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2013-01-30, 10:56   #243
roger

Oct 2006

22×5×13 Posts

Guess I forgot to post this a while ago:

16000<n<17000 done.

17000<n<18000 is 30% done.
18000<n<19000 is 7.7% done.

Attached Files
 16k.txt (15.8 KB, 179 views)

2013-01-30, 11:06   #244
roger

Oct 2006

26010 Posts

Also, an update on the statistics of where these lowest twins are being found:
Attached Files
 Statistics.txt (765 Bytes, 136 views)

2013-02-05, 11:45   #245
kar_bon

Mar 2006
Germany

B1716 Posts

Quote:
 Originally Posted by roger 15000
Just wanted to update my page.

As you can see on my page for First Twin k (on the bottom) for n=15671 I got k=232179 (checked it with NewPGen and LLR).

In your file you gave the value n,k = 15671, 189489369!

Upcoming questions:
Are there other errors? -> independent doublecheck
Are there values given where k is not the lowest?
Where is the error: software, script (if any), copy/paste, what else?

 2013-02-07, 01:42 #246 roger     Oct 2006 1000001002 Posts Apologies, Kar_bon: that would be an oversight on my part. I've been taking the ranges starting at k=1e6 since they've been searched below that previously. I just didn't take n=15671 off the list when I started the range.
2016-12-18, 17:28   #247
sweety439

Nov 2016

214810 Posts

Quote:
 Originally Posted by gd_barnes Citrix, Actually, k=1 to 600 have been searched enough since that's how far the Proth search site goes up to and so is how far up I matched the site with ours. I wasn't able to do any more testing yet but I combined your list with mine and added the value of n that each k has been tested through. Of course all of yours are 250. I also added odd k's divisbile by 3 (i.e. k=3 mod 6) up to k < 1000 where no twins were found and showed (none) by them. People might like to test those with a little more vigor in the future. I suspect there will be plenty of k's that have no twin primes found. It will be interesting to see if the lowest value of k=3 mod 6 where there are no twins really turns out to be k=111 like it is now. It has technically been tested to n=350K. I should be able to extend the search for k > 600 a little on Tuesday sometime. Thanks for your help so far. This might turn out to be an interesting effort and could give us a good base to work from if we wish to find somewhat large triplets, quadruplets, 5-tuples, etc. in the future. My changes are attached. Gary
Of course, these k's should be divisible by 3. However, some k's divisible by 3 cannot have twin primes, see http://www.primepuzzles.net/problems/prob_049.htm.

e.g. k=237, for every integer n>=1, either 237*2^n+1 or 237*2^n-1 is divisible by 5, 7, 13, 17, or 241, i.e. there is a cover set: {5, 7, 13, 17, 241} for k=237.

Another example is k=807, for every integer n>=1, either 807*2^n+1 or 807*2^n-1 is divisible by
5, 7, 13, 19, 37, or 73, i.e. there is a cover set: {5, 7, 13, 19, 37, 73} for k=807.

The k's < 237 divisible by 3 without known twin primes are 111, 123, 153, 159, 171, 183, 189, 219, 222, 225.

k=111 may has twin primes, unlike k=237, k=237 has no possible twin primes.

Last fiddled with by sweety439 on 2016-12-18 at 17:44

2016-12-18, 17:55   #248
sweety439

Nov 2016

22×3×179 Posts

Since all such k's are divisible by 3, I use 3*k*2^n+-1 instead of k*2^n+-1.

Thus, the conjectured k is 79, and the remaining k's are 37, 41, 51, 53, 57, 61, 63, 73, 74, 75.

This is a file for all the k's <= 1024. I tested n<=1024 at first, larger n's are given use the link: 3*97*2^1553+-1 and 3*383*2^3283+-1. (the n for one row is missing in the text file, this row should be "766,3282", not "766,?", like the rows "194,1552", "388,1551", "776,1550". Also, the rows 158, 316, 632 and 538 should be "(not possible)", not "?")

There is a link for all such twin primes: http://www.noprimeleftbehind.net/gary/twins100K.htm.
Attached Files
 least k such that 3n2^k+1 and 3n2^k-1 are twin primes.txt (7.2 KB, 128 views)

Last fiddled with by sweety439 on 2016-12-18 at 18:13

2016-12-18, 18:14   #249
sweety439

Nov 2016

22·3·179 Posts

Update the current right text file.
Attached Files
 least k such that 3n2^k+1 and 3n2^k-1 are twin primes.txt (7.3 KB, 147 views)

Last fiddled with by sweety439 on 2016-12-18 at 18:15

 2016-12-21, 07:49 #250 kar_bon     Mar 2006 Germany 17·167 Posts According to here you should not change the notations of k and n values. So you missed your given k-value = 74 can be omitted (k=37)! Also have a look at here.
2016-12-21, 17:16   #251
sweety439

Nov 2016

214810 Posts

Quote:
 Originally Posted by kar_bon According to here you should not change the notations of k and n values. So you missed your given k-value = 74 can be omitted (k=37)! Also have a look at here.
k=74 is included in the conjecture but excluded from testing, since this k will have the same twin primes (if exist) as k=37.

Last fiddled with by sweety439 on 2016-12-21 at 17:16

2019-07-06, 23:50   #252
The Carnivore

Jun 2010

179 Posts

Quote:
 Originally Posted by Oddball Your table is wrong; there are twins <1M for n=37000-40000. 201843*2^37630+/-1 is twin, and so are 683145*2^38746+/-1 and 126423*2^2^39606+/-1. But I don't blame you, as http://www.rieselprime.de/Related/FirstKTwin.htm doesn't have those twins either. The correct table is below. Code: Range Smallest First Twin k n-value 1000-2000 177 1032 2000-3000 4359 2191
Your ranges don't make sense. If, for example, 95*2^2000+/-1 were twin, which range would it fall under? The 1000-2000 one, or the 2000-3000 one?

Here's the corrected version:
Code:
Range            Smallest First Twin k       n-value
1000-1999           177                        1032
2000-2999          4359                        2191
3000-3999          1149                        3283
4000-4999          2565                        4901
5000-5999          5775                        5907
6000-6999          4737                        6634
7000-7999         33957                        7768
8000-8999           459                        8529
9000-9999         33891                        9869
10000-10999       10941                       10601
11000-11999         915                       11455
12000-12999       73005                       12178
13000-13999        3981                       13153
14000-14999      175161                       14171
15000-15999       74193                       15770
16000-16999      138153                       16436
17000-17999       14439                       17527
18000-18999       56361                       18989
19000-19999       53889                       19817
20000-20999        7485                       20023
21000-21999      195045                       21432
22000-22999       31257                       22312
23000-23999      396213                       23672
24000-24999      177141                       24365
25000-25999      577065                       25879
26000-26999      182697                       26172
27000-27999       70497                       27652
28000-28999      445569                       28353
29000-29999      815751                       29705
30000-30999      249435                       30977
31000-31999      440685                       31989
32000-32999       51315                       32430
33000-33999      143835                       33826
34000-34999      959715                       34895
35000-35999      338205                       35351
36000-36999       47553                       36172
37000-37999      201843                       37630
38000-38999      683145                       38746
39000-39999      126423                       39606
40000-40999      604329                       40315
41000-41999      358965                       41653
42000-42999      272139                       42379
43000-43999      441201                       43167
44000-44999       >1M                          ???
45000-45999      311541                       45439
46000-46999       >1M                          ???
47000-47999      103893                       47122
48000-48999      694599                       48501
49000-49999      197109                       49733*
*This may not be the right k/n pair. It was obtained from https://www.mersenneforum.org/showpo...&postcount=217

which says that only 0<n<49796 has been done for k <1M. A lower k value may be found for n=49796-49999, inclusive.

2019-07-16, 20:04   #253
Dylan14

"Dylan"
Mar 2017

2×3×83 Posts

Quote:
 Originally Posted by The Carnivore Your ranges don't make sense. If, for example, 95*2^2000+/-1 were twin, which range would it fall under? The 1000-2000 one, or the 2000-3000 one? Here's the corrected version: Code: Range Smallest First Twin k n-value 1000-1999 177 1032 2000-2999 4359 2191 3000-3999 1149 3283 4000-4999 2565 4901 5000-5999 5775 5907 6000-6999 4737 6634 7000-7999 33957 7768 8000-8999 459 8529 9000-9999 33891 9869 10000-10999 10941 10601 11000-11999 915 11455 12000-12999 73005 12178 13000-13999 3981 13153 14000-14999 175161 14171 15000-15999 74193 15770 16000-16999 138153 16436 17000-17999 14439 17527 18000-18999 56361 18989 19000-19999 53889 19817 20000-20999 7485 20023 21000-21999 195045 21432 22000-22999 31257 22312 23000-23999 396213 23672 24000-24999 177141 24365 25000-25999 577065 25879 26000-26999 182697 26172 27000-27999 70497 27652 28000-28999 445569 28353 29000-29999 815751 29705 30000-30999 249435 30977 31000-31999 440685 31989 32000-32999 51315 32430 33000-33999 143835 33826 34000-34999 959715 34895 35000-35999 338205 35351 36000-36999 47553 36172 37000-37999 201843 37630 38000-38999 683145 38746 39000-39999 126423 39606 40000-40999 604329 40315 41000-41999 358965 41653 42000-42999 272139 42379 43000-43999 441201 43167 44000-44999 >1M ??? 45000-45999 311541 45439 46000-46999 >1M ??? 47000-47999 103893 47122 48000-48999 694599 48501 49000-49999 197109 49733* *This may not be the right k/n pair. It was obtained from https://www.mersenneforum.org/showpo...&postcount=217 which says that only 0
I have searched n = 49796-49999 through to k = 1M (using twinsieve from the mtsieve suite and LLR) and found no twins. Hence the k/n pair for 49000-49999 is the right one.
If you need residues from that search, I have them.

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