I've included a new page (available under menu 'Related' > 'First SG'):
It shows the first odd kvalue where the numbers k*2[sup]n[/sup]1 and k*2[sup]n+1[/sup]1 are prime and therefore a SophieGermain pair. For now there're only values for n<=70 listed, others will follow. I've also created a DOSbatch to determine such values automatically: [code] @echo off set /a kval=%1 set /a nval=%2 :begin title k=%kval% n=%nval% echo 1:S:0:2:16394>SG.txt echo %kval% %nval% >>SG.txt cllr SG.txt if exist SG.res goto loop_nextn del llr.ini set /a kval=%kval%+6 goto begin :loop_nextn findstr /c:" " sg.res >>found.txt del sg.res sg.txt llr.ini lresults.txt set /a nval=%nval%+1 set /a kval=3 goto begin [/code] Name this batch 'run.bat'. To run this batch, cllr.exe (available from J.PennĂ©, developer of LLR V3.8.1) is needed, too. Calling this script with [b]run start_k start_n[/b] with start_k the kvalue and start_n the nvalue to start with, will search for a SophieGermain pair for n=start_n beginning at k=start_k and further ones (CTRLC will stop this script). After stopping the batch, it can be restarted with the pair given in the file SG.txt (saved during the last run). Every found k/npair will be written to the file 'found.txt'. Note: Starting with start_n < 3 will give the false result for n=2, because the script starts always at k=3 (and incement the kvalue by 6 > only possible values for SG's). Perhaps others want to find some more ranges. Please post your results here. PS: I've changed the script to continue from a certain kvalue. 
I've changed the above script, because it's timings were very lousy!
Now I'm doing it this way: [code] @echo off set /a nval=%1 set /a kmin=1 set /a kmax=1000000 :begin title n=%nval% cnewpgen wp=%nval%.txt t=3 base=2 n=%nval% kmin=%kmin% kmax=%kmax% own osp=1000000000 >nul cllr oStopOnSuccess=1 %nval%.txt >nul if exist %nval%.res goto loop_nextn if %kmin%==1 goto loop_nextk echo 0 %nval%>>%nval%.res goto loop_nextn :loop_nextk set /a kmin=1000000 set /a kmax=10000000 del llr.ini goto begin :loop_nextn findstr /c:" " %nval%.res >>found.txt del %nval%.txt %nval%.res llr.ini lresults.txt set /a kmin=1 set /a kmax=1000000 set /a nval=%nval%+1 goto begin [/code] To run this batch, cllr.exe and cnewpgen.exe are needed. Calling 'run 1' will start to search for a SG at n=1 and further until it will stopped (CTRLC). Steps:  NewPGen will sieve for SG (base=2, n as above, kmin=1, kmax=1e6, pmax=1e9)  LLR will test the sieve file and stops when a SG was found  next nvalue will tested automatically If for 1<=k<=1e6 no SG was found, the range 1e6<=k<=1e7 will be tested again. If this also fails to find a SG, the value "0 nvalue" will be reported in 'found.txt'. This script took about an hour for n=1430 (Q6600, 1 core, stock speed). I've also updated the new page with some more values. 
I've submitted the above sequence to [b]"The OnLine Encyclopedia of Integer Sequences"[/b] and can be found [url=http://www2.research.att.com/~njas/sequences/A179658]here[/url].

Status 3rd Quarter 2010
8055 kvalues (5+)
162942 primes (~1300+) 3457 twins (1+) 9532 Top5000links (308+) Updated also Statistics and Riesel_all / Twins_all download files. 
Found doubled prime in C.Caldwell's Top5000 Database:
[url=http://primes.utm.edu/primes/page.php?id=62875&deleted=1]155*2^67973+1[/url] (now deleted!) and [url=http://primes.utm.edu/primes/page.php?id=8508]155*2^67973+1[/url]. 
I just noticed, that PrimeGrid found another Rieselproblem prime on 20110405 (announcement [url=http://www.primegrid.com/download/trp65531.pdf]here[/url]):
[url=http://primes.utm.edu/primes/page.php?id=99479]65531*2^36293421[/url] is prime (1,092,546 digits, rank #29 on Top5000) There're 'only' 61 kvalues left to proove the Rieselconjecture. 
A new RieselPrime seems to be found yesterday: [url=http://primes.utm.edu/primes/page.php?id=100051]123547*2^38048091[/url]. The verification is still in progress.
So (if it's a new one) 'only' 60 candidates left to proove the RieselConjecture. PS: Verification done. 
And here's the next Riesel Prime in sight:
[url=http://primes.utm.edu/primes/page.php?id=100064]415267*2^37719291[/url] is still in progress (a little bit smaller than the last one). So 59 candidates left. 
New page for RPS 2nd Megabit Drive included.
Factors of Fermats and Generalized Fermats maked for k<=9 and some in 1000<k<100000 on the Prothpages (thanks W.Keller). 
The next Riesel Prime:
141941*2^42994381 is still in progress. So 58 candidates left. 
Next Riesel Prime:
353159*2^43311161 just verifying. Now 57 candidates left. 
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