List of most small twins of form k*2^n+/-1 - Page 23

roger · 2013-01-30, 10:56

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.

Congrats on your twin, MooMoo2!

roger · 2013-01-30, 11:06

Also, an update on the statistics of where these lowest twins are being found:

kar_bon · 2013-02-05, 11:45

Quote:

Originally Posted by roger

15000<n<16000 done:

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!

Please check this.

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?

roger · 2013-02-07, 01:42

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.

sweety439 · 2016-12-18, 17:28

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.

sweety439 · 2016-12-18, 17:55

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.

sweety439 · 2016-12-18, 18:14

Update the current right text file.

kar_bon · 2016-12-21, 07:49

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.

sweety439 · 2016-12-21, 17:16

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.

The Carnivore · 2019-07-06, 23:50

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.

Dylan14 · 2019-07-16, 20:04

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

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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2013-02-07, 01:42	#246
roger Oct 2006 2²·5·13 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.

2016-12-21, 07:49	#250
kar_bon Mar 2006 Germany 2·1,481 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.