues mod 2310 There are no valid residues... 2019-05-01, 22:08 #13 henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 2·2,861 Posts Quote:  Originally Posted by danaj Code: $ perl -Mntheory=:all -E 'prime_set_config(verbose=>2); say for sieve_prime_cluster(0,1e14,2,6,8,18,20,30,32,36,38,48,50,60,62,78,80);' cluster sieve found 1 residues mod 30 cluster sieve found 1 residues mod 210 cluster sieve using 0 residues mod 2310 There are no valid residues...
And that's what I get for blindly continuing to search 2310*x+1451 without testing for factors <=11.

The best I can now find checking more carefully is: -24 -22 0 2 6 8 18 20 30 32 36 38 48 50 60 62

 2019-05-02, 17:04 #14 mart_r     Dec 2008 you know...around... 58110 Posts During my lunch break today, and just for fun, I calculated some of the different possibilities for dense twin prime patterns: 2 Twins: p+{0,2,6,8} 3 Twins: p+{0,2,6,8,18,20} p+{0,2,12,14,18,20} 4 Twins: p+{0,2,12,14,24,26,30,32} p+{0,2,12,14,18,20,30,32} p+{0,2,6,8,18,20,30,32} 5 Twins: p+{0,2,6,8,18,20,30,32,36,38} 6 Twins: p+{0,2,12,14,18,20,30,32,42,44,48,50} p+{0,2,6,8,18,20,30,32,36,38,48,50} 7 Twins: p+{0,2,12,14,24,26,30,32,42,44,54,56,60,62} p+{0,2,6,8,18,20,30,32,36,38,48,50,60,62} 8 Twins: p+{0,2,12,14,24,26,30,32,42,44,54,56,60,62,84,86} p+{0,2,12,14,24,26,30,32,42,44,54,56,72,74,84,86} p+{0,2,24,26,30,32,42,44,54,56,60,62,72,74,84,86} p+{0,2,12,14,30,32,42,44,54,56,60,62,72,74,84,86} 9 Twins: p+{0,2,12,14,24,26,30,32,42,44,54,56,60,62,84,86,102,104} p+{0,2,12,14,18,20,42,44,48,50,60,62,72,74,90,92,102,104} p+{0,2,18,20,42,44,48,50,60,62,72,74,78,80,90,92,102,104} p+{0,2,12,14,30,32,42,44,54,56,60,62,84,86,90,92,102,104} 10 Twins: p+{0,2,12,14,30,32,42,44,54,56,60,62,84,86,90,92,102,104,132,134} p+{0,2,18,20,30,32,42,44,48,50,72,74,78,80,90,92,120,122,132,134} p+{0,2,12,14,30,32,42,44,54,56,72,74,84,86,90,92,114,116,132,134} p+{0,2,12,14,30,32,42,44,54,56,72,74,90,92,102,104,114,116,132,134} p+{0,2,18,20,30,32,42,44,60,62,72,74,78,80,102,104,120,122,132,134} p+{0,2,12,14,30,32,54,56,60,62,72,74,90,92,102,104,114,116,132,134} p+{0,2,18,20,30,32,42,44,60,62,78,80,90,92,102,104,120,122,132,134} p+{0,2,18,20,42,44,48,50,60,62,78,80,90,92,102,104,120,122,132,134} p+{0,2,12,14,42,44,54,56,60,62,84,86,90,92,102,104,114,116,132,134} p+{0,2,30,32,42,44,48,50,72,74,78,80,90,92,102,104,120,122,132,134} 11 Twins: p+{0,2,12,14,30,32,42,44,54,56,60,62,84,86,90,92,102,104,132,134,144,146} p+{0,2,12,14,30,32,42,44,54,56,72,74,84,86,90,92,114,116,132,134,144,146} p+{0,2,12,14,30,32,42,44,54,56,72,74,90,92,102,104,114,116,132,134,144,146} (note the symmetric pattern here) p+{0,2,12,14,30,32,54,56,60,62,72,74,90,92,102,104,114,116,132,134,144,146} p+{0,2,12,14,42,44,54,56,60,62,84,86,90,92,102,104,114,116,132,134,144,146} Does anyone need more patterns?
2019-05-03, 08:46   #15
robert44444uk

Jun 2003
Oxford, UK

22×3×157 Posts

Quote:
 Originally Posted by mart_r During my lunch break today, and just for fun, I calculated some of the different possibilities for dense twin prime patterns: 2 Twins: p+{0,2,6,8} Does anyone need more patterns?
Well Done mart_r, Extremely useful. I'm not sure we need more than this given we are already needing to locate 22 primes - that is probably at the limit of what can be discovered right now.

 2019-05-03, 10:12 #16 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 2·2,861 Posts I have failed so far to find 8 twins. I have searched mart_r's third type of 8 twins upto 2310*1e16. I will attempt the others upto the same bound and then tap out.
2019-05-03, 11:28   #17
danaj

"Dana Jacobsen"
Feb 2011
Bangkok, TH

2·3·151 Posts

Quote:
 Originally Posted by henryzz I have failed so far to find 8 twins. I have searched mart_r's third type of 8 twins upto 2310*1e16.
I ran to 10^20 last night without finding any. I just spent a few minutes and tested the other three types to 10^17 without finding any.

I did a simple look at the 3rd type of 11 twins to 10^19 without finding any.

 2019-05-03, 19:13 #18 mart_r     Dec 2008 you know...around... 7×83 Posts And here I was hoping to be fast enough to post the list of patterns before someone else does I found all dense twin patterns up to 26 twins today. Here's a small overview, just in case someone is interested: Code: #tw width #patterns 2 8 1 3 20 2 4 32 3 5 38 1 6 50 2 7 62 2 8 86 4 9 104 4 10 134 10 11 146 5 12 170 4 13 182 2 14 212 18 15 224 2 16 254 34 17 266 2 18 290 8 19 302 6 20 338 8 21 350 2 22 380 12 23 392 2 24 410 4 25 422 2 26 440 2 (27 >=470 ?)
2019-05-04, 06:34   #19
robert44444uk

Jun 2003
Oxford, UK

111010111002 Posts

Quote:
 Originally Posted by mart_r And here I was hoping to be fast enough to post the list of patterns before someone else does I found all dense twin patterns up to 26 twins today. Here's a small overview, just in case someone is interested: Code: #tw width #patterns 2 8 1 3 20 2 4 32 3 5 38 1 6 50 2 7 62 2 8 86 4 9 104 4 10 134 10 11 146 5 12 170 4 13 182 2 14 212 18 15 224 2 16 254 34 17 266 2 18 290 8 19 302 6 20 338 8 21 350 2 22 380 12 23 392 2 24 410 4 25 422 2 26 440 2 (27 >=470 ?)
This is good work! Even if we haven't the computer resources to explore these upper reaches it is worth posting the detail for posterity. I found it annoying that the detail on longer prime constellations was not readily available on the web.

Last fiddled with by robert44444uk on 2019-05-04 at 06:35

 2019-05-08, 19:40 #20 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 2·2,861 Posts 1667+4108566605770697*(4290)+{0,2,12,14,24,26,30,32,42,44,54,56,72,74,84,86} are all prime. The 1st and 3rd types for 8 twins are searched upto 2310e16 The 2nd and 4th types for 8 twins are searched upto 4290e16.
2019-06-01, 22:30   #21
Bobby Jacobs

May 2018

193 Posts

Quote:
 Originally Posted by mart_r And here I was hoping to be fast enough to post the list of patterns before someone else does I found all dense twin patterns up to 26 twins today. Here's a small overview, just in case someone is interested: Code: #tw width #patterns 2 8 1 3 20 2 4 32 3 5 38 1 6 50 2 7 62 2 8 86 4 9 104 4 10 134 10 11 146 5 12 170 4 13 182 2 14 212 18 15 224 2 16 254 34 17 266 2 18 290 8 19 302 6 20 338 8 21 350 2 22 380 12 23 392 2 24 410 4 25 422 2 26 440 2 (27 >=470 ?)

What do the patterns look like?

2019-06-09, 12:51   #22
mart_r

Dec 2008
you know...around...

11058 Posts

Quote:
 Originally Posted by Bobby Jacobs What do the patterns look like?

All right, don't panic
I've attached a file with patterns for up to 31 twins. Had to re-write my program and I'm actually not 100% sure if it works correctly, for example I found 82 (!) different dense patterns for 29 twins.
Attached Files
 Twin Prime Patterns.txt (57.4 KB, 49 views)

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