Some new k-tuplets - Page 2

henryzz · 2013-12-28, 20:42

You seem to be finding some good records here.
How large a tuple do you think you will be able to find efficiently?

Batalov · 2013-12-28, 21:11

Just up to 7-tuplets with this approach (as shown above).

At 8-tuplets, this form becomes too sparse (e.g. k*p#/154+d can be barely used, with d=±4, ±2, 8, 14, 16, 22 and the same on the negative side; not d=±8, ±4, ±2, 14 because this set obviously covers all residues mod 7). The symmetry (and the nice set of ± powers of 2) breaks and more and more primes have to be excluded from the primorial and the efficiency of the form is gone.

P.S. I call them "small sets" for fun. I did write to Tony Forbes for his list.

Batalov · 2013-12-28, 22:18

And a (semi-conventional) 5-tuplet, to boot. (This one took a few days to find.)

9039840848561*3299#/35+d, d=-5,-1,1,5,7 (1401 digits)

cmd · 2014-01-05, 03:36

SB@|°\/

in more human dimensions us from here ...
(Twins) 1000037, 1000039
k = 73632
What signify our arrows in the drawing, for calculation?

Puzzle-Peter · 2014-04-18, 06:50

Quote:

Originally Posted by Batalov

I can post the patches later; they are too ugly to show to anyone, now. I am simply replacing the "mode 15" (4-tuple) with a different hack each time and have specific binaries for each trick.

Any progress on the "disuglification" yet?

Found with the help of standard NewPGen (started sieving with gsieve):

1288726869465789*2^34567 -5/-1/+1

Batalov · 2014-04-18, 07:19

Congrats! I've seen it in the top.

Nope, those hacks are still butt ugly - I haven't looked back at them since December.
I hacked, I compiled, I ran the code, I found. Never looked back.

Puzzle-Peter · 2014-04-18, 07:42

That's fine, I was just wondering.

2014-01-05, 03:36	#15
cmd "(^r'°:.:)^n;e'e" Nov 2008 ;t:.:;^ 3³×37 Posts	SB@\|°\/ in more human dimensions us from here ... (Twins) 1000037, 1000039 k = 73632 What signify our arrows in the drawing, for calculation? Attached Thumbnails

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2013-12-28, 20:42	#12
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 5887₁₀ Posts	You seem to be finding some good records here. How large a tuple do you think you will be able to find efficiently?

2013-12-28, 21:11	#13
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	Just up to 7-tuplets with this approach (as shown above). At 8-tuplets, this form becomes too sparse (e.g. kp#/154+d can be barely used, with d=±4, ±2, 8, 14, 16, 22 and the same on the negative side; not* d=±8, ±4, ±2, 14 because this set obviously covers all residues mod 7). The symmetry (and the nice set of ± powers of 2) breaks and more and more primes have to be excluded from the primorial and the efficiency of the form is gone. P.S. I call them "small sets" for fun. I did write to Tony Forbes for his list.

2013-12-28, 22:18	#14
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2519₁₆ Posts	And a (semi-conventional) 5-tuplet, to boot. (This one took a few days to find.) 9039840848561*3299#/35+d, d=-5,-1,1,5,7 (1401 digits)

2014-04-18, 07:19	#17
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10010100011001₂ Posts	Congrats! I've seen it in the top. Nope, those hacks are still butt ugly - I haven't looked back at them since December. I hacked, I compiled, I ran the code, I found. Never looked back.

2014-04-18, 07:42	#18
Puzzle-Peter Jun 2009 2²·3²·19 Posts	That's fine, I was just wondering.