-   Riesel Prime Data Collecting (k*2^n-1) (
-   -   News (

kar_bon 2008-11-27 12:32

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

kar_bon 2008-12-11 11:17

i've inserted a new data-page for Constant-n Searches.

see the 'Data Section' menu. more to come.

kar_bon 2009-01-07 10:55

i made a greater update of all pages (changed html-code: 'class' instead of 'id', no visible change of the pages, only html-restrictions) so all will be shown updated, but without any new data on most of them.

- page with download(s): all shown prime in the DataSection in a ZIP-file in LLR-input-format (one k/n-pair per line ascending in n)

the ToDo-list 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)

kar_bon 2009-02-11 10:28

Update of the Statistics-page (without Sophie-Germain yet) and a new Download (all Twins).

kar_bon 2010-01-04 01:44

Resume 2009
It's time for a [b]resume for 2009[/b]:

I've updated the statistics-page (Sophie-Germain not yet):

currently in the Database:

- 7900 k-values
- 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 k-values, 14000 primes, 70 twins and 3700 Top5000-links
(to consider: all k-values < 10000 and all twins < 10000 were already in the Database!).

[b]Historical note[/b]:

My first page from April 2007 contained about 1500 k-values 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 Constant-n-Search page and the Payam-page
- finding some errors (i'm sure there're some)
- finding much primes myself (44 Top5000 in 2009 and many small ones)


kar_bon 2010-04-01 15:38

Status 1.Quarter 2010
7915 k-values
153084 primes
3125 twins
8460 Top5000-links

kar_bon 2010-05-28 09:14

I've updated all k-values from the Riesel-Problem with current search limits from PrimeGrid.

There're 64 k-values. Two of them (342847 and 444637) are done to n=5.0M, because of their very low Nash-weights.

kar_bon 2010-06-03 20:54

I've updated the Download-page with entries for LLRnet V0.72 and V0.73 and the history of this tool.

kar_bon 2010-07-09 10:25

Status 2.Quarter 2010
8050 k-values (135+)
161669 primes (~8600+)
3456 twins (~330+)
9224 Top5000-links (~760+)

kar_bon 2010-07-13 10:16

1 Attachment(s)
Graph of all primes of the form k*2^n-1 with 1 <= k <= 10000 and 1 <= n <= 3,000,000 in the Database as of 2010-07-11: 123,139 counting.

18 primes with n>3,000,000 are not shown here.

kar_bon 2010-07-20 10:37

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.

kar_bon 2010-07-22 02:11

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

It shows the first odd k-value where the numbers k*2[sup]n[/sup]-1 and k*2[sup]n+1[/sup]-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

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

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
[b]run start_k start_n[/b]
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'.

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.

I've changed the script to continue from a certain k-value.

kar_bon 2010-07-23 18:06

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

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

set /a kmin=1000000
set /a kmax=10000000
del llr.ini
goto begin

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).

- 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 2010-07-28 00:38

I've submitted the above sequence to [b]"The On-Line Encyclopedia of Integer Sequences"[/b] and can be found [url=]here[/url].

kar_bon 2010-10-06 09:12

Status 3rd Quarter 2010
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 2010-10-17 17:12

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

[url=]155*2^67973+1[/url] (now deleted!) and [url=]155*2^67973+1[/url].

kar_bon 2011-04-21 10:48

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

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

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

kar_bon 2011-05-12 07:23

A new Riesel-Prime seems to be found yesterday: [url=]123547*2^3804809-1[/url]. 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 2011-05-13 23:49

And here's the next Riesel Prime in sight:

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

So 59 candidates left.

kar_bon 2011-05-24 19:53

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 2011-05-29 15:30

The next Riesel Prime:

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

So 58 candidates left.

kar_bon 2011-06-01 11:09

Next Riesel Prime:

353159*2^4331116-1 just verifying.

Now 57 candidates left.

kar_bon 2011-06-14 23:09

I've included a new page:

First odd k, for which k*2^n-1 is prime, n<=10000

Maximum k-value 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.

henryzz 2011-06-15 17:10

[QUOTE=kar_bon;263806]I've included a new page:

First odd k, for which k*2^n-1 is prime, n<=10000

Maximum k-value 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.

kar_bon 2011-06-16 07:40

[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 k-values >10000 were done new.

kar_bon 2011-07-08 09:49

Status 2nd Quarter 2011
8062 k-values (7+)
164378 primes (1436+)
3462 twins (5+)
10565 Top5000-links (1033+)

5000 k-values
149539 primes
2271 twins
21819 Top5000-links

- Changes since last Status (3rd Quarter 2010)
- Proth-side still only k-values < 10000
- Stats-page, Prime- and Twin-lists (for download) will be updated later today

kar_bon 2011-07-09 01:24

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'.

kar_bon 2011-07-15 22:02

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.

Christenson 2011-07-17 03:46

I need to ask if you are interested in having CUDA TF available...

kar_bon 2011-07-17 11:13

[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.

Christenson 2011-07-17 12:51

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.

davieddy 2011-07-17 16:13

[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

Christenson 2011-07-17 16:24

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.

mdettweiler 2011-07-18 18:43

[QUOTE=Christenson;266655]I need to ask if you are interested in having CUDA TF available...[/QUOTE]
FYI, for Riesel numbers (k*2^n-1) 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=""]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=3M-6M, with n=6M-9M 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:

Christenson 2011-07-19 00:22

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 mfaktc-style 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.

wblipp 2011-07-19 13:02

[QUOTE=Christenson;266875]what wblipp had asked for was an mfaktc-style 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.

kar_bon 2011-08-03 19:56


- k-values in page 8000<k<10000 are sorted
- page for RPS Drive #7 completed (some missing countings still there)

kar_bon 2011-09-09 11:23

New page for RPS Drive #11 inserted.

kar_bon 2011-10-24 16:27

I've included a page for the Project [b]"TPS - Twin Prime Search"[/b] (under "Other Projects").

Data included (up to 2010-10-19 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

kar_bon 2011-11-24 00:46

I've included an ASCII-file with Riesel-primes 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 k-values
- 560708 primes
- 15280 twins

The table gives for all k-values the number of primes and the Nash-weight, too.
Twins are marked with '*'.

kar_bon 2011-12-26 09:32

[url=]PrimeGrid[/url] found (by Timothy D. Winslow) the lagest Twin so far: [url=]3756801695685*2^666669±1[/url] on 2011-12-25.

Dubslow 2011-12-31 23:19

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.)

kar_bon 2012-02-03 10:30

New Riesel Prime found by [url=]PrimeGrid[/url]:

[url=]162941*2^993718-1[/url] found by D.Domanov.

This prime was overlooked by the RieselSieve-project.

Now 56 candidates left.

kar_bon 2012-06-23 17:48

Next Riesel Prime just verifying:

[url=]252191*2^5497878-1[/url] should be place 21 on Top5000.

kar_bon 2012-09-11 21:32

On occasion of the recent finds I've updated my pages for [url=]Home Prime Base 10 (49)[/url] and the [url=]Euclid-Mullin-Sequence[/url].

kar_bon 2012-11-23 17:49

I've extended the page with [url=]First odd k with Sophie Germain[/url] from n=4000 to n=10000.

LaurV 2012-11-24 06:44

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 one-liner in pari stops indeed at 141:

[CODE] gp > k=1; until(isprime(a)&&isprime(b), k++; print(k", "a=1024*k-1", "factorint(a)",\t"b=2048*k-1", "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])

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?

kar_bon 2012-11-24 10:29

[QUOTE=LaurV;319476]So, what exactly is the meaning of the yellow cells?[/QUOTE]

The table shows the first odd k-value of Riesel-type numbers a=k*2^n-1 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 k-value is higher than the last yellow, it is marked yellow as new highest.

LaurV 2012-11-24 10:59

Ah, got it now. Not very useful, however...

All times are UTC. The time now is 20:44.

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.