20130130, 10:56  #243 
Oct 2006
104_{16} 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. Congrats on your twin, MooMoo2! 
20130130, 11:06  #244 
Oct 2006
2^{2}×5×13 Posts 
Also, an update on the statistics of where these lowest twins are being found:

20130205, 11:45  #245 
Mar 2006
Germany
17·167 Posts 
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? 
20130207, 01:42  #246 
Oct 2006
2^{2}·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.

20161218, 17:28  #247  
Nov 2016
2148_{10} Posts 
Quote:
e.g. k=237, for every integer n>=1, either 237*2^n+1 or 237*2^n1 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^n1 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 20161218 at 17:44 

20161218, 17:55  #248 
Nov 2016
864_{16} 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. Last fiddled with by sweety439 on 20161218 at 18:13 
20161218, 18:14  #249 
Nov 2016
2^{2}·3·179 Posts 
Update the current right text file.
Last fiddled with by sweety439 on 20161218 at 18:15 
20161221, 17:16  #251 
Nov 2016
4144_{8} Posts 
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 20161221 at 17:16 
20190706, 23:50  #252  
Jun 2010
179 Posts 
Quote:
Here's the corrected version: Code:
Range Smallest First Twin k nvalue 10001999 177 1032 20002999 4359 2191 30003999 1149 3283 40004999 2565 4901 50005999 5775 5907 60006999 4737 6634 70007999 33957 7768 80008999 459 8529 90009999 33891 9869 1000010999 10941 10601 1100011999 915 11455 1200012999 73005 12178 1300013999 3981 13153 1400014999 175161 14171 1500015999 74193 15770 1600016999 138153 16436 1700017999 14439 17527 1800018999 56361 18989 1900019999 53889 19817 2000020999 7485 20023 2100021999 195045 21432 2200022999 31257 22312 2300023999 396213 23672 2400024999 177141 24365 2500025999 577065 25879 2600026999 182697 26172 2700027999 70497 27652 2800028999 445569 28353 2900029999 815751 29705 3000030999 249435 30977 3100031999 440685 31989 3200032999 51315 32430 3300033999 143835 33826 3400034999 959715 34895 3500035999 338205 35351 3600036999 47553 36172 3700037999 201843 37630 3800038999 683145 38746 3900039999 126423 39606 4000040999 604329 40315 4100041999 358965 41653 4200042999 272139 42379 4300043999 441201 43167 4400044999 >1M ??? 4500045999 311541 45439 4600046999 >1M ??? 4700047999 103893 47122 4800048999 694599 48501 4900049999 197109 49733* which says that only 0<n<49796 has been done for k <1M. A lower k value may be found for n=4979649999, inclusive. 

20190716, 20:04  #253  
"Dylan"
Mar 2017
498_{10} Posts 
Quote:
If you need residues from that search, I have them. 

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