News

[kar_bon]

I've included a new page (available under menu 'Related' -> 'First SG'):

It shows the first odd k-value where the numbers k*2ⁿ-1 and k*2ⁿ⁺¹-1 are prime and therefore a Sophie-Germain pair.

For now there're only values for n<=70 listed, others will follow.

I've also created a DOS-batch to determine such values automatically:

@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

Name this batch 'run.bat'.
To run this batch, cllr.exe (available from J.Penné, developer of LLR V3.8.1) is needed, too.

Calling this script with
run start_k start_n
with start_k the k-value and start_n the n-value to start with, will search for a Sophie-Germain pair for n=start_n beginning at k=start_k and further ones (CTRL-C 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/n-pair 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 k-value 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 k-value.

[kar_bon]

I've changed the above script, because it's timings were very lousy!

Now I'm doing it this way:

@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

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 (CTRL-C).

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 n-value 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 n-value" will be reported in 'found.txt'.

This script took about an hour for n=1-430 (Q6600, 1 core, stock speed).

I've also updated the new page with some more values.

[kar_bon]

I've submitted the above sequence to "The On-Line Encyclopedia of Integer Sequences" and can be found here.

[kar_bon]

8055 k-values (5+)
162942 primes (~1300+)
3457 twins (1+)
9532 Top5000-links (308+)

Updated also Statistics and Riesel_all / Twins_all download files.

[kar_bon]

Found doubled prime in C.Caldwell's Top5000 Database:


155*2^67973+1 (now deleted!) and 155*2^67973+1.

[kar_bon]

I just noticed, that PrimeGrid found another Riesel-problem prime on 2011-04-05 (announcement here):

65531*2^3629342-1 is prime (1,092,546 digits, rank #29 on Top5000)

There're 'only' 61 k-values left to proove the Riesel-conjecture.

[kar_bon]

A new Riesel-Prime seems to be found yesterday: 123547*2^3804809-1. The verification is still in progress.

So (if it's a new one) 'only' 60 candidates left to proove the Riesel-Conjecture.

PS: Verification done.

[kar_bon]

And here's the next Riesel Prime in sight:

415267*2^3771929-1 is still in progress (a little bit smaller than the last one).

So 59 candidates left.

[kar_bon]

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 Proth-pages (thanks W.Keller).

[kar_bon]

The next Riesel Prime:

141941*2^4299438-1 is still in progress.

So 58 candidates left.

[kar_bon]

Next Riesel Prime:

353159*2^4331116-1 just verifying.

Now 57 candidates left.