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-   -   Bases 501-1030 reservations/statuses/primes (https://www.mersenneforum.org/showthread.php?t=12994)

 rogue 2010-02-17 21:19

[QUOTE=gd_barnes;205942]Do you set factoring to 100% with the -f switch when running the new bases script? If not, that would explain things. Without trial factoring, you can't go too far before sieving is more CPU efficient.[/QUOTE]

No, I have used -f with a script. I hadn't really even thought about it. If and when I tackle another difficult base (such as 928), I will use it.

 rogue 2010-02-19 02:28

Riesel base 923

Primes found:

2*923^2-1
4*923^1-1
6*923^114-1

The conjecture is proven.

 rogue 2010-02-19 02:29

Riesel Base 881

Primes found:

2*881^132-1
4*881^3-1

k=6 has trivial factors. The conjecture is proven.

 rogue 2010-02-19 02:30

Riesel base 860

Primes found:

2*860^62-1
3*860^1-1
4*860^3-1
5*860^12-1
6*860^4-1
7*860^5-1

k=1 has trivial factors. This conjecture is proven.

 rogue 2010-02-19 02:31

Riesel Base 818

Primes found:

2*818^2-1
3*818^4-1
4*818^1-1
5*818^4-1
6*818^2-1
7*818^3-1

k=1 has trivial factors. The conjecture is proven

 rogue 2010-02-19 02:32

Riesel base 797

Primes found:

2*797^2-1
4*797^1-1
6*797^2-1

This conjecture is proven.

 rogue 2010-02-19 02:33

Riesel Base 776

Primes found:

2*776^4-1
3*776^2-1
4*776^3-1
5*776^12-1
7*776^1-1

k=1 and k=6 have trivial factors. This conjecture is proven.

 rogue 2010-02-19 02:34

Riesel Base 762

Primes found:

2*762^1-1
3*762^116-1
4*762^7-1
5*762^4-1
6*762^2-1
7*762^1-1

k=1 has trivial factors. This conjecture is proven.

 rogue 2010-02-19 02:35

Riesel Base 755

Primes found:

2*755^62-1
4*755^1-1
6*755^18-1

The conjecture is proven.

 rogue 2010-02-19 12:14

Riesel Base 520

1 Attachment(s)
The primes are attached.

These k remain
[code]
179*520^n-1
216*520^n-1
324*520^n-1
330*520^n-1
576*520^n-1
638*520^n-1
1094*520^n-1
[/code]

The other k have trivial factors.

I have tested to n=25000 and am releasing the base.

 gd_barnes 2010-02-19 21:37

From my former k=2 search:

R515 is complete to n=25K; only k=2 remains; base released.

 rogue 2010-02-20 06:16

I'll take Riesel base 515 and see if I can prove it.

 rogue 2010-02-23 13:25

2*515^58466-1 is prime.

This prove the Riesel conjecture for base 515 and takes one off the list.

 rogue 2010-02-23 13:31

Taking Sierpinski base 969 with conjectured k = 96.

BTW, I proved Riesel conjecture for base 515. 2*515^58466-1 is prime.

 rogue 2010-02-23 21:29

Sierpinski base 969

Primes found:

[code]
2*969^4+1
4*969^1+1
6*969^5888+1
8*969^1+1
12*969^8+1
14*969^1+1
16*969^16+1
18*969^1+1
20*969^1+1
22*969^1+1
24*969^83+1
26*969^8714+1
28*969^5+1
30*969^24+1
34*969^5+1
36*969^2+1
38*969^3+1
40*969^12+1
42*969^1+1
44*969^107+1
46*969^56+1
48*969^8+1
50*969^6+1
52*969^621+1
56*969^4+1
58*969^2+1
60*969^4+1
62*969^2+1
64*969^1+1
66*969^1068+1
68*969^8+1
70*969^2+1
72*969^2+1
74*969^1+1
78*969^1+1
80*969^1+1
82*969^2+1
84*969^5+1
86*969^90+1
88*969^9+1
90*969^1+1
92*969^7+1
94*969^113+1
[/code]

The other k have trivial factors.

This conjecture is proven.

 rogue 2010-02-23 21:30

I'm taking Riesel base 679.

 gd_barnes 2010-02-23 21:41

[quote=rogue;206458]Taking Sierpinski base 969 with conjectured k = 96.

BTW, I proved Riesel conjecture for base 515. 2*515^58466-1 is prime.[/quote]

Wow, excellent on the proof! Very good.

I'm just amazed at how easily k=2 continues falling on the Riesel side but how difficult it is to find a prime for on the Sierp side. At the moment, there are 7 Sierp bases <= 500 that have k=2 remaining but only 2 Riesel bases; 170 and 303. There are also FAR more remaining on the Sierp side for bases 501 thru 1024.

 KEP 2010-02-25 09:04

Reserving Riesel base=900 k=22, sieving is already (and paused) at ~½ T.

KEP

Ps. More detailed status update will follow as of tomorrow :smile:

 KEP 2010-02-26 13:12

Detailed and way more factbased status update as of February 26th 2010:

Reserved from Riesel single k test on February 25th 2010: k=22 b=900, for later testing on the Quad.

Regarding Sierpinski base 955 (all k's): Limiting my reservation to n=10K. Estimated completion date is July 31st 2010 (Did anyone of you know that July is the month of Julius Ceasar and that there is 31 days in July in honor of Julius Ceasar).

Here after, it will be all six cores hammering the single k's remaining and starting with Riesel base 900 k=22 :smile:

KEP

Ps. This makes a total of 5 reservations, with 1 new and 4 outstanding reservations :smile:

 Batalov 2010-03-01 06:33

Reserving R729 to 100K.

 rogue 2010-03-03 17:17

Sierpinski base 928

1 Attachment(s)
I have finally finished this base to n=10000 and am releasing it. This was a very difficult base.

Here is a summary. The conjectured k is 27871. This base has 2 GFNS (1 and 928), 11 MOB, 9470 are trivially factored, 17701 primes, and 686 k remaining.

Riesel base 928 is even harder. It will be a few days before that completed to n=10000.

 rogue 2010-03-04 14:01

Riesel Base 928

I have finally finished this base to n=10000. This has been the most difficult base I've tackled.

Here is a summary. The conjectured k is 32514. This base has 19 MOB, 11048 are trivially factored, 20569 primes, and 834 k remaining.

I will continue this base a while longer, possibly as far as n=25000.

The difficulty in this base comes from two factors. First, the numbers take longer to test than a smaller base (such as base 58, which I completed a few weeks ago). Second, this base does not produce as many primes below n=10000. Most bases have < 1% of k remaining at n=10000. This base has a little more than 2.5% remaining.

Here is a question for Gary or anyone else in "the know". Which bases have the highest percent of remaining k at n=25000 where the conjuectured k > 100?

 mdettweiler 2010-03-05 02:01

1 Attachment(s)
S782: conjectured k 28, proven
S783: conjectured k 36, proven
S784: conjectured k 156, 3 k's remaining at 5K, not reserved
S785: conjectured k 130, 2 k's remaining at 5K, not reserved
S788: conjectured k 40, 5 k's remaining at 5K, not reserved

All requisite files for these are attached.

 rogue 2010-03-05 02:57

[QUOTE=mdettweiler;207411]S782: conjectured k 28, proven
S783: conjectured k 36, proven
S784: conjectured k 156, 3 k's remaining at 5K, not reserved
S785: conjectured k 130, 2 k's remaining at 5K, not reserved
S788: conjectured k 40, 5 k's remaining at 5K, not reserved

All requisite files for these are attached.[/QUOTE]

For so few k's you should be taking them to n=25000. Who knows, you might be able to prove one of those conjectures.

 mdettweiler 2010-03-05 03:34

[quote=rogue;207415]For so few k's you should be taking them to n=25000. Who knows, you might be able to prove one of those conjectures.[/quote]
Well, I don't quite have a spare core to put them on to take them to 25K; what I did to squeeze them in was pause one of the primary jobs for a few minutes while each of these ran. My hope was that I'd be able to prove most or all of them trivially, but yes, the ones with k's remaining would be worth coming back to when a core frees up.

 henryzz 2010-03-05 07:35

[quote=mdettweiler;207418]Well, I don't quite have a spare core to put them on to take them to 25K; what I did to squeeze them in was pause one of the primary jobs for a few minutes while each of these ran. My hope was that I'd be able to prove most or all of them trivially, but yes, the ones with k's remaining would be worth coming back to when a core frees up.[/quote]
If you don't want to spend time fiddling around proving these bases then I would be willing to load them into another personal prpnet server and set my clients to run 50/50. I could do with some variation in my prpnet testing plus i am still yet to find a prime with prpnet:sad:

 rogue 2010-03-05 13:47

[QUOTE=henryzz;207428]If you don't want to spend time fiddling around proving these bases then I would be willing to load them into another personal prpnet server and set my clients to run 50/50. I could do with some variation in my prpnet testing plus i am still yet to find a prime with prpnet:sad:[/QUOTE]

Wow! You have obviously been very unlucky. Have you considered throwing a prime into your server just to know that the software is working correctly? :smile:

You must be working with some very stubborn k/b combos. I know that some of the entries in this thread ([url]http://www.mersenneforum.org/showthread.php?t=12980[/url]) have had a lot of work, but no success, but it doesn't appear that you are working on any of them.

 mdettweiler 2010-03-05 17:04

[quote=henryzz;207428]If you don't want to spend time fiddling around proving these bases then I would be willing to load them into another personal prpnet server and set my clients to run 50/50. I could do with some variation in my prpnet testing plus i am still yet to find a prime with prpnet:sad:[/quote]
Feel free to take them if you like. :smile: FYI, just because I've mentioned that "I may come back to something" (which I do somewhat often) doesn't mean that I've got an exclusive hold on it--the way I see it, whoever gets the work done the quickest can have it.

 henryzz 2010-03-05 17:34

[quote=rogue;207451]Wow! You have obviously been very unlucky. Have you considered throwing a prime into your server just to know that the software is working correctly? :smile:

You must be working with some very stubborn k/b combos. I know that some of the entries in this thread ([URL]http://www.mersenneforum.org/showthread.php?t=12980[/URL]) have had a lot of work, but no success, but it doesn't appear that you are working on any of them.[/quote]
The remaining k of riesel 173 from 25k-100k and so far 280 test on 56627*2^n-1 at n=~630k
all large tests
i dont count myself that unlucky

ok reserving:
S784: conjectured k 156, 3 k's remaining at 5K
S785: conjectured k 130, 2 k's remaining at 5K
S788: conjectured k 40, 5 k's remaining at 5K
Hopefully there are some primes here:smile:

 henryzz 2010-03-05 20:25

[quote=henryzz;207469]The remaining k of riesel 173 from 25k-100k and so far 280 test on 56627*2^n-1 at n=~630k
all large tests
i dont count myself that unlucky

ok reserving:
S784: conjectured k 156, 3 k's remaining at 5K
S785: conjectured k 130, 2 k's remaining at 5K
S788: conjectured k 40, 5 k's remaining at 5K
Hopefully there are some primes here:smile:[/quote]
All ks tested to 10k no primes yet. Maybe i am unlucky.

 henryzz 2010-03-05 20:36

[quote=henryzz;207497]All ks tested to 10k no primes yet. Maybe i am unlucky.[/quote]
finally 8*788^11407+1 is prime
the PRPs/ Primes column of server_stats.html wasn't updated although it is now listed as the lowest prime

 rogue 2010-03-05 20:52

[QUOTE=henryzz;207498]finally 8*788^11407+1 is prime
the PRPs/ Primes column of server_stats.html wasn't updated although it is now listed as the lowest prime[/QUOTE]

That is definitely a bug, which I have now fixed in the leading edge.

If you aren't afraid to edit the source, add these lines:
[code]
" PRPandPrimesFound = (select count(*) from Candidate " \
" where b = CandidateGroupStats.b " \
" and k = CandidateGroupStats.k " \
" and c = CandidateGroupStats.c " \
" and (IsPRP = 1 or IsPrime = 1)), " \
[/code]

to the select statement in SierpinskiRieselStatsUpdater::UpdateGroupStats. Insert these lines immediately before the setting of the SierpinskiRieselPrime column. Then use the admin tool to recompute server stats (after restarting the server with the new code) and you'll be good to go.

 gd_barnes 2010-03-05 21:07

I won't be updating the web pages except sporadically until Monday or Tuesday. Most efforts will be reflected then.

 gd_barnes 2010-03-05 21:11

[quote=mdettweiler;207411]S782: conjectured k 28, proven
S783: conjectured k 36, proven
S784: conjectured k 156, 3 k's remaining at 5K, not reserved
S785: conjectured k 130, 2 k's remaining at 5K, not reserved
S788: conjectured k 40, 5 k's remaining at 5K, not reserved

All requisite files for these are attached.[/quote]

Max, to put conjectured efforts on the pages, I've generally asked that people search them to at least n=10K. Otherwise it takes too long to update everything. Before starting any effort, can you please take that into account? Thanks.

I now see that David has searched them all to at least n=10K so I'll show them when I have time.

Gary

 henryzz 2010-03-05 21:13

[quote=gd_barnes;207506]Max, to put conjectured efforts on the pages, I've generally asked that people search them to at least n=10K. Otherwise it takes too long to update everything. Before starting any effort, can you please take that into account? Thanks.

I now see that David has searched them all to at least n=10K so I'll show them when I have time.

Gary[/quote]
My search depth is continuously increasing fast. Currently i am at 12.7k and counting. Ask just before u do the webpages.

 gd_barnes 2010-03-05 21:24

[quote=rogue;207336]I have finally finished this base to n=10000. This has been the most difficult base I've tackled.

Here is a summary. The conjectured k is 32514. This base has 19 MOB, 11048 are trivially factored, 20569 primes, and 834 k remaining.

I will continue this base a while longer, possibly as far as n=25000.

The difficulty in this base comes from two factors. First, the numbers take longer to test than a smaller base (such as base 58, which I completed a few weeks ago). Second, this base does not produce as many primes below n=10000. Most bases have < 1% of k remaining at n=10000. This base has a little more than 2.5% remaining.

Here is a question for Gary or anyone else in "the know". Which bases have the highest percent of remaining k at n=25000 where the conjuectured k > 100?[/quote]

Very good question and unknown. The higher the base, the more likely it is to have a higher percentage of k's remaining. So we'd have to break it up into bases <= 32, 33-100, 100-250, etc.

The problem with such a computation of all of the bases is that we would need to "normalize" them by calculating an estimated # of k's that would be remaining at n=25K or some other similar point. We also need to get a "starting point" of possible k's that are not already eliminated by trivial factors, MOBs, GFNs, or algebraic factors. The starting bases script should be able to mostly tell you the exact # of k's that a base starts with(sans algebraic factors). If you set max n to 0, it should show all possible k's remaining after dropping k's that don't need a prime.

It would take some effort but that would be something interesting. Tim, Mark, or other "numbers guys", would you like to take on such a task for bases <= 32? I suspect bases 19 and 30 will be up there on their "compositness".

I know one thing: Sierp 143 is extremely bad! For a conjecture of k=~7000-8000, it has 302 k's remaining at n=2500. I expect that it will have 180-200 k's remaining at n=25K. I've just now reserved it becaue (I think) it is the only base <= 200 with a conjecture < 10K that is still unsearched.

Gary

 rogue 2010-03-05 21:55

[QUOTE=gd_barnes;207509]I know one thing: Sierp 143 is extremely bad! For a conjecture of k=~7000-8000, it has 302 k's remaining at n=2500. I expect that it will have 180-200 k's remaining at n=25K. I've just now reserved it because (I think) it is the only base <= 200 with a conjecture < 10K that is still unsearched.[/QUOTE]

That is definitely worse than Riesel base 928. Even though the remaining percentage will be similar to mine, because it is an odd base, you had half as many k to test to begin with.

 mdettweiler 2010-03-05 22:22

[quote=gd_barnes;207506]Max, to put conjectured efforts on the pages, I've generally asked that people search them to at least n=10K. Otherwise it takes too long to update everything. Before starting any effort, can you please take that into account? Thanks.

I now see that David has searched them all to at least n=10K so I'll show them when I have time.

Gary[/quote]
Ah, sorry about that. I'll keep that in mind for the future.

 MyDogBuster 2010-03-06 00:23

Reserving Riesel 635, 688 and 741 as new to n=25K.

 MyDogBuster 2010-03-06 17:19

Reserving Riesel 506 and Sierp 506 as new to n=25K

 gd_barnes 2010-03-08 08:48

David,

You asked me to ask where you are at on Sierp bases 784, 785, and 788 shortly before I update the pages. I expect to do at least a partial updating of them by late Monday afternoon U.S. So if you can let me know their status sometime by ~6-8 PM GMT, that would work.

Thanks,
Gary

 henryzz 2010-03-08 16:41

[quote=gd_barnes;207716]David,

You asked me to ask where you are at on Sierp bases 784, 785, and 788 shortly before I update the pages. I expect to do at least a partial updating of them by late Monday afternoon U.S. So if you can let me know their status sometime by ~6-8 PM GMT, that would work.

Thanks,
Gary[/quote]
The three primes i have found:(including already posted)
8*788^11407+1
105*784^14268+1
139*784^23965+1

My currently search depth is 34.7k.:smile: I hopefully will remember to post nearer the time you said with completion to 35k.:smile:

 Batalov 2010-03-08 17:09

Reserving S780 to 50K.

 henryzz 2010-03-08 18:58

[quote=henryzz;207729]I hopefully will remember to post nearer the time you said with completion to 35k.:smile:[/quote]
Completed to 35k

 gd_barnes 2010-03-09 03:16

Serge reported in an Email on March 2nd:

R729 is at n=61.9K; continuing to n=100K

Serge, you might check this one. I had to extrapolate from the 24*729^n-1 reservation to your 8*3^n-1 testing.

You said you were going to the next n=50K on all of your reservations. So I'm taking that to mean that you'll be testing this one to n=100K base 729, which would be n=600K base 3. Is that correct?

Gary

 Batalov 2010-03-09 06:25

R784

Yes. I've sieved to 900K but will have a look how slow it will be at 600K.

base-3 is testing faster (PFGW doesn't decompose the base and goes into awkward FFT sizes).
example:

[FONT=Arial Narrow]-f0 -l../Bextra -q8*3^200017-1[/FONT]
[FONT=Arial Narrow]Output logging to file ../Bextra[/FONT]
[FONT=Arial Narrow]No factoring at all, not even trivial division[/FONT]
[FONT=Arial Narrow]Special modular reduction using FFT length [B]20K[/B] on 8*3^200017-1[/FONT]
[FONT=Arial Narrow]8*3^200017-1 is composite: RES64: [2A3BFDAF3B7C8E79] ([B]96.7036s[/B]+0.0059s)[/FONT]
[FONT=Arial Narrow]Done.[/FONT]

[FONT=Arial Narrow]-f0 -l../Bextra -q24*729^33336-1[/FONT]
[FONT=Arial Narrow]PFGW Version 3.3.1.20100111.Win_Dev [GWNUM 25.13][/FONT]
[FONT=Arial Narrow]Output logging to file ../Bextra[/FONT]
[FONT=Arial Narrow]No factoring at all, not even trivial division[/FONT]
[FONT=Arial Narrow]Special modular reduction using FFT length [B]40K[/B] on 24*729^33336-1[/FONT]
[FONT=Arial Narrow]24*729^33336-1 is composite: RES64: [2A3BFDAF3B7C8E79] ([B]196.6488s[/B]+0.0059s)[/FONT]

[FONT=Verdana]For the same reduction reason, I'd like to reserve R784 to 50K (in base-28, 100K). Will try to get it to a single-k status.[/FONT]

[COLOR=green]P.S. I've been doing the same with S961 as far as I remember, when I first found this. [/COLOR]
[COLOR=green]I thought that the new version was immune to that, but found the same after testing.[/COLOR]

 gd_barnes 2010-03-09 06:33

[quote=rogue;207336]I have finally finished this base to n=10000. This has been the most difficult base I've tackled.

Here is a summary. The conjectured k is 32514. This base has 19 MOB, 11048 are trivially factored, 20569 primes, and 834 k remaining.

I will continue this base a while longer, possibly as far as n=25000.

The difficulty in this base comes from two factors. First, the numbers take longer to test than a smaller base (such as base 58, which I completed a few weeks ago). Second, this base does not produce as many primes below n=10000. Most bases have < 1% of k remaining at n=10000. This base has a little more than 2.5% remaining.

Here is a question for Gary or anyone else in "the know". Which bases have the highest percent of remaining k at n=25000 where the conjuectured k > 100?[/quote]

Mark,

Did you want to post the primes and k's remaining on R928? If so, I'll show them on the pages.

Gary

 gd_barnes 2010-03-09 06:46

[quote=Batalov;207793]Yes. I've sieved to 900K but will have a look how slow it will be at 600K.

base-3 is testing faster (PFGW doesn't decompose the base and goes into awkward FFT sizes).
example:

[FONT=Arial Narrow]-f0 -l../Bextra -q8*3^200017-1[/FONT]
[FONT=Arial Narrow]Output logging to file ../Bextra[/FONT]
[FONT=Arial Narrow]No factoring at all, not even trivial division[/FONT]
[FONT=Arial Narrow]Special modular reduction using FFT length [B]20K[/B] on 8*3^200017-1[/FONT]
[FONT=Arial Narrow]8*3^200017-1 is composite: RES64: [2A3BFDAF3B7C8E79] ([B]96.7036s[/B]+0.0059s)[/FONT]
[FONT=Arial Narrow]Done.[/FONT]

[FONT=Arial Narrow]-f0 -l../Bextra -q24*729^33336-1[/FONT]
[FONT=Arial Narrow]PFGW Version 3.3.1.20100111.Win_Dev [GWNUM 25.13][/FONT]
[FONT=Arial Narrow]Output logging to file ../Bextra[/FONT]
[FONT=Arial Narrow]No factoring at all, not even trivial division[/FONT]
[FONT=Arial Narrow]Special modular reduction using FFT length [B]40K[/B] on 24*729^33336-1[/FONT]
[FONT=Arial Narrow]24*729^33336-1 is composite: RES64: [2A3BFDAF3B7C8E79] ([B]196.6488s[/B]+0.0059s)[/FONT]

[FONT=Verdana]For the same reduction reason, I'd like to reserve R784 to 50K (in base-28, 100K). Will try to get it to a single-k status.[/FONT][/quote]

Now, THAT is surprising! Here is what I suspect:

PFGW (or LLR for that matter) can reduce it to a smaller base OR it can reduce it to a smaller k in order to save testing time, but it cannot do both.

Nice job finding that out.

For everyone's reference: Although it's fairly rare that you could reduce both the k and the base on a form as is the case with 24*729^n-1, if you can reduce them, it can save a lot of testing time!

I wonder if this happens for powers-of-2 bases? The main forms that I can think of that come to mind here at CRUS are:

19464*4^n-1 and 19464*16^n-1

They would reduce to:
2433*2^(2n+3)-1 and 2433*2^(4n+3)-1

Anyone care to test those and see if there is a timing difference?

Gary

 Batalov 2010-03-09 07:05

I added a P.S. above, and ah yes,
[FONT=Arial Narrow]230*780^11159+1 is prime! (25.1733s+0.0018s)[/FONT]
making S780 now a single-k contender (passed 28K recently for k=43).

 henryzz 2010-03-09 07:28

[quote=henryzz;207729]
105*784^14268+1
139*784^23965+1
[/quote]
I should have mentioned:
riesel 784 now only has one k remaining

 gd_barnes 2010-03-09 07:39

[quote=henryzz;207800]I should have mentioned:
riesel 784 now only has one k remaining[/quote]

I already noticed that Sierp 784 had one k remaining and added it to the official list.

Serge has Riesel 784 reserved with 2 k's remaining. :smile:

 MyDogBuster 2010-03-09 13:19

Riesel 506

Riesel Base 506
Conjectured k = 14
Covering Set = 3, 13
Trivial Factors k == 1 mod 5(5) and k == 1 mod 101(101)

Found Primes:
2*506^16-1
3*506^2-1
4*506^11-1
5*506^2-1
7*506^1-1
8*506^146-1
9*506^3-1
10*506^1-1
12*506^2-1
13*506^1-1

Trivial Factor Eliminations:
6
11

Conjecture Proven

 MyDogBuster 2010-03-09 13:20

Sierp Base 506

Sierp Base 506
Conjectured k = 25
Covering Set = 3, 13
Trivial Factors k == 4 mod 5(5) and k == 100 mod 101(101)

Found Primes:
2*506^1+1
3*506^3+1
5*506^1+1
6*506^1+1
7*506^6+1
8*506^1+1
10*506^2+1
11*506^269+1
12*506^1+1
13*506^2+1
15*506^1+1
16*506^1066+1
17*506^3+1
18*506^1+1
20*506^11+1
21*506^1+1
22*506^22+1
23*506^3+1

Trivial Factor Eliminations:
4
9
14
19
24

Conjecture Proven

 rogue 2010-03-09 13:31

[QUOTE=gd_barnes;207794]Mark,

Did you want to post the primes and k's remaining on R928? If so, I'll show them on the pages.
[/QUOTE]

Go ahead and show them. I doubt anyone will poach the base.

 rogue 2010-03-09 13:35

[QUOTE=Batalov;207793]Yes. I've sieved to 900K but will have a look how slow it will be at 600K.

base-3 is testing faster (PFGW doesn't decompose the base and goes into awkward FFT sizes).
example:

[FONT=Arial Narrow]-f0 -l../Bextra -q8*3^200017-1[/FONT]
[FONT=Arial Narrow]Output logging to file ../Bextra[/FONT]
[FONT=Arial Narrow]No factoring at all, not even trivial division[/FONT]
[FONT=Arial Narrow]Special modular reduction using FFT length [B]20K[/B] on 8*3^200017-1[/FONT]
[FONT=Arial Narrow]8*3^200017-1 is composite: RES64: [2A3BFDAF3B7C8E79] ([B]96.7036s[/B]+0.0059s)[/FONT]
[FONT=Arial Narrow]Done.[/FONT]

[FONT=Arial Narrow]-f0 -l../Bextra -q24*729^33336-1[/FONT]
[FONT=Arial Narrow]PFGW Version 3.3.1.20100111.Win_Dev [GWNUM 25.13][/FONT]
[FONT=Arial Narrow]Output logging to file ../Bextra[/FONT]
[FONT=Arial Narrow]No factoring at all, not even trivial division[/FONT]
[FONT=Arial Narrow]Special modular reduction using FFT length [B]40K[/B] on 24*729^33336-1[/FONT]
[FONT=Arial Narrow]24*729^33336-1 is composite: RES64: [2A3BFDAF3B7C8E79] ([B]196.6488s[/B]+0.0059s)[/FONT]

[FONT=Verdana]For the same reduction reason, I'd like to reserve R784 to 50K (in base-28, 100K). Will try to get it to a single-k status.[/FONT]

[COLOR=green]P.S. I've been doing the same with S961 as far as I remember, when I first found this. [/COLOR]
[COLOR=green]I thought that the new version was immune to that, but found the same after testing.[/COLOR][/QUOTE]

The FFT size is chosen by gwnum. PFGW has little control over it. I could modify PFGW to look for bases that are perfect powers and change the parameters that it passes to gwnum.

 henryzz 2010-03-09 16:46

[quote=rogue;207820]The FFT size is chosen by gwnum. PFGW has little control over it. I could modify PFGW to look for bases that are perfect powers and change the parameters that it passes to gwnum.[/quote]
PFGW could have passed the faster 8*3^200017-1 to gwnum rather than 24*729^33336-1 when asked to test 24*729^33336-1

 gd_barnes 2010-03-09 18:47

[quote=rogue;207818]Go ahead and show them. I doubt anyone will poach the base.[/quote]

???

How can I show them? You didn't post them. lol

What I'm asking is that you post (i.e. attach) them.

 rogue 2010-03-09 19:44

1 Attachment(s)
[QUOTE=gd_barnes;207846]???

How can I show them? You didn't post them. lol

What I'm asking is that you post (i.e. attach) them.[/QUOTE]

Oops. I swear I had attached it, but I suspect I chose the file without uploading. It is attached to this post.

 Batalov 2010-03-09 23:54

[quote=rogue;207820]The FFT size is chosen by gwnum. PFGW has little control over it. I could modify PFGW to look for bases that are perfect powers and change the parameters that it passes to gwnum.[/quote]
Intuitively, nobody expects that effect, so I didn't mean it as any criticism.

That would be a very nice addition. Time savings! Plus, if you will be implementing this, then you may want to chisel the new smaller base from the [I]k[/I] and add it to the exponent.

If you (internally to PF, before GWnum) completely factor the [I]k[/I] and [I]b[/I], pfgw could also immediately catch and report some algebraic factorizations; here's a test case: suppose I submit [FONT=Fixedsys]26*234^149885-1[/FONT][FONT=Verdana] (or amidst the ABC file) then[/FONT]

[FONT=Courier New]k= 26=2*13[/FONT]
[FONT=Courier New]b=234=2*3^2*13[/FONT]
[FONT=Courier New]n is odd[/FONT]

...and the program could immediately report "is composite by algebraic" and optionally report the factors (or the smaller one): all a^2-b^2 and a^odd+-b^odd could be caught (it is not always trivial to catch all of them by eye, right?).

I am sure a lot of users could be very happy with that addition.

-Serge

[SIZE=1][COLOR=green]P.S. I thought of a small obvious caveat in this algebra (not relevant for the Sierp/Riesel forms): [/COLOR][/SIZE]
[SIZE=1][COLOR=green]If a-b=1 (which is rare but we don't want any induced bugs), then no use for the minus form. (Example 6^2-5^2.)[/COLOR][/SIZE]

 gd_barnes 2010-03-10 10:59

[quote=Batalov;207886]Intuitively, nobody expects that effect, so I didn't mean it as any criticism.

That would be a very nice addition. Time savings! Plus, if you will be implementing this, then you may want to chisel the new smaller base from the [I]k[/I] and add it to the exponent.

If you (internally to PF, before GWnum) completely factor the [I]k[/I] and [I]b[/I], pfgw could also immediately catch and report some algebraic factorizations; here's a test case: suppose I submit [FONT=Fixedsys]26*234^149885-1[/FONT][FONT=Verdana] (or amidst the ABC file) then[/FONT]

[FONT=Courier New]k= 26=2*13[/FONT]
[FONT=Courier New]b=234=2*3^2*13[/FONT]
[FONT=Courier New]n is odd[/FONT]

...and the program could immediately report "is composite by algebraic" and optionally report the factors (or the smaller one): all a^2-b^2 and a^odd+-b^odd could be caught (it is not always trivial to catch all of them by eye, right?).

I am sure a lot of users could be very happy with that addition.

-Serge

[SIZE=1][COLOR=green]P.S. I thought of a small obvious caveat in this algebra (not relevant for the Sierp/Riesel forms): [/COLOR][/SIZE]
[SIZE=1][COLOR=green]If a-b=1 (which is rare but we don't want any induced bugs), then no use for the minus form. (Example 6^2-5^2.)[/COLOR][/SIZE][/quote]

That would be an outstanding addition to PFGW but...here is where I really think it is needed: In sr(x)sieve! Sr(x)sieve will tell you that certain k's have algebraic factors but all that means is that there are even n's remaining in the file on k's that are perfect squares. (I think it may do higher powers now but am not sure. I'm also not sure if it can deduce such a situation on 26*234^n-1 where the odd n's have algebraic factors.)

I guess my question about sr(x)sieve is: If it can tell me that there are some n's that have algebraic factors, why not just remove them automatically instead of forcing one to manually remove them?

Serge, wouldn't you agree that such k's and/or n-values should be removed by a sieving program instead of being found by a primality searching program?

Gary

 MyDogBuster 2010-03-10 13:22

Reserving Riesel Bases 654 and 694 as new to n=25K.

 rogue 2010-03-10 13:46

[QUOTE=Batalov;207886]Intuitively, nobody expects that effect, so I didn't mean it as any criticism.

That would be a very nice addition. Time savings! Plus, if you will be implementing this, then you may want to chisel the new smaller base from the [I]k[/I] and add it to the exponent.

If you (internally to PF, before GWnum) completely factor the [I]k[/I] and [I]b[/I], pfgw could also immediately catch and report some algebraic factorizations; here's a test case: suppose I submit [FONT=Fixedsys]26*234^149885-1[/FONT][FONT=Verdana] (or amidst the ABC file) then[/FONT]

[FONT=Courier New]k= 26=2*13[/FONT]
[FONT=Courier New]b=234=2*3^2*13[/FONT]
[FONT=Courier New]n is odd[/FONT]

...and the program could immediately report "is composite by algebraic" and optionally report the factors (or the smaller one): all a^2-b^2 and a^odd+-b^odd could be caught (it is not always trivial to catch all of them by eye, right?).

I am sure a lot of users could be very happy with that addition.[/QUOTE]

I agree with Gary. Sieving should be used to remove algebraic factorizations. You can find some here, [url]http://www.leyland.vispa.com/numth/factorization/cullen_woodall/algebraic.txt[/url] and those are just for generalized Cullens and Woodalls. There are undoubtably more than listed on that page.

 MyDogBuster 2010-03-10 14:32

Riesel 635

Riesel Base 635
Conjectured k = 52
Covering Set = 3, 53
Trivial Factors k == 1 mod 2(2) and k == 1 mod 317(317)

Found Primes: 23k's File attached

Remaining k's: Tested to n=25K
6*635^n-1
38*635^n-1

Base Released

 MyDogBuster 2010-03-10 14:35

Riesel 688

Riesel Base 688
Conjectured k = 105
Covering Set = 13, 53
Trivial Factors k == 1 mod 3(3) and k == 1 mod 229(229)

Found Primes: 68 k's File attached

Remaining k's: Tested to n=25K
9*688^n-1

Trivial Factor Eliminations: 34k's

Base Released

 MyDogBuster 2010-03-10 14:38

Riesel 741

Riesel Base 741
Conjectured k = 160
Covering Set = 7, 53
Trivial Factors k == 1 mod 2(2) and k == 1 mod 5 and k == 1 mod 37(37)

Found Primes: 60k's File attached

Remaining k's: Tested to n=25K
64*741^n-1

Trivial Factor Eliminations: 18k's

Base Released

 Batalov 2010-03-11 10:46

[quote=Batalov;208043]R288:
[I]b[/I]=288 = [B]2[/B][sup][B]5[/B][/sup]*3[sup]2[/sup]
[I]k[/I]=18 = [B]2[/B]*3[sup]2[/sup]
[I]k[/I]=392 = [B]2[/B][sup][B]3[/B][/sup]*7[sup]2[/sup]
For both [I]k[/I] and even [I]n[/I], trivial factors, for odd [I]n[/I], we have differences of squares.
[/quote]
Similar elimination for R864, with k=6 and 96.
[I]b[/I]=864 = 2[sup]5[/sup]*3[sup]3[/sup]
[I]k[/I]=6 = 2*3
[I]k[/I]=96 = 2[sup]5[/sup]*3 (all odd powers; with n odd they pair up nicely)

 rogue 2010-03-11 19:04

Riesel Base 1007

2*1007^8-1
4*1007^1-1
6*1007^2-1

With conjectured k=8, this conjecture is proven.

 rogue 2010-03-11 19:05

Riesel Base 993

2*993^2-1
4*993^3-1
6*993^18-1

With conjectured k=8, this conjecture is proven.

 rogue 2010-03-11 19:09

Riesel Base 857

2*857^2-1
4*857^195-1
8*857^22-1

With a conjecture of k=10, k=6 remains. I'll continue on it

 gd_barnes 2010-03-11 22:17

Serge has uncovered a whole slew of "new" algebraic factors and there appears to be a clear pattern. Sometime after I get back from my trip, I'll have to add it to the "generalizing algebraic factors for Riesel bases" thread.

Although not all of the time, frequently on bases where k's are eliminated by partial algebraic factors on even n with odd n having a factor of x, there are other k's that are eliminated by partial algebraic factors on ODD n with EVEN n having a factor of x.

Serge, you've already uncovered at least 3 bases with this situation. If you have time and haven't done it already and would like to go through all of the Riesel bases looking for just that situation, that would help us greatly. Thanks! :-)

In the mean time, I'll mention this again: If after sieving to a nominal depth, you find a k that has < ~0.5% of all n-values remaining, there is a very good chance that it has partial algebraic factors that will help eliminate it. Frequently they will be < 0.1%. If you come up with that situation and cannot see algebraic factors, post the situation somewhere here and one of us will take a look at it.

Algebraic factors are far more numerous than I would have imagined when I started the project. Alas, the project was originally intended for bases <= 32 and powers-of-2 bases <= 1024 so I would not have thought to check for these exception situations.

Gary

 MyDogBuster 2010-03-12 01:16

Riesel Base 999 k = 1776
k=1776 even n's trivial - odd n's difference of squares

 MyDogBuster 2010-03-12 02:15

Riesel Base 639 (One of my reservations)

k=1136 even n's trivial - odd n's are difference of squares

I have removed this from my testing

 kar_bon 2010-03-12 06:29

[QUOTE=MyDogBuster;207953]Riesel Base 741
Remaining k's: Tested to n=25K
64*741^n-1
[/QUOTE]

64*741^n-1 got a divisor of 11 when n=7,17,27,37,47,57,...

a sieve-file for 25000<n<100000 contains no n ending in 7! any hint why?

 MyDogBuster 2010-03-12 07:47

64*741^n-1 got a divisor of 11 when n=7,17,27,37,47,57,...

a sieve-file for 25000<n<100000 contains no n ending in 7! any hint why? [/quote]First of all, my covering set was wrong. s/b 7, 37 not 5, 37

Other than that, I don't have a clue. I am NOT a math person. I'm sure k=64 is probably algebraic, but don't ask me why.

 rogue 2010-03-12 13:27

[QUOTE=rogue;208087]2*857^2-1
4*857^195-1
8*857^22-1

With a conjecture of k=10, k=6 remains. I'll continue on it[/QUOTE]

6*857^23082-1 is prime

Conjecture proven

 rogue 2010-03-12 13:31

64*741^n-1 got a divisor of 11 when n=7,17,27,37,47,57,...

a sieve-file for 25000<n<100000 contains no n ending in 7! any hint why?[/QUOTE]

I don't understand the question. All n where n%10=7 are divisible by 11, thus there would be no n where n%10=7 in the output file after sieving. You can remove all n where n is even since 64=8^2.

 rogue 2010-03-12 13:34

Sierpinski Base 1007

2*1007^7+1
4*1007^6+1
6*1007^1+1

The conjectured k = 8. This conjecture is proven.

 rogue 2010-03-12 13:35

Sierpinski Base 986

2*986^1+1
3*986^3+1
5*986^1+1
7*986^6+1

1 is a GFN (which has not been tested).
4 has trivial factors.

k=6 remains. I'll continue testing it.

 rogue 2010-03-12 20:52

[QUOTE=rogue;208144]2*986^1+1
3*986^3+1
5*986^1+1
7*986^6+1

1 is a GFN (which has not been tested).
4 has trivial factors.

k=6 remains. I'll continue testing it.[/QUOTE]

6*986^21633+1 is prime. This conjecture is proven.

 Batalov 2010-03-15 06:23

Reserving R1011 as new (conj. k=208).

 Batalov 2010-03-15 08:31

Likewise, reserving R/S1001 and S1011.

 rogue 2010-03-15 12:50

Riesel Base 898

The conjectured k is 30.

Primes found:

2*898^6-1
3*898^1-1
5*898^16-1
6*898^1-1
8*898^2-1
9*898^1-1
11*898^2-1
12*898^2-1
15*898^1-1
17*898^54-1
18*898^45-1
20*898^1-1
21*898^2-1
23*898^6-1
26*898^15-1
29*898^1-1

The other k have trivial factors. This conjecture is proven.

 rogue 2010-03-15 12:52

Riesel Base 531

2*531^1-1
4*531^5-1
8*531^5-1
10*531^1-1
12*531^2-1
14*531^1-1
18*531^6-1

k=6 and k=16 have trivial factors. With conjectured k=20, this conjecture is proven.

 rogue 2010-03-15 12:54

Riesel Base 821

This has a conjectured k=958. I will reserve it to n=25000.

 Batalov 2010-03-17 03:04

S637 and S1011 are proven

1 Attachment(s)
S637 and S1011 are proven.

R1011 has 3 k remaining.

 Batalov 2010-03-18 06:45

R931

1 Attachment(s)
R931 with conjectured k=3960 has a very smooth [I]b[/I]-1.
At n=2000, there are only 11 [I]k[/I]'s left. Reserving to 25K.
Initial files are attached.

[SIZE=1]Another one is R361. It is a square which allows for some trivial eliminations, plus some primes can be borrowed from R19. Will reserve in the other thread.[/SIZE]

 MyDogBuster 2010-03-18 23:24

Riesel Base 709

Riesel Base 709
Conjectured k = 924
Covering Set = 5, 71
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 59(59)

Found Primes: 289k's File attached

Remaining k's: 13k's - Tested to n=25k
144*709^n-1 <<<< Proven composite by partial algebraic factors
170*709^n-1
174*709^n-1
218*709^n-1
234*709^n-1
324*709^n-1 <<<< Proven composite by partial algebraic factors
354*709^n-1
408*709^n-1
606*709^n-1
746*709^n-1
774*709^n-1
776*709^n-1
834*709^n-1

Trivial Factor Eliminations: 159k's

Base Released

 gd_barnes 2010-03-19 03:34

[quote=MyDogBuster;208107]Riesel Base 999 k = 1776
k=1776 even n's trivial - odd n's difference of squares[/quote]

Hah! Saved ME some testing time. Thanks Ian. :smile:

I was able to generalize this across all of base 999. It would happen where:
k=111*m^2 and m==(1 or 4 mod 5)

k=1776=111*4^2 is the lowest one.
The next one would be k=111*6^2=3996. Since k=3996 is above the conjecture, k=1776 is the only k on this base with this condition.

I saw the pattern where even-n has a factor of 5 as consistent with bases 24 and 54. It is:
k=f*m^2 and k==(6 mod 10)

Where f is the product of all prime factors of the base that are not raised to an even power with powers removed. Hence for base 999, since b=999=3^3*37 then f=3*37=111. For base 24, b=24=2^3*3 and hence f=2*3=6. You can also see that for base 54, f would also be 6. Also, for base 294, b=2*3*7^2, hence you would eliminate the 7^2 and would end up with f=2*3=6.

Seeing this, I'm getting close to generalizing it across all bases where even-n gives a factor of 5 and odd-n is the algebraic product of squares. Since that is the most common of this type, I hope to eliminate a large percentage of the problem from many bases by Friday. I'm also aware there are some where even-n has a factor of 17 and 41 at this point bases on your guys analysis.

Gary

 gd_barnes 2010-03-19 12:28

64*741^n-1 got a divisor of 11 when n=7,17,27,37,47,57,...

a sieve-file for 25000<n<100000 contains no n ending in 7! any hint why?[/quote]

A divisor of 11 always occurs every 5th or 10th n-value if it is going to occur at all. In this case, all n==(7 mod 10) are divisible by 11, hence the reason why no remaining n-values end in a 7.

Also, since k=64 is a perfect square and cube, you could remove all even n-values and n's divisible by 3.

But neither of those help a lot. Most n's==(1 or 5 mod 6) still remain. The fact that n=19 has an 18-digit smallest factor means there is virtually no chance for a full covering set.

Gary

 gd_barnes 2010-03-19 12:36

[quote=MyDogBuster;208118]First of all, my covering set was wrong. s/b 7, 37 not 5, 37

Other than that, I don't have a clue. I am NOT a math person. I'm sure k=64 is probably algebraic, but don't ask me why.[/quote]

Your covering set is still wrong. lol

It should be 7, 53 -not- 7, 37 or 5, 37.

I corrected your original post where you reported the status.

Alas, the covering set of the conjectured k=160 makes no difference for k=64.

 gd_barnes 2010-03-20 03:25

[quote=Batalov;208600]S637 and S1011 are proven.

R1011 has 3 k remaining.[/quote]

Serge,

I have to have test limits on any k's remaining. This is 4-5 bases now without them in different threads. For R1011, what are its remaining k's testing limits and are you keeping the base reserved?

In the future, if I don't have a test limit, I'm just going to ignore the work and it won't be reflected anywhere.

Gary

 mdettweiler 2010-03-20 03:32

[quote=gd_barnes;208972]Serge,

I have to have test limits on any k's remaining. This is 4-5 bases now without them in different threads. For R1011, what are its remaining k's testing limits and are you keeping the base reserved?

In the future, if I don't have a test limit, I'm just going to ignore the work and it won't be reflected anywhere.

Gary[/quote]

 gd_barnes 2010-03-20 04:21

Thanks Max.

Serge, I still need to know if you are keeping R1011 reserved. In cases where you don't specify a limit, I'll go ahead and assume that you will not be taking it further.

If anyone happens to read this, I'm completely ignoring my PMs and Email until I finish all of the updates here, which I'm finally hoping to finish tonight.

Gary

 Batalov 2010-03-20 04:48

25K, all of them. It's a default.

[QUOTE]So are you keeping any of them reserved?[/QUOTE]

If I reserved something and didn't unreserve, then they are reserved.

 gd_barnes 2010-03-20 05:03

[quote=Batalov;208982]25K, all of them. It's a default.[/quote]

So are you keeping any of them reserved? That was my question in the last post for R1011.

 gd_barnes 2010-03-20 05:46

[quote=Batalov;208982]25K, all of them. It's a default.

If I reserved something and didn't unreserve, then they are reserved.[/quote]

That is very confusing. You've got me really lost now. What if you say so-and-so base has 3 k's left and give no other specifics? At first I thought you were keeping them, then I thought you weren't, now I think you are but am still not completely sure on those bases that you gave no specifics. I keep changing the pages one way and then the other and now I'm going back again and it keeps taking me longer and longer. I'll tell you what. I'll have the pages all updated within 30 mins. of this post now. Please look at them and see if I have your reservations correct.

I also have to reflect them correctly in the 1k thread, which adds even more time.

With 40-50 new bases over the last week, I'd appreciate specifics on each posting like: "Complete to n=25K and continuing to xxx" or something like that.

If we didn't do another new base for the next year, I'd be perfectly happy. lol

Thanks.

 Batalov 2010-03-20 06:17

The "3 k's left" message was already an update. The originals was above it:
[quote=Batalov;208427]Reserving R1011 as new (conj. k=208).[/quote]

Some PHP or perl-cgi based automation could do wonders to your (already wonderful) webpages. Don't you see that you turn yourself into a human-power-driven CGI? And from that CGI-like behaviour stems your frustration when people are not specific enough. I can understand that. Sorry, but the best way to restrict the vocabulary and remove ambiguities is a set of simple forms:
[code]User [......] Email [as a weak authentication + for the followups]

Reserve {Riesel|Sierp} base [...] from n= [1|default] to n=[25000|value]. [Submit]. [I]=> return a four-digit reservation "code"[/I]

Release {Riesel|Sierp} base [...]. Release code: [user can insert old [I]"code"[/I] here to prevent poaching]

{Riesel|Sierp} base [...] is proven. [Browse file=...] [Submit].[/code]
See M.Kamada's site for a prototype. It is not awfully hard. I think manual editing of pages is way harder and [I]'makes[/I] you hard' (quote from the [URL="http://www.chicagotribune.com/news/columnists/chi-schmich-sunscreen-column,0,4054576.column"]fake Vonnegut's address[/URL] to the class of '97.

Don't get frustrated. Simplify it.

I was going to suggest a very good base, but now I am not sure.
I honor your moratorium. Anything but a new base! :-)

Peace! -Serge

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