20100507, 19:33  #12 
May 2007
Kansas; USA
23551_{8} Posts 

20100507, 19:54  #13  
May 2007
Kansas; USA
3^{2}·19·59 Posts 
Quote:
The main thing that I found is that they just "die off" for n>~1500. BTW, one hint that you may have already realized: You only need to check k's divisible by 3. It's not possible for a 1 and +1 prime for k's that are not divisible by 3. Either k*b^n1 or k*b^n+1 will have a factor of 3. Another interesting effort would be to check k*b^n1 primes for k*b^n3 primes to make a twin in that manner. Of course you could not prove anything that would make the top 20 but you probably could prove n<=10K in a reasonable amount of time and the chances are very small that you would find anything larger than that anyway. Gary 

20100507, 20:45  #14 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
way to ruin my fun GD I was just going to post about that though I related 3 slightly differently (no surprise on that). I got it through (p+1/2^n)*2^n1, must switch to (p1/2^n)*2^n+1. I found that p gave a x in my comparison that was always a multiple of 3*2^n all minus 1. Anyways for now PM me if you want more info if I don't figure anything new out.
Last fiddled with by science_man_88 on 20100507 at 20:56 
20100507, 23:46  #15  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
Status: n=283k. 471 numbers remaining to test, ignoring any future sieving (I've got it sieved to 600M and am ready to break off n=300k400k). Nothing new to report. I've only confirmed primes.
Quote:
Quote:
Quote:
Last fiddled with by MiniGeek on 20100507 at 23:51 

20100508, 12:01  #16 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
Status: complete to n=400k. No surprises so far.
Previously I've been running on one core only, now I'm running n=400k+ on all 4 cores, with manual LLR with the work split roughly evenly (figured it'd be less trouble than getting PRPnet to run it...and I don't really care if the slowest core, or largest work chunk, takes 50% longer than the shortest one, because I've got PRPnet running below it to use my CPU when it can, and with work like this such a thing would mean hours longer to wait, not days). The candidates become very thin after about n=700000 (something like how the twins become very thin after about n=1500). This may be due to the search depths of efforts to find Riesel primes, the sparseness of primes that large, or a combination (I'd guess most likely a combination based mostly on the search depths). e.g. there are only 27 candidates for n>700k remaining after sieving to 2G. For comparison, there are 254 with 400k<n<700k, and 662 in 100k<n<400k) The odds of a twin in that few candidates is exceedingly slim. But there's always a chance. And it's much less effort than directly looking for a twin that large. Unfortunately, it means you're limited to a small search space, until people hurry up and find more huge primes! Even though I don't expect to find any large primes now, it's not as if the work was all wasted. Now everyone can know that the Riesel primes as of 20100507 were checked for twins, and that they don't need to duplicate that work. Plus it's helped fill in twin primes in Karsten's list. This check should be redone now and then with the new primes. To that end, the current list of primes should be archived somewhere. Karsten? Would anyone like me to post all of the results, for possible doublechecking? Some (interesting?) trivia: the median n (median=half are smaller, half are larger) for all known primes of the form k*2^n1 (assuming Karsten's list is exhaustive, which is a close enough assumption) is 923. The median n for all known twin primes of the form k*2^n±1 (assuming my current list of twins is exhaustive, which is also a close enough assumption) is 15. Since the odds of finding another twin are so slim, I'll post the lists now. This is the list of new twin primes: (ones that I found that were not on Karsten's list) Code:
1164735 1 1587045 1 5154945 1 14421825 1 18544365 1 26277285 1 65737005 1 94708605 1 1770403635 1 20887630335 1 67740637965 1 202635 2 1082115 2 1105845 2 2447445 2 2448855 2 17179515 2 26277285 2 31400085 2 42932385 2 1355509155 2 2794023375 2 52873540005 2 323169 3 589305 3 1669995 3 2448855 3 31400085 3 47915595 3 94708605 3 99311355 3 1355509155 3 43455956115 3 3710369067405 3 237915 4 422427 4 1303035 4 1669995 4 2222415 4 2332125 4 5128905 4 13867245 4 25308855 4 39598845 4 60627945 4 74784765 4 76298145 4 2995125705 4 666945 5 979125 5 1303035 5 2448855 5 3536385 5 18544365 5 49619895 5 2305225065 5 3234846615 5 4042850955 5 52890983145 5 101413071045 5 979125 6 1164735 6 2448855 6 8311875 6 18544365 6 31400085 6 1810322085 6 1885495755 6 2794023375 6 43455956115 6 1164735 7 5128905 7 5775915 7 14421825 7 39418665 7 56591535 7 2995125705 7 944007 8 42932385 8 5128905 9 5169615 9 56591535 9 1810322085 9 1587045 10 2995125705 10 3234846615 10 52890983145 10 20049 11 17179515 12 88335225 13 76220123265 13 101413071045 13 26277285 14 76220123265 14 1164735 15 6553365 15 1064887395 15 69234960795 15 237915 16 3271575 16 2995125705 16 43455956115 16 52873540005 17 59463215955 17 13935645 18 1105845 19 74784765 19 3234846615 19 72992835135 20 1164735 21 4849845 21 944007 22 39598845 22 323169 25 5169615 27 72992835135 27 14361 29 420147 30 99311355 30 1946388015 31 5128905 33 3710369067405 33 323169 37 8311875 37 67740637965 38 323169 39 20049 41 6021525 41 1946388015 43 1105845 44 25308855 45 2305225065 45 1105845 46 104598726375 51 46650333015 52 3234846615 57 48797387925 61 76298145 64 3710369067405 69 74784765 79 2995125705 84 104598726375 92 420147 110 6021525 121 13867245 127 4849845 132 2889081195 133 3710369067405 150 237123 154 5154945 162 52654604145 201 59463215955 207 4849845 272 8311875 295 8311875 411 52873540005 443 69234960795 459 59463215955 461 99311355 464 56591535 468 2305225065 485 67740637965 668 104598726375 761 42932385 832 srfile changed "58644190679703485491635 29" to "1991269380820904371 29". I think srfile must have truncated it to 16 hexdigits (64 bits), as in hex those k's are c6b1ba268f39ff129b3 and 1ba268f39ff129b3, respectively. 58644190679703485491635*2^29±1 are indeed prime. 1991269380820904371*2^29±1 are not prime. Because of this bug, 58644190679703485491635 29 is not on my list of twins, but is really a twin. (I only discovered this while writing this post) Last fiddled with by MiniGeek on 20100508 at 12:43 
20100508, 13:55  #17 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
good work mini by the way I got my mouse working again switched ports which let windows download a driver.

20100508, 17:01  #18 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
Status: various, but ~over half done (n=454k is the status of 400k500k)
Correction: 919. I forgot to sort the list, and Karsten's list has some very large k's prime's outoforder. This pushed the apparent median to the incorrect value of 923. Last fiddled with by MiniGeek on 20100508 at 17:21 
20100508, 17:12  #19 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
17·251 Posts 

20100508, 22:06  #20 
Mar 2006
Germany
2765_{10} Posts 
I've just updated the Summary pages at RieselPrimeDatabase with the last 164 missing Twin primes so far.
Tim, if you find some more, please post here, too. I've not yet updated the Download list of all Twin primes. 
20100509, 11:58  #21 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
I've completed the search with no more primes found.
Again, if anybody wants results or anything, they're available on request. Factors aren't, as I used srsieve and didn't tell it to write the factors out (it just removed them from the sieve file). Last fiddled with by MiniGeek on 20100509 at 12:00 
20101117, 22:02  #22 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
I reran this on the list of primes as of 20101006 (only running on the difference between this and the earlier list, which was 20100507) and found just one new twin:
1071495*2^49±1 are prime (21 digits) 
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