News
The next days i will create several threads for some described categories where results can be posted.

i've inserted a new datapage for Constantn Searches.
see the 'Data Section' menu. more to come. 
i made a greater update of all pages (changed htmlcode: 'class' instead of 'id', no visible change of the pages, only htmlrestrictions) so all will be shown updated, but without any new data on most of them.
new:  page with download(s): all shown prime in the DataSection in a ZIPfile in LLRinputformat (one k/npair per line ascending in n) the ToDolist grows but i keep the data current (new primes from Top5000 added)! i'll include more low primes 10k<n<20k for 3000<k<10000 from T.Ritschel (thanks) 
Update of the Statisticspage (without SophieGermain yet) and a new Download (all Twins).

Resume 2009
It's time for a [b]resume for 2009[/b]:
I've updated the statisticspage (SophieGermain not yet): currently in the Database:  7900 kvalues  150000 primes  3100 twins  added [b]all[/b] Aliquot Sequences < 1000000: currently 9345 open ended  added pages for Home Primes Base 2, 6 and 10 So for 2009 i've added about 350 kvalues, 14000 primes, 70 twins and 3700 Top5000links (to consider: all kvalues < 10000 and all twins < 10000 were already in the Database!). [b]Historical note[/b]: My first page from April 2007 contained about 1500 kvalues with 12000 primes! Although i've added such an amout of data the last 3 years, there's much more data to fill in and to update. As my real life will allow me, i'll try to spend much time on updating almost every day although it's not visible at all. I thank everybody contributing their results here/me for including in the Database. Information is what i need: i'm aware of new primes in the Top5000 Database from C.Caldwell but 'small' primes everybody should send them to me. And of course it's important for me to know the ranges done. [b]Lookout for 2010[/b]:  Updating [b]all[/b] Project pages  including more primes from Top5000 (older/smaller ones)  extending the ConstantnSearch page and the Payampage  finding some errors (i'm sure there're some) and  finding much primes myself (44 Top5000 in 2009 and many small ones) Karsten 
Status 1.Quarter 2010
7915 kvalues
153084 primes 3125 twins 8460 Top5000links 
I've updated all kvalues from the RieselProblem with current search limits from PrimeGrid.
There're 64 kvalues. Two of them (342847 and 444637) are done to n=5.0M, because of their very low Nashweights. 
I've updated the Downloadpage with entries for LLRnet V0.72 and V0.73 and the history of this tool.

Status 2.Quarter 2010
8050 kvalues (135+)
161669 primes (~8600+) 3456 twins (~330+) 9224 Top5000links (~760+) 
1 Attachment(s)
Graph of all primes of the form k*2^n1 with 1 <= k <= 10000 and 1 <= n <= 3,000,000 in the Database as of 20100711: 123,139 counting.
18 primes with n>3,000,000 are not shown here. 
I've finished the RPS 9 k's drive page. This drive was done in 2009 for 9'ks < 300.
I've also updated the k<300 page but not yet for the 6th drive and k=5, 15, 17, 105. Those pages will be the next goal for updates. 
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.Penné, 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. 
I've included a new page:
First odd k, for which k*2^n1 is prime, n<=10000 Maximum kvalue so far: k=55999 for n=8867. A graph presents all values. I plan to continue this table and add such page for k*2^n+1, too. 
[QUOTE=kar_bon;263806]I've included a new page:
First odd k, for which k*2^n1 is prime, n<=10000 Maximum kvalue so far: k=55999 for n=8867. A graph presents all values. I plan to continue this table and add such page for k*2^n+1, too.[/QUOTE] Are you using ppsieve for this? I suspect for sieving a large range of starting k from 1 it would be faster. 
[QUOTE=henryzz;263856]Are you using ppsieve for this? I suspect for sieving a large range of starting k from 1 it would be faster.[/QUOTE]
No. I used pfgw for this range of small primes. Most of the values are already known in my database (where k<10000), so only the kvalues >10000 were done new. 
Status 2nd Quarter 2011
[b]Riesel:[/b]
8062 kvalues (7+) 164378 primes (1436+) 3462 twins (5+) 10565 Top5000links (1033+) [b]Proth:[/b] 5000 kvalues 149539 primes 2271 twins 21819 Top5000links  Changes since last Status (3rd Quarter 2010)  Prothside still only kvalues < 10000  Statspage, Prime and Twinlists (for download) will be updated later today 
I've included a 'new' page with my first version of these pages online in 2007 at RPS to see, how much the data and lookalike changed since then.
There's also a link to the thread in this forum, where I announced that page and the development is shown. You can find these updates in the Menu 'General' > 'History'. 
I've included a new page for the first odd k, for which k*2^n+1 is prime, n<=10000.
A graph is shown, too. 
I need to ask if you are interested in having CUDA TF available...

[QUOTE=Christenson;266655]I need to ask if you are interested in having CUDA TF available...[/QUOTE]
About 95% of my time I'm participating in the NPLB project and the ranges are already sieved to best fit. The last page I've done with PFGW, so no need to sieve fast and deep. 
At least with Mersennes, TF on CUDA can be ~100x faster than TF on CPUs...moving up the optimum sieving by half a dozen bits.

[QUOTE=Christenson;266679]At least with Mersennes, TF on CUDA can be ~100x faster than TF on CPUs...moving up the optimum sieving by half a dozen bits.[/QUOTE]
Not quite sure what you mean by "optimum", but I do understand "hitting the wall". That is the nature of exponential growth. 2^7 =128 
By optimum I mean minimizing the total expected effort expended against a given set of interesting expressions/numbers to classify them all. For mersenne numbers, that means showing that a factor exists and once in a long while showing that it doesn't. For these, it might be getting to a known factor or knowing the expression is prime.

[QUOTE=Christenson;266655]I need to ask if you are interested in having CUDA TF available...[/QUOTE]
FYI, for Riesel numbers (k*2^n1) and their close cousins the Proth numbers (k*2^n+1), the prefactoring process is a little different than how it's done for Mersennes. Instead of trial factoring each individual candidate to a specific bit level, the most efficient way to do it for these numbers is to use a sieve to screen out factors over a wide range of candidates: for instance, all n<10M at once. The current state of the art sieving programs for these numbers are tpsieve and the srsieve family of sieves (srsieve, sr1sieve, sr2sieve, and sr5sieve, each being particularly applicable for different scenarios). tpsieve has been ported to CUDA (where a similar speedup over CPUs has been realized, akin to that with mfaktc for Mersenne numbers); it works most efficiently on very large continuous ranges of k and n, and as such it is most well suited to a large project. Currently, the [URL="http://www.primegrid.com/"]PrimeGrid[/URL] project is using this program through BOINC to sieve all of k<10000, n<6M on both the Riesel and Proth sides simultaneously; the sieve files produced by this effort are then made freely available to other projects (such as NPLB and RPS in the mersenneforum, and individual searchers coordinating in this subforum). With all the GPU power being thrown at this effort, everything below n=3M is at this point fully sieved to the optimal factor depth (the point at which CPUs can run primality tests faster than the GPUs can find factors); the current range in progress is for n=3M6M, with n=6M9M in the early initial stages of sieving. For some more specialized searches (for instance, such as those done by the Conjectures 'R Us project here at mersenneforum), tpsieve's preference for large swaths of k and n works against it; for these, one needs to use the srsieve programs, which unfortunately have not yet been ported to CUDA. I talked to the developer of tpsieve (Ken_g6 on this forum) about this, and he explained that srsieve's algorithm is much more difficult to implement on a GPU; he thus is not planning to undertake the effort in the near future. If anyone else, however, would like to try it, he would have the everlasting gratitude of the Conjectures 'R Us participants and others doing similar searches. :smile: Hopefully this explains things a bit! :geek: Max :smile: 
Terrible job...just terrible....*not!* :smile:
It does put a good bound on what to do with mfaktc, though...if I can ever get out from under work.... what wblipp had asked for was an mfaktcstyle TF on (41)^(large prime * various small, very smooth composites such as 2^3)1. It doesn't sound like it's worth it to extend to reisel or proth numbers. 
[QUOTE=Christenson;266875]what wblipp had asked for was an mfaktcstyle TF on (41)^(large prime * various small, very smooth composites such as 2^3)1.[/QUOTE]
I hope you are using 41 as a representative small number, not a hard coded constant. I'm interested in this for many small primes, not just 41. I'm worried that I have not accurately conveyed that idea. 
Updates:
 kvalues in page 8000<k<10000 are sorted  page for RPS Drive #7 completed (some missing countings still there) 
New page for RPS Drive #11 inserted.

I've included a page for the Project [b]"TPS  Twin Prime Search"[/b] (under "Other Projects").
Data included (up to 20101019 so far):  primes found (with person, date)  number of candidates tested and primes found by user  distribution of primes (table and graph)  graph with pairs returned to LLRnet/PRPnet server per day  ranges overview Some data from that:  159 primes found  804016 candidates tested 
I've included an ASCIIfile with Rieselprimes for 10000 < k < 100000 and
 all k's: n<=1007 (from G.Barnes)  k < 15000: n<=20000 (from T.Ritschel) Thanks both for the data. Some numbers:  the file is ~3MB in size  45000 kvalues  560708 primes  15280 twins The table gives for all kvalues the number of primes and the Nashweight, too. Twins are marked with '*'. 
[url=http://www.primegrid.com/forum_thread.php?id=3874]PrimeGrid[/url] found (by Timothy D. Winslow) the lagest Twin so far: [url=http://primes.utm.edu/primes/page.php?id=103792]3756801695685*2^666669±1[/url] on 20111225.

That's my last name. Who the hell is he? :razz:
Hmm. I found another Timothy Winslow online (and a whole family of Winslows. Presumably there are many of us.) 
New Riesel Prime found by [url=http://www.primegrid.com/download/trp162941.pdf]PrimeGrid[/url]:
[url=http://primes.utm.edu/primes/page.php?id=104170]162941*2^9937181[/url] found by D.Domanov. This prime was overlooked by the RieselSieveproject. Now 56 candidates left. 
Next Riesel Prime just verifying:
[url=http://primes.utm.edu/primes/page.php?id=107886]252191*2^54978781[/url] should be place 21 on Top5000. 
On occasion of the recent finds I've updated my pages for [url=http://www.rieselprime.de/Others/HomePrime10.htm]Home Prime Base 10 (49)[/url] and the [url=http://www.rieselprime.de/Others/EuclidMullin.htm]EuclidMullinSequence[/url].

I've extended the page with [url=http://www.rieselprime.de/Related/FirstSG.htm]First odd k with Sophie Germain[/url] from n=4000 to n=10000.

I don't really understand what the yellow values in that table are. The comment say "jumping champion  the highest k so far", but this can't be. For some of them there are very easy to find higher k's. For example for n=10, the table say k=141, in yellow. A oneliner in pari stops indeed at 141:
[CODE] gp > k=1; until(isprime(a)&&isprime(b), k++; print(k", "a=1024*k1", "factorint(a)",\t"b=2048*k1", "factorint(b))) 2, 2047, [23, 1; 89, 1], 4095, [3, 2; 5, 1; 7, 1; 13, 1] 3, 3071, [37, 1; 83, 1], 6143, Mat([6143, 1]) 4, 4095, [3, 2; 5, 1; 7, 1; 13, 1], 8191, Mat([8191, 1]) 5, 5119, Mat([5119, 1]), 10239, [3, 1; 3413, 1] 6, 6143, Mat([6143, 1]), 12287, [11, 1; 1117, 1] .... snip many lines .... 139, 142335, [3, 2; 5, 1; 3163, 1], 284671, [23, 1; 12377, 1] 140, 143359, [23, 2; 271, 1], 286719, [3, 1; 31, 1; 3083, 1] 141, 144383, Mat([144383, 1]), 288767, Mat([288767, 1]) gp> [/CODE] But then we can continue higher, removing the "k=1" in front, and it still stops at [B]153[/B], then a couple of uninteresting (even) values, then [B]735[/B], etc. These are not primes, but they are odd. From the other columns I see the numbers in the table are odd, not necessary primes (and there is no mention of primarity, indeed). I could easily "extend" some of the yellow cells higher. So, what exactly is the meaning of the yellow cells? 
[QUOTE=LaurV;319476]So, what exactly is the meaning of the yellow cells?[/QUOTE]
The table shows the first odd kvalue of Rieseltype numbers a=k*2^n1 and b=k*2^(n+1)1 for which a and b both primes (Sophie Germains). The yellow values are the highest [b]in this table[/b], so for n=10 k=141 is highest of all lower n and every time a kvalue is higher than the last yellow, it is marked yellow as new highest. 
Ah, got it now. Not very useful, however...

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