mersenneforum.org

mersenneforum.org (https://www.mersenneforum.org/index.php)
-   Conjectures 'R Us (https://www.mersenneforum.org/forumdisplay.php?f=81)
-   -   Bases 251-500 reservations/statuses/primes (https://www.mersenneforum.org/showthread.php?t=12993)

gd_barnes 2007-12-27 20:05

Bases 251-500 reservations/statuses/primes
 
I started an attempt to prove Sierp base 256, which has a low conjecture of k=1221. There are 2 k's remaining that need a prime, one of which has already been searched to top-5000 territory. See the web pages.

gd_barnes 2008-01-20 05:33

I am reserving Riesel base 256. I'll take it to either n=15K or n=25K and post the k's that are left on a separate web page.

I started on it yesterday and am currently at n=6K with 85 k's remaining.

The conjecture is k=10364. It takes quite a while to test so many k's on such a high base. Alas, we'll be in top-5000 territory at n=41.7K! :smile:


Gary

gd_barnes 2008-01-21 20:55

Status on Riesel base 256: Now up to n=12.5K on all k's. 65 k's remaining. About 8-10 more k's can be removed with base 2 primes shown at rieselprime.org but I'm leaving them in to see if there are lower primes, at least until n=25K.

I will be continuing on to n=25K after doing a little more sieving.

If you've never messed around with a HUGE base before, it's a trip! :wink:


Gary

gd_barnes 2008-02-03 10:33

Status for Riesel base 256
 
For Riesel base 256, I'm now up to n=17.5K. There are 51 k's remaining, which includes the removal of 8 k's with primes for n>17.5K that were found in base 2 testing at various times. Progress is very slow at effectively n=140K base 2 for this many k's.

I'll post all k's remaining once I reach n=25K.

This will be a challenging one! :smile:


Gary

gd_barnes 2008-02-06 22:42

Riesel base 256 status and released
 
I have tested Riesel base 256 up through n=20K. I am releasing this base to everyone now because its been quite a bit of work to get it up to n=160K base 2! I have created a new base 256 reservations web page that shows all 51 k's remaining. A few are effectively reserved by drive 2 as a result of converting from Riesel base 16.

Important note: Since the base is a power of 2, it LLRs as fast as base 2. A top-5000 prime will be reached at n=41.7K.

There are 51 k's remaining and I have added a sieved file for n=20K-25K for all k's to the new reservations page. The file is ~3-6 days work due to the large # of k's and large base.

I checked all for all possible base 2 conversions from [URL="http://www.rieselprime.org"]www.rieselprime.org[/URL] and the top-5000 site and I found 8 primes for n>20K. That brought it down from 59 k's remaining.


Gary

grobie 2008-02-17 12:23

Reserving Sierp base 256 k=831 to n=50k

gd_barnes 2008-02-18 03:12

[quote=grobie;125962]Reserving Sierp base 256 k=831 to n=50k[/quote]

Thanks for clarifying Grobie. Good luck on base 256. With top-5000 primes starting at n=41.7K, it won't take you long to get there! :smile:


Gary

grobie 2008-02-27 10:42

1 Attachment(s)
sierp base 256 k=831 completed to n=50k. No Primes

gd_barnes 2008-02-28 19:02

Reserving Riesel base 256 to take all its k's from n=20K to 25K using the sieve file that I originally posted.

gd_barnes 2008-02-29 04:06

6414*256^20939-1 is prime

6815*256^21006-1 is prime

gd_barnes 2008-03-03 06:36

Riesel base 256 completed for n=20K-25K; 2 primes previously reported.

Now released.

grobie 2008-04-18 17:26

reserving the following 7 Riesel Base 256 k's:
1695
2237
2715
2759
3039
3147
3155

I am not sure how far I will take them, but no more than 50k might be less, I am going to orientation for a new job soon out of town, so I don't want to commit to anything big.

grobie 2008-04-20 04:42

3155*256^27010-1 is prime
3155*2^216080-1 is prime!

Let me know if I need to do anything else with this.

gd_barnes 2008-04-20 07:08

[quote=grobie;131887]3155*256^27010-1 is prime
3155*2^216080-1 is prime!

Let me know if I need to do anything else with this.[/quote]

Nope, nothing more to do. Karsten should automatically list it on his 2000 < k < 4000 page when he gets it updated.

Nice work! It's good to knock out some of the base 256 k's. There's a very large # of k's remaining for such a high base.


Gary

grobie 2008-04-30 02:56

[QUOTE=grobie;131887]3155*256^27010-1 is prime
3155*2^216080-1 is prime!

Let me know if I need to do anything else with this.[/QUOTE]

Here is another one for Riesel Base 256:
3039*2^281056-1 is prime!:smile:

grobie 2008-05-29 02:00

1 Attachment(s)
[QUOTE=grobie;131843]reserving the following 7 Riesel Base 256 k's:
1695
2237
2715
2759
3039
3147
3155

[/QUOTE]

All k's completed to 50k 2 primes already reported, no additional primes.

gd_barnes 2008-06-27 20:22

I'm reserving all remaining unreserved Riesel base 256 k-values (41 total k's). I'll take them from n=25K-75K (n=200K-600K base 2). This will be a double-check for the lower ranges on some of them.

Sieving has complete to P=1T, which is sufficient up to n=50K. Starting at only n=25K, I will initially will have only one high-speed core on it but will work up to having a full quad on it.

My goal is to have all powers-of-2 bases k-values up to n=600K base 2 by the end of Sept. Riesel and Sierp base 16 are close (n=560K base 2) and there are several even-n and odd-n conjectures k-values that are near n=400K that need to be pushed a little to accomplish this.

Edit: Although I am double-checking several k's that are already searched past n=75K, I won't show them as reserved since technically I'm not searching any new range on them. Anyone is free to reserve any k-value and test it above n=75K.


Gary

gd_barnes 2008-06-29 19:09

5139*256^30740-1 is prime

gd_barnes 2008-07-02 08:43

2 primes from Riesel base 256:

5027*256^28873-1 is prime
4137*256^29273-1 is prime

44 k's to go and testing is complete to n=32.8K on two cores.


Gary

gd_barnes 2008-07-04 01:23

Riesel base 256 at n=33.5K; one prime reported for n=30K-35K; continuing.

gd_barnes 2008-07-08 20:49

3855*256^36666-1 is prime

Riesel base 256 currently at n=37K with 43 k's remaining.

gd_barnes 2008-07-10 00:01

5247*256^36991-1 is prime

42 k's now remaining.

KEP 2008-07-12 12:56

These sierpinski conjectures have I come up with:

Base: k : Covering set:
----- ------- -------------
251 8 (3,7,43,1471,17,109,13,1609,37,9601,1553,1249) (most likely 4 else n>900000000, covering set will be p<=5, most likely 3,5)**
252 45 (11,23,103,619,5,13,977,43,1471,337,997,4057,17,193,241)
253 65914 (127,31,691,5,37,173,103,619,17,257,13,353, 8369,1201)
254 4 (3,5,17,7,19,487,149,433,31,691,13,401) *
255 110094 (97,673,13,41,61,7,19,487,89,1621,1609,3529)

* Proven
** Most likely proven, but lack of covering set

Notice that Sierpinski base 254 is proven. Also base 251 is msot likely 4 with a covering set of 3 and 5 else n>900M :smile:

Is not going to work any further on these conjectures, accept conjecture 255, it is going to be taken to n<=2,500. Base 252 has 2 k's remaining, 1 and 27. I'm going to take these to n<=25,000. (at 11351 there is still no prime). This will most likely be my last contribution...

Thank you.

Kenneth!

KEP 2008-07-12 16:19

@all: Forgot to tell that I'm about to take base 255 Sierpinski to n<=2500. Also at the moment I'm searching through the log files of Riesel base 3 k<=500M for PRP being composites... at the moment 3 has been found :smile:

gd_barnes 2008-07-12 18:42

Thanks for the info. guys. It's kind of fun doing those new bases isn't it? :smile: After a short review, I'll post it on the web pages.

KEP, I'm not sure I understand your large covering sets. Most will have small covering sets of 6 or less factors. Examples:

For Sierp base 254, k=4 has a covering set of {3, 5}. That is the factors of 3 and 5 knock out all n-values for k=4.

You are correct, it is proven because:
k n-prime
2 1
3 2
k=1 is a GFN and is not considered, although it does have a prime at n=4.

On Sierp base 251, your later analogy is correct. k=4 has a covering set of {3, 5}. As you stated, it is proven:
k n-prime
2 1
k=1 and 3 have trivial factors of 2.

One more thing, you do not need to test k=1 on any Sierp base. k=1 makes the form a Generalized Fermat number (GFN). GFN's can only have a prime when n is a perfect power of 2.

Based on the above, on your base 252, if you wanted to test k=1, you would only need to test n=1, 2, 4, 8, 16, 32, etc. There would be no need to test any other n-values as they would yield composites. But it's not necessary to test at all to prove the conjecture because it is a GFN. So per your analysis, for base 252, only k=27 is considered remaining.


Gary

KEP 2008-07-12 19:59

[quote=gd_barnes;137715]Thanks for the info. guys. It's kind of fun doing those new bases isn't it? :smile: After a short review, I'll post it on the web pages.

KEP, I'm not sure I understand your large covering sets. Most will have small covering sets of 6 or less factors. Examples:

For Sierp base 254, k=4 has a covering set of {3, 5}. That is the factors of 3 and 5 knock out all n-values for k=4.

You are correct, it is proven because:
k n-prime
2 1
3 2
k=1 is a GFN and is not considered, although it does have a prime at n=4.

On Sierp base 251, your later analogy is correct. k=4 has a covering set of {3, 5}. As you stated, it is proven:
k n-prime
2 1
k=1 and 3 have trivial factors of 2.

One more thing, you do not need to test k=1 on any Sierp base. k=1 makes the form a Generalized Fermat number (GFN). GFN's can only have a prime when n is a perfect power of 2.

Based on the above, on your base 252, if you wanted to test k=1, you would only need to test n=1, 2, 4, 8, 16, 32, etc. There would be no need to test any other n-values as they would yield composites. But it's not necessary to test at all to prove the conjecture because it is a GFN. So per your analysis, for base 252, only k=27 is considered remaining.



Gary[/quote]

The covering sets was copied directly from the output presented by the covering.exe program. Maybe I missunderstood and copied to much, but I decided to copy the entire amount of numbers, to make sure that you got what was needed.

Regarding base 252, it actually appears that k=1 is also very easily sieved. At n<=17426 I've completed 826 tests, and only 8 of these were for k=1 the remaining were for k=27.

Glad that you could use this work. Actually it's kind of need to have a thread were people can tell which bases they try to conjecture. However if I remember correctly, there is no way to verify PRPs for bases>255 (unless they are powers of 2?), so maybe we should encourage people to only work on bases <=255 for both Riesel or Sierpinski.

Take care.

Kenneth!

gd_barnes 2008-07-12 20:14

[quote=KEP;137719]The covering sets was copied directly from the output presented by the covering.exe program. Maybe I missunderstood and copied to much, but I decided to copy the entire amount of numbers, to make sure that you got what was needed.

Regarding base 252, it actually appears that k=1 is also very easily sieved. At n<=17426 I've completed 826 tests, and only 8 of these were for k=1 the remaining were for k=27.

Glad that you could use this work. Actually it's kind of need to have a thread were people can tell which bases they try to conjecture. However if I remember correctly, there is no way to verify PRPs for bases>255 (unless they are powers of 2?), so maybe we should encourage people to only work on bases <=255 for both Riesel or Sierpinski.

Take care.

Kenneth![/quote]


The "exponent" that you are entering is too large on the covering software. On each base, start with an exponent of 4 and if no covering set found, go to an exponent of 6, 8, 12, 16, 24, 36, 48, 60, 72, 96, 120, and 144 until you find a conjectured k. (Actually keep going after you find a conjectured k because you may find a slightly lower k with a larger covering set; although this is unlikely.)

Besides being the lowest conjectured k-value, the covering set needs to be the smallest number of factors that make the k-value always composite.

The "exponent" is the first value that you enter after typing "covering" to start the program.

To be blunt, you are wasting your time on k=1. It is mathematically proven that n must be a power of 2 because it is a GFN for all Sierp bases. Also, you don't need to test it to prove the conjecture. Just remove it from your sieved file. If you really want to test it for n>10K, all you need to do is test n=16384, 32768, 65536, 131072, 262144, and 524288 and TA-DA; you've now tested it all the way to n=1M (actually n=1048575) because the next test would be at n=1048576. In other words, at these high bases, you don't want to do even one test for high n-values that is a mathematically proven composite.

Getting into finding primes on GFN's is a whole other topic. There are several web pages (links are in the top-5000 site) dedicated to finding the primes and factors of them for various bases < 20 that can be generalized for all bases.

Edit: I wasn't aware that PRP's for bases > 256 that are not power of 2 could not be proven. If that is true then I agree, we need to keep bases that are not powers of 2 at < 256.


Gary

gd_barnes 2008-07-13 08:57

[quote=gd_barnes;137715]
On Sierp base 251, your later analogy is correct. k=4 has a covering set of {3, 5}. As you stated, it is proven:
k n-prime
2 1
k=1 and 3 have trivial factors of 2.
[/quote]

My quick analogy was incorrect. Sierp base 251 has trivial k's of k==(1 mod 2) and (4 mod 5) so k=4 could not be the conjecture. KEP, you're original conjecture of k=8 was correct.

I don't know what you meant by "most likely 4 else n>900000000" because k=8 is quickly proven:

k=8 covering set {3 7}
k n-prime
2 1
6 17
k=1, 3, 5, 7 have trivial factors of 2.
k=4 has a trivial factor of 5.

I have to check myself too! :smile:


Gary

KEP 2008-07-13 11:00

[QUOTE=gd_barnes;137735]I don't know what you meant by "most likely 4 else n>900000000"[/QUOTE]

Well I did use NewPGen to test base 251 for k=4, for as many n as NewPGen could by curtan verify (before starting to test -2148....), the limit of n is higher than 900M, for k=4 for base 251, but I decided to stop testing there since p<=5 for the entire range removed all n's. Well I guess it has something to do with the trivial factors :smile:

Also I'm sorry that I concluded wrong, concerning the bases. Well there you have it, then I actually learned new stuff today also. Actually I was also kind of puzzled why base 255 should in fact be the limit, since I figured that the coding should be kind of general for any bases as compared to a fixed amount of bases :smile:

Tonight, I'll hand over the last work that I have for the conjectures I found, and then I'll hopefully next weekend be able to hand over the remaining work for Riesel base 3. Once I hand over Riesel base 3 work, it will also conclude my stay here. At the moment, I guess that even though I check out, I'll not entirely leave, just like in "hotel california" :smile: But heck it has been a need a very educational time for me, and I'm glad that whatever I contributed with was actually needfull.

Regards

Kenneth!

gd_barnes 2008-07-13 13:17

[quote=KEP;137736]Well I did use NewPGen to test base 251 for k=4, for as many n as NewPGen could by curtan verify (before starting to test -2148....), the limit of n is higher than 900M, for k=4 for base 251, but I decided to stop testing there since p<=5 for the entire range removed all n's. Well I guess it has something to do with the trivial factors :smile:
[/quote]

Definition of trivial factors for the conjectures: Each and every n-value has the same factor.

Hence k's with trivial factors cannot be considered the conjecture nor can they beconsidered remaining if they are lower than the conjecture. This is because they will always be composite.

As you found, NewPGen or Srsieve would quickly sieve all n-values out.

Here: 4*251^n+1 always has a trivial factor of 5. Here's a demonstration:

4*251^1+1 = 1005 = 3*5*67
4*251^2+1 = 252005 = 5*13*3877
4*251^3+1 = 63253005 = 3*5*17*248051
4*251^4+1 = 15876504005 = 5*41*3061*25301
etc.


If factors and covering sets confuse you, try plugging the above into Alperton's excellent [URL="http://www.alpertron.com.ar/ECM.HTM"]prime factoring web page[/URL] to get the prime factors of the first few n-values of a base before starting on it. I learn a lot by looking at the patterns of factors that occur in the various forms. It is also how I determine the smallest covering set after determining the lowest conjectured k.

One more thing: If you still plan on testing Sierp base 255 to n=2500, be sure and remove the following k's before reporting primes remaining:
k==(1 mod 2) [odd k values]
k==(126 mod 127) [k's that leave a remainder of 126 after dividing by 127, i.e. 126, 253, 380, etc.]

When starting new bases, it's essential to understand how all of the trivial factors work or you wind up with k's remaining that you shouldn't and you end up searching things that are proven composite for all n-values.

I hope this helps.


Gary

KEP 2008-07-13 21:02

@Gary:

About the base 255 Sierpinski, it actually helped a lot. It has at the moment been taken to n=1968 and is continueing to n<=2500. I will try to see if I remember to remove all k's that you mentioned :smile:... I'm not sure you will get the base 255 Sierpinski primes as well as k's remaining before the coming friday, since I don't think it will finish getting to n<=2500 before I leave this machine for the next ~110 hours :smile:

Regards

Kenneth

EDIT: Forgot to supply with the info, that I'm only testing even k's and no odd k's, hence the fact that the odd k's never yield a prime :smile:

gd_barnes 2008-07-14 02:16

KEP reported in an Email that he has completed Sierp base 252 k=27 to n=25K. No primes were found and he is unreserving it.

KEP, the only reservations I now have you down for are Sierp base 255 up to n=2500 and Riesel base 3 up to k=500M and n=25K.


Gary

gd_barnes 2008-07-14 02:24

For Sierp bases not already done so in KEP's list that had a conjecture < 100, I searched them to a shallow depth and proved a couple of them as follows:

Sierp base 251; conjecture k=8 proven; highest prime is k=6 at n=17. (Shown previously by me.)

Additional info. for the bases on the web pages.

I'm not working on these further.


Gary

KEP 2008-07-14 03:37

[QUOTE=gd_barnes;137772]KEP reported in an Email that he has completed Sierp base 252 k=27 to n=25K. No primes were found and he is unreserving it.

KEP, the only reservations I now have you down for are Sierp base 255 up to n=2500 and Riesel base 3 up to k=500M and n=25K.


Gary[/QUOTE]

That checks out. All dependent on the verification and testing speed, I hope to have it all to you on friday :smile:

KEP 2008-07-14 16:16

I'm going to begin to make conjectures for all b<=1024. I'll begin conjecturing base 1024 and then move my way down, since I've no idea which bases>31 (besides those mentioned on the website) that is actually conjectured :smile: I'll start working on the Sierpinski bases and then (unless someone reaches it before me) start conjecturing the Riesel bases.

Why bases<=1024 selected? Well it makes no sence to get to work on too high bases with current technology, and also there will be plenty of work for us to work on proving all bases <= 2^10 (1024)...

Is by the way going to use following exponents:

4, 6, 8, 12, 16, 24, 36, 48, 60, 72, 96, 120, and 144

when using conjecture.exe program.

Regards

KEP

Ps. Is sieving Sierpinski base 252 k=27 for n<=100K. After sieving completes, I'll begin LLR the range.

gd_barnes 2008-07-14 18:05

Riesel base 256 all k's at n=40K; continuing.

Two primes already reported for n=35K-40K.

gd_barnes 2008-07-15 10:08

[quote=KEP;137800]I'm going to begin to make conjectures for all b<=1024. I'll begin conjecturing base 1024 and then move my way down, since I've no idea which bases>31 (besides those mentioned on the website) that is actually conjectured :smile: I'll start working on the Sierpinski bases and then (unless someone reaches it before me) start conjecturing the Riesel bases.

Why bases<=1024 selected? Well it makes no sence to get to work on too high bases with current technology, and also there will be plenty of work for us to work on proving all bases <= 2^10 (1024)...

Is by the way going to use following exponents:

4, 6, 8, 12, 16, 24, 36, 48, 60, 72, 96, 120, and 144

when using conjecture.exe program.

Regards

KEP

Ps. Is sieving Sierpinski base 252 k=27 for n<=100K. After sieving completes, I'll begin LLR the range.[/quote]

Prof. Caldwell at the top-5000 site provided me with a list of the Sierp conjectures for bases <= 100 in an unpublished math paper shortly after I started the project. His university also did searches on all of them to a shallow depth; n=~10K-40K it appears. They did not work on the Riesel side.

I could have shown those had I so chosen on the web pages but the scope of this effort is already huge. I doubt that I'll post many more conjectures on the web pages in the near future; let alone 900-1000 of them. So you can leave us with the info. if you like but don't expect to see it 'up in lights' so to speak. Perhaps you'll want to create your own web pages with them on there.

On the exponent, although I found that to be part of the issue with the covering set, you also had to reduce the maximum factor. New suggestion; try this:
Exponents of 4, 12, 48, and 144
Max factors of 100, 300, 1000, and 10000.

Even the above is unlikely to give the covering set with the fewest factors in some instances. For that reason, you have to experiment with each base at Alperton's site, which can take up to 15-20 mins. to get it correct. You have to carefully analyze which factors are eliminating which modulos of n.

Doing 900-1000 exponents correctly is a huge task. Combine that with k=27 on base 252 to n=100K (~2-3 CPU months!) and Riesel base 3 to k=500M & n=25K and I see where this is leading...

KEP, you're taking on too much work again and I see you getting bored with it before it's finished! Let's take it easy; please! Please think through your reservations before posting here.

Why don't you try it with 100 bases, see how comfortable figuring out what the correct covering sets are, and then see if you want to continue?

I have an alternative suggestion: Consider doing some searches on our LLRnet server port 6 for Sierp base 6. Well sieved files are ready to test. We'd really like to have some work done on that. There are also manual reservations with sieved files available for both Riesel and Sierp base 16, well into the top-5000 range. Bases that are powers of 2 test far faster than bases that are not. What I'm getting at is that there is plenty of work without making more.


Thank you,
Gary

KEP 2008-07-18 18:25

[QUOTE=gd_barnes;137833]Prof. Caldwell at the top-5000 site provided me with a list of the Sierp conjectures for bases <= 100 in an unpublished math paper shortly after I started the project. His university also did searches on all of them to a shallow depth; n=~10K-40K it appears. They did not work on the Riesel side.

I could have shown those had I so chosen on the web pages but the scope of this effort is already huge. I doubt that I'll post many more conjectures on the web pages in the near future; let alone 900-1000 of them. So you can leave us with the info. if you like but don't expect to see it 'up in lights' so to speak. Perhaps you'll want to create your own web pages with them on there.

On the exponent, although I found that to be part of the issue with the covering set, you also had to reduce the maximum factor. New suggestion; try this:
Exponents of 4, 12, 48, and 144
Max factors of 100, 300, 1000, and 10000.

Even the above is unlikely to give the covering set with the fewest factors in some instances. For that reason, you have to experiment with each base at Alperton's site, which can take up to 15-20 mins. to get it correct. You have to carefully analyze which factors are eliminating which modulos of n.

Doing 900-1000 exponents correctly is a huge task. Combine that with k=27 on base 252 to n=100K (~2-3 CPU months!) and Riesel base 3 to k=500M & n=25K and I see where this is leading...

KEP, you're taking on too much work again and I see you getting bored with it before it's finished! Let's take it easy; please! Please think through your reservations before posting here.

Why don't you try it with 100 bases, see how comfortable figuring out what the correct covering sets are, and then see if you want to continue?

I have an alternative suggestion: Consider doing some searches on our LLRnet server port 6 for Sierp base 6. Well sieved files are ready to test. We'd really like to have some work done on that. There are also manual reservations with sieved files available for both Riesel and Sierp base 16, well into the top-5000 range. Bases that are powers of 2 test far faster than bases that are not. What I'm getting at is that there is plenty of work without making more.


Thank you,
Gary[/QUOTE]

Well again I may have not expressed myself clear enough :smile:... I was not reserving the conjectures for working on all the conjectures for b<=1024 down to anyone else not worked on for both Riesel and Sierpinski. I was only thinking about finding the conjectured value for each bases.

So here is what I have left to do:

1. Sierpinski base 252 for k=27: Take it to n<=100K (currently at n=42287, ~600 sec. per k/n pair)
2. Finish Riesel base 3 for all k<=500M... ETA between 2 or most likely 4 weeks :smile:

Well if you can send me a PM or an e-mail containing the files that I need to launch and run LLRNet, I would really like to see if I can get the LLRNet working. A lonely/abandoned base is never a good thing to have :smile:... please notice that I can't guarantee that any work will actually be done :smile:

So now I'll sit back and wait patiently... and see if the LLRNet system is the same as for Riesel and Sierp Base 5 :smile:

Regards

KEP

gd_barnes 2008-07-19 10:08

[quote=KEP;137982]Well again I may have not expressed myself clear enough :smile:... I was not reserving the conjectures for working on all the conjectures for b<=1024 down to anyone else not worked on for both Riesel and Sierpinski. I was only thinking about finding the conjectured value for each bases.

So here is what I have left to do:

1. Sierpinski base 252 for k=27: Take it to n<=100K (currently at n=42287, ~600 sec. per k/n pair)
2. Finish Riesel base 3 for all k<=500M... ETA between 2 or most likely 4 weeks :smile:

Well if you can send me a PM or an e-mail containing the files that I need to launch and run LLRNet, I would really like to see if I can get the LLRNet working. A lonely/abandoned base is never a good thing to have :smile:... please notice that I can't guarantee that any work will actually be done :smile:

So now I'll sit back and wait patiently... and see if the LLRNet system is the same as for Riesel and Sierp Base 5 :smile:

Regards

KEP[/quote]


[URL="http://www.mersenneforum.org/showpost.php?p=123860&postcount=1"]Here[/URL] is the thread about a general discussion about setting up and running LLRnet servers. It is virtually the same as Riesel and Sierp base 5.

[URL="http://www.mersenneforum.org/showpost.php?p=134808&postcount=1"]Here[/URL] is the thread that contains the server and port for Sierp base 6.

Everything is explained somewhere in these threads. Any questions...just ask.

On coming up with the conjectures for all bases <=1024, you communicated correctly. What I'm saying is this:
When coming up with the conjectures, correct covering sets are also needed. Otherwise it is of only small help to us.

In order to come up with the conjectures, you can run covering.exe in several batch processes and accomplish it quickly: perhaps < 1 CPU day if the parameters are set up correctly.

Coming up with the correct covering sets takes far longer. I know of no software yet developed that gives the correct smallest covering set so it must be done manually. I explained how I do it previously. Perhaps Willem has an idea on how he does it.

If you want to provide us with all of the conjectured values only, that's fine. We will keep them for future use but it is of only a small amount of help and is generally outside the scope of the current project.

How many tests remain for Sierp base 252 at n=42287? Some info. for you: A test at n=2*42287=84574 will take you 600 secs * 4 = 2400 secs. (40 mins.) so hopefully you will find a prime before that. :smile:


Gary

em99010pepe 2008-07-19 10:23

I would stick to manual LLRing and not use llrnet, the latter is slower, default 10 % but can go as high as 20 % upon the n size of the number.

KEP 2008-07-19 10:25

[QUOTE=gd_barnes;137998][URL="http://www.mersenneforum.org/showpost.php?p=123860&postcount=1"]Here[/URL] is the thread about a general discussion about setting up and running LLRnet servers. It is virtually the same as Riesel and Sierp base 5.

[URL="http://www.mersenneforum.org/showpost.php?p=134808&postcount=1"]Here[/URL] is the thread that contains the server and port for Sierp base 6.

Everything is explained somewhere in these threads. Any questions...just ask.

On coming up with the conjectures for all bases <=1024, you communicated correctly. What I'm saying is this:
When coming up with the conjectures, correct covering sets are also needed. Otherwise it is of only small help to us.

In order to come up with the conjectures, you can run covering.exe in several batch processes and accomplish it quickly: perhaps < 1 CPU day if the parameters are set up correctly.

Coming up with the correct covering sets takes far longer. I know of no software yet developed that gives the correct smallest covering set so it must be done manually. I explained how I do it previously. Perhaps Willem has an idea on how he does it.

If you want to provide us with all of the conjectured values only, that's fine. We will keep them for future use but it is of only a small amount of help and is generally outside the scope of the current project.

How many tests remain for Sierp base 252 at n=42287? Some info. for you: A test at n=2*42287=84574 will take you 600 secs * 4 = 2400 secs. (40 mins.) so hopefully you will find a prime before that. :smile:


Gary[/QUOTE]

2597 tests remain at that level for Sierp base 252 for k=27. I'll take a look at the LLRNet if I decide to run it, at a later scale. Since you have a way to find the conjectured values automatically and I've to do it manually, I'll not continue that effort. So for now only Base 252 Sierp is remaining and hopefully in 2 weeks the first batches of k's remaining can be delivered to you for Riesel base 3 k<=500M :smile:

Take care

Kenneth!

gd_barnes 2008-07-19 10:46

[quote=KEP;138003]2597 tests remain at that level for Sierp base 252 for k=27. I'll take a look at the LLRNet if I decide to run it, at a later scale. Since you have a way to find the conjectured values automatically and I've to do it manually, I'll not continue that effort. So for now only Base 252 Sierp is remaining and hopefully in 2 weeks the first batches of k's remaining can be delivered to you for Riesel base 3 k<=500M :smile:

Take care

Kenneth![/quote]

Based on the provided info. that you gave me, it will take you ~54 CPU days to take Sierp base 252 from n=42287 to n=100K. Not bad.


Gary

gd_barnes 2008-07-19 11:05

[quote=em99010pepe;138001]I would stick to manual LLRing and not use llrnet, the latter is slower, default 10 % but can go as high as 20 % upon the n size of the number.[/quote]


People make way too big of a deal about a 10-20% boost in speed. Anon and I had a PM exchange about this. My motto:

Slow and steady wins the race.

In the long run, if your machines are always running, you will outpace most searchers whose computers spend at least 10-20% of their time idle because of reserving manual ranges or deciding what to do next. I suspect that for many people, it is longer than that because they are trying to decide what to do.

It's why I keep finding primes day-in and day-out at NPLB with almost no effort since I moved 5+ quads to drive 1. Those babies never stop! :smile: I'm out of town right now and I can't do anything with my machines. They just crunch away and suck my electricity while I'm gone. lol

So my opinion: Ignore the speed boost and put over half of your machines on LLRnet from some project. For less than half that you can always quickly add manual files to: Use those for manual reservations.

The best of both worlds...


Gary

Siemelink 2008-07-19 13:09

[QUOTE=gd_barnes;137998]
Coming up with the correct covering sets takes far longer. I know of no software yet developed that gives the correct smallest covering set so it must be done manually. I explained how I do it previously. Perhaps Willem has an idea on how he does it.

Gary[/QUOTE]

I wrote a program that generates covering sets and then it calculates the lowest conjecture. I am optimizing it this weekend, after that I can make it available.
By hand it is easy to do with pfgw.

Willem.

em99010pepe 2008-07-19 15:48

[quote=gd_barnes;138008]People make way too big of a deal about a 10-20% boost in speed. Anon and I had a PM exchange about this. My motto:

Slow and steady wins the race.

In the long run, if your machines are always running, you will outpace most searchers whose computers spend at least 10-20% of their time idle because of reserving manual ranges or deciding what to do next. I suspect that for many people, it is longer than that because they are trying to decide what to do.

It's why I keep finding primes day-in and day-out at NPLB with almost no effort since I moved 5+ quads to drive 1. Those babies never stop! :smile: I'm out of town right now and I can't do anything with my machines. They just crunch away and suck my electricity while I'm gone. lol

So my opinion: Ignore the speed boost and put over half of your machines on LLRnet from some project. For less than half that you can always quickly add manual files to: Use those for manual reservations.

The best of both worlds...


Gary[/quote]

10-20 % idle times?! Where did you get that? It's stupid.
Make a test with different bases and ranges for llrnet and llr standard client and then don't come with that crap of ignoring the speed boost. That's the talk of someone who is ignorant on this matter.

You would get a lot of primes if you run the standard client in all your cores. Leave one to llrnet and the probability will low, you have all your cores in there! You know what's the problem with llrnet for NPLB? Waste of time by running llrnet and doublecheks at the same time.

A few timings for base 2 high n:

llrnet:
64494*2^1937858+1 is not prime. RES64: 069AD8EFB4AA8A0A Time: 7396.367 sec.
64494*2^1938146+1 is not prime. RES64: 560645A6CB1D4FD7 Time: 7139.231 sec.
64494*2^1938506+1 is not prime. RES64: FF5B25D71A310702 Time: 7514.914 sec.


llr 3.7.1c

64494*2^1955306+1 is not prime. Proth RES64: D1E445EF4A40DF51 Time : 6389.697 sec.
64494*2^1955426+1 is not prime. Proth RES64: 57365A75AE2CB681 Time : 6380.260 sec.
64494*2^1955954+1 is not prime. Proth RES64: A22BFC12F6A94C7A Time : 6381.957 sec.

If you have Win XP install logmein free to remotely control all your cores and use the standard client for testing.

mdettweiler 2008-07-19 18:39

[quote=em99010pepe;138017]10-20 % idle times?! Where did you get that? It's stupid.
Make a test with different bases and ranges for llrnet and llr standard client and then don't come with that crap of ignoring the speed boost. That's the talk of someone who is ignorant on this matter.

You would get a lot of primes if you run the standard client in all your cores. Leave one to llrnet and the probability will low, you have all your cores in there! You know what's the problem with llrnet for NPLB? Waste of time by running llrnet and doublecheks at the same time.

A few timings for base 2 high n:

llrnet:
64494*2^1937858+1 is not prime. RES64: 069AD8EFB4AA8A0A Time: 7396.367 sec.
64494*2^1938146+1 is not prime. RES64: 560645A6CB1D4FD7 Time: 7139.231 sec.
64494*2^1938506+1 is not prime. RES64: FF5B25D71A310702 Time: 7514.914 sec.


llr 3.7.1c

64494*2^1955306+1 is not prime. Proth RES64: D1E445EF4A40DF51 Time : 6389.697 sec.
64494*2^1955426+1 is not prime. Proth RES64: 57365A75AE2CB681 Time : 6380.260 sec.
64494*2^1955954+1 is not prime. Proth RES64: A22BFC12F6A94C7A Time : 6381.957 sec.

If you have Win XP install logmein free to remotely control all your cores and use the standard client for testing.[/quote]
That's all fine and good for base 2, but actually there's no speed difference at all between LLRnet and manual LLR (or even PRP, for that matter) when doing non-base-2 numbers. :smile: No changes were made to LLR's PRP code between LLR 3.5 (i.e. LLRnet) and LLR 3.7.1c.

So, for non-base-2 stuff, LLRnet truly is the best way to do it (unless, of course, your machine is offline, in which case you have to use manual LLR). :smile:

em99010pepe 2008-07-19 18:43

[quote=Anonymous;138023]That's all fine and good for base 2, but actually there's no speed difference at all between LLRnet and manual LLR (or even PRP, for that matter) when doing non-base-2 numbers. :smile: No changes were made to LLR's PRP code between LLR 3.5 (i.e. LLRnet) and LLR 3.7.1c.

So, for non-base-2 stuff, LLRnet truly is the best way to do it (unless, of course, your machine is offline, in which case you have to use manual LLR). :smile:[/quote]

Put here the comparison, I believe seeing. In base 5 llr is quicker than llrnet.

Lennart 2008-07-19 21:20

156511*2^4771128+1 is not prime. Proth RES64: E519F45588C4D5C9 Time: 5753.949 sec.

156511*2^4771128+1 is not prime. Proth RES64: 3B4D28175B337C21 Time: 2998.044 sec.

156511*2^4771128+1 is not prime. Proth RES64: E7844006985CE642 Time: 7437.252 sec.

156511*2^4771128+1 is not prime. Proth RES64: FD85563B91194E69 Time: 4925.604 sec.

Just to give you something more to think on :smile::w00t:

/Lennart :whistle:

em99010pepe 2008-07-20 00:08

[quote=Lennart;138031]

Just to give you something more to think on :smile::w00t:

[/quote]

What about some clues about the llr version?!

Lennart 2008-07-20 00:56

[quote=em99010pepe;138035]What about some clues about the llr version?![/quote]

3.7.0 on all.

This is from Boinc and it shows that you need to check res64 !

The 5th is out now.

/Lennart

gd_barnes 2008-07-20 02:23

[quote=em99010pepe;138017]10-20 % idle times?! Where did you get that? It's stupid.
Make a test with different bases and ranges for llrnet and llr standard client and then don't come with that crap of ignoring the speed boost. That's the talk of someone who is ignorant on this matter.

You would get a lot of primes if you run the standard client in all your cores. Leave one to llrnet and the probability will low, you have all your cores in there! You know what's the problem with llrnet for NPLB? Waste of time by running llrnet and doublecheks at the same time.

A few timings for base 2 high n:

llrnet:
64494*2^1937858+1 is not prime. RES64: 069AD8EFB4AA8A0A Time: 7396.367 sec.
64494*2^1938146+1 is not prime. RES64: 560645A6CB1D4FD7 Time: 7139.231 sec.
64494*2^1938506+1 is not prime. RES64: FF5B25D71A310702 Time: 7514.914 sec.


llr 3.7.1c

64494*2^1955306+1 is not prime. Proth RES64: D1E445EF4A40DF51 Time : 6389.697 sec.
64494*2^1955426+1 is not prime. Proth RES64: 57365A75AE2CB681 Time : 6380.260 sec.
64494*2^1955954+1 is not prime. Proth RES64: A22BFC12F6A94C7A Time : 6381.957 sec.

If you have Win XP install logmein free to remotely control all your cores and use the standard client for testing.[/quote]


I'm not referring to mega-tests. Of course it makes sense to do what you did regarding the mega-tests you did here. I'm referring to the amount of time people let their computers sit idle because they are reserving manual ranges and those ranges finish in the middle of the night or while on vacation. Once again...slow and steady wins the race.

It happened to me; I know. It takes tremendous effort to make sure that 20-25 cores are busy constantly with no idle time when running manual processes. Invarabily there would be 2-3 that I would forget about and they would finish in the middle of the night or while I was on vacation.

Of course you can use remote access to control things while you are on vacation but who really wants to mess with that in a tropical resort somewhere? If I'm on a TRUE vacation such as I was in Mexico in March, the last thing I want to be doing is managing my machines.

If you like playing with your machines a lot, I suppose the manual system is the way to go. For me, I like some of both with a majority LLRnet because it takes too much of my personal time otherwise.

Why don't you take a survey of people with 50+ cores and see which they prefer?


Gary

gd_barnes 2008-07-20 02:26

[quote=Lennart;138031]156511*2^4771128+1 is not prime. Proth RES64: E519F45588C4D5C9 Time: 5753.949 sec.

156511*2^4771128+1 is not prime. Proth RES64: 3B4D28175B337C21 Time: 2998.044 sec.

156511*2^4771128+1 is not prime. Proth RES64: E7844006985CE642 Time: 7437.252 sec.

156511*2^4771128+1 is not prime. Proth RES64: FD85563B91194E69 Time: 4925.604 sec.

Just to give you something more to think on :smile::w00t:

/Lennart :whistle:[/quote]


HUH?? OK, which is the right residue and which program correctly computed the correct residue? This does not look good.


Gary

em99010pepe 2008-07-20 08:49

[quote=gd_barnes;138039]HUH?? OK, which is the right residue and which program correctly computed the correct residue? This does not look good.


Gary[/quote]

That's the problem of using BOINC...

KEP 2008-07-20 09:22

[QUOTE=em99010pepe;138052]That's the problem of using BOINC...[/QUOTE]

LLR at BOINC is not the problem. The code is somewhat the same for LLR for BOINC as for the manual version. Only the few changes needed to make LLR work with BOINC was added (according to my memory). But the coding giving the outputting the residues is the same in BOINC LLR aswell as in manual LLR. So if something is wrong with the Residuals, it is most likely a hardware issue on the machines testing it or maybe it is just the result of an extreme summersday or to much overclocking. So to sum up, if the input is the same in BOINC LLR aswell as in manual LLR, the Residual should always looks the same, unless mistakes has occured during calculation of the LLR task.

Regards

Kenneth!

em99010pepe 2008-07-20 10:03

[quote=KEP;138053]LLR at BOINC is not the problem. The code is somewhat the same for LLR for BOINC as for the manual version. Only the few changes needed to make LLR work with BOINC was added (according to my memory). But the coding giving the outputting the residues is the same in BOINC LLR aswell as in manual LLR. So if something is wrong with the Residuals, it is most likely a hardware issue on the machines testing it or maybe it is just the result of an extreme summersday or to much overclocking. So to sum up, if the input is the same in BOINC LLR aswell as in manual LLR, the Residual should always looks the same, unless mistakes has occured during calculation of the LLR task.

Regards

Kenneth![/quote]

It's BOINC guilt because the people who run it don't understand nothing about what they are doing. They don't know they need to have a stable machine to test numbers, they just run BOINC for the stats, to help their teams climb in the stats. It's intrinsic. Of course with the amount of CPU power they have they can easily doublecheck 3, 4, 5 times but that's ridiculous. By 3 or 4 clicks you can easily change BOINC projects even when you are an ignorant on the matter. That should not be like that. People should understand what they are doing, study a little bit of LLR and prime stuff.
Do you want to know the lastes problem of BOINC? It's possible to hijack the teams...true, check [url=http://www.free-dc.org/forum/showthread.php?t=15365]here[/url].

KEP 2008-07-20 10:33

[QUOTE=em99010pepe;138056]It's BOINC guilt because the people who run it don't understand nothing about what they are doing. They don't know they need to have a stable machine to test numbers, they just run BOINC for the stats, to help their teams climb in the stats. It's intrinsic. Of course with the amount of CPU power they have they can easily doublecheck 3, 4, 5 times but that's ridiculous. By 3 or 4 clicks you can easily change BOINC projects even when you are an ignorant on the matter. That should not be like that. People should understand what they are doing, study a little bit of LLR and prime stuff.
Do you want to know the lastes problem of BOINC? It's possible to hijack the teams...true, check [url=http://www.free-dc.org/forum/showthread.php?t=15365]here[/url].[/QUOTE]

I admit, BOINC has its issues. However if bad residues or faulty results gets validated as "Valid" in stead of "Invalid" as they should be if the result doesn't match, then it still has nothing to do with the user, then it has something to do with the validator and the software running the validator. BOINC can never be underestimated for its power, and the need thing about BOINC is that you can always find somewhere to help out even if you have a faulty machine. Actually it appears that it is only LLR based projects, which can be hard to help if the machine gets faulty, however such projects, i.e. PrimeGrid and RieselSieve are supported by a great community where one gets several heads up, if one starts producing faulty results. I've tried it before myself, just before I lost my last machine, it started producing bad results because of a faulty PowerSupply and later it crashed the HDD. However due to the support among the community (and the halfing of results per day when one bad result is returned) I rather shortly stopped producing bad results. So I guess if people keep on eye on their results list and start asking into the reasons why red results show up, then a lot of mess can be avoided. But overall BOINC is no matter what skills one has a great and powerfull tool for science, give and take the few hick ups in security, though I must admit that since the past 5 years (since the beginning of BOINC) it has improved its safety a lot... but well whos perfect, I know I'm not and I guess no one else on this planet actually is perfect, its just a matter of being able to admit to it or not :smile:

Kenneth!

gd_barnes 2008-07-24 08:03

9675*256^41822-1 is prime
7788*256^42163-1 is prime

Riesel base 256 is currently at n=44K; still going to n=75K. 40 k's are still remaining.


One month ago and the larger prime would have been top-5000.

3 months ago and they both would have been top-5000. :cry:

I should have started sooner. lol


Gary

gd_barnes 2008-08-13 05:09

Riesel base 256 is now complete to n=50K. 2 primes for n=40K-50K previously reported.

Continuing on to n=75K after pausing for 2-3 weeks to continue Sierp base 12 from n=167K.

gd_barnes 2008-09-06 04:31

[quote=gd_barnes;139245]Riesel base 256 is now complete to n=50K. 2 primes for n=40K-50K previously reported.

Continuing on to n=75K after pausing for 2-3 weeks to continue Sierp base 12 from n=167K.[/quote]


I've now restarted Riesel base 256 from n=50K...still going to n=75K. With some extra fire power now, I'll keep on running base 12 and 256 and possibly reserve some base 16 stuff within the next few weeks.


Gary

gd_barnes 2008-09-10 23:00

Riesel base 256 is now at n=54K. No new primes to report.

gd_barnes 2008-09-22 01:17

[quote=KEP;143328]I've no idea exactly how long it is going to take, regarding the Sierp. base 19 but I guess around 2 weeks from now. Regarding Sierp. base 252 it is most likely only 2 days of work left on the Quad, after that it will most likely have progressed (if not finished) very far with the remaining ranges for Riesel base 3 k<=500M.

KEP![/quote]

Sierp base 252 for n=51K-100K is FAR more than 2 days work on a quad (i.e. 8 CPU days). What is your testing time per candidate at n=51K and how many candidates are remaining to be tested?

Keep in mind that a test at n=100K will take FOUR times as long as a test at n=50K.

If you give me the above info., I can, in effect, use the equivalent of compound interest formulas to give you a fairly accurate estimate of how long base 252 should take for n=51K-100K.


Gary

KEP 2008-09-22 05:34

[QUOTE=gd_barnes;143367]OK, for now I'll reserve sieving only to you on k=100M-200M for Sierp base 3.

Sierp base 252 for n=51K-100K is FAR more than 2 days work on a quad (i.e. 8 CPU days). What is your testing time per candidate at n=51K and how many candidates are remaining to be tested?

Keep in mind that a test at n=100K will take FOUR times as long as a test at n=50K.

If you give me the above info., I can, in effect, use the equivalent of compound interest formulas to give you a fairly accurate estimate of how long base 252 should take for n=51K-100K.


Gary[/QUOTE]

At n=52000 it takes 1045 sec per test. A total of ~2200 tests is left to test.

KEP

gd_barnes 2008-09-22 05:53

[quote=KEP;143383]At n=52000 it takes 1045 sec per test. A total of ~2200 tests is left to test.

KEP[/quote]

Expected time is 5.074M CPU secs. or ~58.7 CPU days. Running all 4 cores of a quad 24 hours a day 7 days a week will take ~14.7 calendar days.

A bit longer than 2 days. :smile:

Even if all tests took the same amount of time, it would be 1045*2200/86400 = 26.6 CPU days or 6.65 days on all 4 cores of a quad. But clearly all tests don't take the same amount of time.

To get to the original calculation, I assumed a constant rate of change in the n-values being tested and a constant SQUARED rate of change in the time each test would take.

So if n=52K takes 1045 secs., then n=52K*2=104K would take 1045*4=4180 secs. Also:
n = 52K * sqrt(2) = 73.5K would take 1045*2=2090 secs.

Obviously LLR time goes up in fits and spurts with fftlen changes so this can only be said to be a rough estimate. But it should be in the ball park since in the long run, LLR times varies with the square of the exponent.


Gary

KEP 2008-10-20 18:01

Reserving Riesel base 255 for a future "Riesel base 255 attack". I expect it to overtake the "Riesel base 3 attack" website. I've already begun some initial testings and it seems very prime dense, so I will have no problem running this conjecture up to PG level, if Rytis wanna help out. Expect by no terms any further work from me beyound k<=500M to n<=25K for Riesel base 3 conjecture. It turns out to be to much of a handfull for me to handle, I still like the conjectures, so therefor I'm doing the initial preparations to launch a fullscale attack on the Riesel base 255 conjecture :smile:

Hope no one mind. Also I'm gonna need something to keep my computers busy as they slowly runs out of work for previously reservations :smile:

Regards

KEP!

gd_barnes 2008-10-20 21:32

[quote=KEP;145927]Reserving Riesel base 255 for a future "Riesel base 255 attack". I expect it to overtake the "Riesel base 3 attack" website. I've already begun some initial testings and it seems very prime dense, so I will have no problem running this conjecture up to PG level, if Rytis wanna help out. Expect by no terms any further work from me beyound k<=500M to n<=25K for Riesel base 3 conjecture. It turns out to be to much of a handfull for me to handle, I still like the conjectures, so therefor I'm doing the initial preparations to launch a fullscale attack on the Riesel base 255 conjecture :smile:

Hope no one mind. Also I'm gonna need something to keep my computers busy as they slowly runs out of work for previously reservations :smile:

Regards

KEP![/quote]

This is a multi CPU-year effort to test such a high base with a high conjecture up to PrimeGrid level, regardless of how prime the base is. I'm assuming that PrimeGrid level would be defined as tests that would yield top-5000 primes. For base 255, that would be at n=42K-43K now; higher when you get up that far later.

Didn't you test Sierp base 255 up to n=2500? Do you remember how long it took for you to get that tested? Now, you're going to test the Riesel side with a conjecture that is twice as high?

You are correct, it seems that all bases (b) where b=2^q-1, i.e. 3, 7, 15, 31, etc. are prime dense but because they are so primeful, they also have very high conjectures vs. their neighbor bases, which makes them more difficult to prove then a large majority of other bases.

I have 3 alternatives for you if you want to test base 255 up to PrimeGrid level in a reasonable amount of time:
(a) Do Sierp base 255 instead. It's already at n=2500 and the conjecture is half as high.
(b) Start a new thread here at CRUS and attempt to get some help testing Riesel base 255.
(c) Buy several new quads. (lol) :smile:

Even if you do (a), you'll likely still need to enlist some help here at some point.


Gary

KEP 2008-10-21 16:42

[QUOTE=gd_barnes;145965]This is a multi CPU-year effort to test such a high base with a high conjecture up to PrimeGrid level, regardless of how prime the base is. I'm assuming that PrimeGrid level would be defined as tests that would yield top-5000 primes. For base 255, that would be at n=42K-43K now; higher when you get up that far later.

Didn't you test Sierp base 255 up to n=2500? Do you remember how long it took for you to get that tested? Now, you're going to test the Riesel side with a conjecture that is twice as high?

You are correct, it seems that all bases (b) where b=2^q-1, i.e. 3, 7, 15, 31, etc. are prime dense but because they are so primeful, they also have very high conjectures vs. their neighbor bases, which makes them more difficult to prove then a large majority of other bases.

I have 3 alternatives for you if you want to test base 255 up to PrimeGrid level in a reasonable amount of time:
(a) Do Sierp base 255 instead. It's already at n=2500 and the conjecture is half as high.
(b) Start a new thread here at CRUS and attempt to get some help testing Riesel base 255.
(c) Buy several new quads. (lol) :smile:

Even if you do (a), you'll likely still need to enlist some help here at some point.


Gary[/QUOTE]

I'm not going to reserve any of these bases anyway. Even taking it to n<=25000 is more work than I really feels like doing anymore... so I'm wrapping my final works (8 weeks to go at least) amd then I'll decide what (if any) to reserve when that time comes. Sorry for yabbing again, but I made a mistake by simply forgetting how many more weeks of work I've left. Hope you understand and accept my appology... Anyway base 19 Sierp is going to be wrapped somewhere close to next weekend (maybe already the coming weekend) :smile:

Take care everyone and happy crunching :smile:

KEP

KEP 2008-10-22 14:01

[quote=gd_barnes;146107]?? You're doing it again KEP, stating different things on different days on huge efforts. On one hand, you want to reserve something to PrimeGrid level, which will be a multi-year CPU effort, and then on the other hand, you allow the fact that you have a few weeks on your current efforts to stop you? That is, to put it mildly, quite confusing.

Let me see if I have you down correctly now:
Sierp base 252 k=27 up to n=100K. (No status since Sept. 14th)

If you need some filler work to keep your machines busy, please take something smaller; perhaps some files from the Riesel and Sierp base 3 mini-drives.


Thanks,
Gary[/quote]

If it wasn't clear, I'm sorry, it all refers to some of the reasons earlier e-mailed to you. I suffered a setback this week, and also I forgot how much more work I've left. You've put my reservations right. Some status:

Sierp base 252 no movement since september 14th.

Again I ask you to accept my appologize, it all refers to private reasons, and a matter of concentration aswell memory. Expect no more reservations (or at least just ignore them) within the next 6 months, since my intention is to wrap what is now reserved and then leave for at least a while.

Thanks for understanding, and good luck on your own challenges :smile:

gd_barnes 2008-10-31 08:18

Riesel base 256 is at n=63K. No new primes to report.

This has turned out to be an annoyingly primeless stretch for this base. With top-5000 primes starting at n=~42.3K, the last 2 primes on the base were just below that with none since then in an n=20K+ stretch for the 36 k's being tested.

Continuing on to n=75K. With so many k's being tested, it's somewhat slow going but with a full quad on it, it should be done in < 2 weeks.


Gary

gd_barnes 2008-11-26 07:12

Riesel base 256 now at n=70K.

Nothing new to report; continuing on...

gd_barnes 2008-12-02 21:33

Riesel base 256 is complete to n=75K and now unreserved.

Only one prime was found for n=50K-75K...very disappointing. There are still 39 k's remaining.


Gary

gd_barnes 2008-12-02 22:09

Reserving the 2 k's on Sierp base 256 to get them to n=75K by year end.

gd_barnes 2008-12-10 05:42

[quote=gd_barnes;151713]Reserving the 2 k's on Sierp base 256 to get them to n=75K by year end.[/quote]


The two Sierp base 256 k's are now at n=72K. I started them at n=40K and hence did some overlap double-checking.

I'm going to take these to n=100K instead. (n=800K base 2) I went ahead and sieved the entire n=40K-100K range and will just keep it going.

With only 2 k's remaining, this may be the most promising power-of-2 base to prove in the forseeable future.


Gary

gd_barnes 2008-12-14 04:36

The 2 k's for Sierp base 256 are now at n=85K (n=680K base 2). Nothing to report. Still going to n=100K.

All powers-of-2 bases are now officially complete to n=600K base 2! :smile:

gd_barnes 2008-12-20 12:00

The 2 k's on Sierp base 256 are complete to n=100K. No primes.

This base is now unreserved.

gd_barnes 2008-12-31 09:36

Reserving Sierp base 255 to n=5K to knock out some k's. KEP had previously tested it to n=2.5K and 732 k's remainined. I'm currently at n=3K with 47 primes found so 685 k's remain. Depending on resource availability in a couple of weeks, I may continue on to n=10K.

Reserving Sierp base 33 to n=25K. I'm currently at n=8K with 6 k's remaining. This one may be provable!

It will be slow going on one slower core each but they should complete in a couple of weeks.


Gary

gd_barnes 2009-01-08 04:17

KEP has completed testing k=27 on Sierp base 252 to n=100K and has released it.

gd_barnes 2009-01-16 11:16

Sierp base 255 is complete to n=5100 and now unreserved.

For n=2500-5100, 185 primes were found, which reduced the k's remaining from 732 to 547. Info. on the web pages.

Kenneth, the k's remaining dropped from 732 to 551 from n=2500 to 5000; a 25% reduction...very high for such a high base but close to the 20% that I had expected for a high-prime 2^q-1 base.

I expect that base 127 will come in somewhere near 30%.


Gary

gd_barnes 2009-10-05 07:45

Max,

I have now posted all bases <= 360 from my prior k=2 search on the web pages with 3 exceptions that are shown in the details below. Here are the newly posted bases > 250 with some footnotes:

Riesel:
278 (a)
298

Sierp:
257
305 (c)
353 (b)

Footnotes:
(a) Only k=2 is remaining at n=25K.

(b) Two k<>2 remaining at n=10K.

(c) Proven.

More details:

1. All k=2 have been tested to n=25K for bases <= 360 and to n=10K for bases 361-1024.

2. All k<>2 have been tested to n=10K for bases <= 500 and to n=2500 for bases 501-1024. Some straggling bases > 500 with few k's remaining had their k<>2 k's also searched to n=10K.

3. As stated above, there were 3 bases <= 360 not posted. This is because the base conjecture was not done due to a high conjecture. They are: Riesel bases 276 (k=2 prime at n=2484) and 303 (no k=2 prime at n=25K) and Sierp base 287 (k=2 prime at n=5467).

4. There are 19 Riesel bases and 28 Sierp bases with k=2 remaining. To give an idea of how much more difficult it is to find a prime for the higher bases, at n=10K, there were 20 Riesel and 30 Sierp bases remaining. Of those, in the lower half of the bases, i.e. bases <= 512, only 5 Riesel and 10 Sierp bases remained or only 30% of all of bases. At this time, there are only 4 Riesel bases <= 512 remaining. They are: 170, 278, 303, & 383. Only base 383 k=2 is at n=10K. The other k=2 are at n=25K.

5. I ran the base conjectures only where k=2 still remained at n=1500 and the conjecture was reasonable sized. So all of the above will have k=2 remaining or a prime for k=2 at n>1500.

6. Many more bases > 360 still need to be posted. They are extremely low priority and so will be posted when I get in the mood. :smile:


Now you have 1 more base with only 1 k remaining at n=25K (or n=10K if k<>2). Another one that you might consider after Sierp bases 101 and 206 that had already been posted is Riesel base 170. It only has 2 k's remaining (also k=8 at n=10K) and is currently the lowest Riesel base that has k=2 remaining at n=25K.

A warning to anyone interested in taking on such high bases: With some possible exceptions, most of these high bases are extremely difficult to find primes for. The size grows far more rapidly than bases <= 32. Even bases in the 20's grow in size much faster than bases <= 10. The good news is that if you search base 300, a prime at n=100K comes in at ~247,000 digits (base 200 at ~230,000). It doesn't take long to get into top-5000 territory.


Gary

appeldorff 2009-10-16 07:45

Reserving Sierp Base 257 (all k's) from n=10K-25K

appeldorff 2009-10-16 20:22

1 Attachment(s)
Awesome... starting out with a double post -.- anyway

Sierp base 257 n=10k to n=25k is complete (no primes)

Results attached

gd_barnes 2009-10-16 23:18

[quote=appeldorff;193066]Awesome... starting out with a double post -.- anyway

Sierp base 257 n=10k to n=25k is complete (no primes)

Results attached[/quote]


Hi Appeldorff. Welcome to Conjectures R Us! If you have any questions, be sure and ask. People are quite helpful and responsive here. The co-admin is out of town right now but I'm usually on a few times each day.

I'll delete your duplicate post.

That was nice and quick work of Sierp base 257! Thanks for posting the results. :smile:


Gary

appeldorff 2009-10-26 20:17

Sierp Base 255
 
I'd like to reserve Sierp base 255 from 5.1k - 25k (all k's)

I already started work on this range but it's still going to take some time :smile:

gd_barnes 2009-10-27 06:03

[quote=appeldorff;193917]I'd like to reserve Sierp base 255 from 5.1k - 25k (all k's)

I already started work on this range but it's still going to take some time :smile:[/quote]

Good luck! Since it is a high base, that will be a lot of work. You'll probably want at least a full quad on it, otherwise it will likely take many months.

If you'd like to stop before n=25K, feel free to unreserve it and post the remainder of your sieve file. Eventually someone always tests the bases with available files.


Gary

mdettweiler 2009-10-29 15:13

1 Attachment(s)
2*278^43908-1 is prime! (5764.2308s+0.0959s)

Another k=2 conjecture bites the dust. :smile:

One thing of note is that the proof of this prime by N+1 took an extremely long time. Even as the only thing running on its core, it still took upwards of 20 seconds just to get to the next 2500-iteration progress mark. As such, I left it running overnight alongside my usual two-core load, which means that in reality it didn't quite take the 5764 seconds shown above (my guess would be about 2/3 of that). Nonetheless, this still is an extremely long time considering that the original PRP test took only 247 seconds. Also, when I went to prove the prime I first accidentally ran an N-1 test instead of N+1, and didn't notice until it went through two runs and was starting on its third; interestingly enough, the N-1 test took only 717 seconds to do two runs.

Anyone know why the N+1 test took so long? Is it something peculiar to do with the high base?

gd_barnes 2009-10-29 20:10

Nice! Now you'll have to take a crack at the lowest Riesel base where k=2 remains and see if you can knock out both k=2 and k=8...base 170. Note: k=8 is at n=10K.

It can vary widely on how long it takes to prove similarly-sized numbers prime. It depends on how many PRP bases it has to go through. If you watch it, you can see how many. It usually takes the same amount of time per base but varies on the number of them. I don't know why this is but I'm pretty sure it has to do with the factorization of P+1 (or P-1 for Sierp).

Congrats on yet another proof! This is becoming old hat. :smile:


Gary

mdettweiler 2009-10-29 23:10

[quote=gd_barnes;194250]It can vary widely on how long it takes to prove similarly-sized numbers prime. It depends on how many PRP bases it has to go through. If you watch it, you can see how many. It usually takes the same amount of time per base but varies on the number of them. I don't know why this is but I'm pretty sure it has to do with the factorization of P+1 (or P-1 for Sierp).[/quote]
I recall that it only did one PRP base, which is why I was confused by this. It seems that only one base with N+1 took many times the amount it took to do TWO bases with N-1.

Batalov 2009-11-09 03:53

Will take [B]Sierp. base 353[/B] to 50K: 1 k down, 1 last k to go.
12*353^20261+1 is prime

appeldorff 2009-11-28 17:01

Sierp255
 
1 Attachment(s)
An update on my Sierp255 reservation:

I am currently at the halfway mark (n=15000). 208 primes found and proven so far. I've attached them to this post.

Also, it appears there is a small typo regarding Sierp base 255. It says there are 547 k's remaining yet there are 548 k's listed.

208 down, 340 to go

gd_barnes 2009-12-01 13:04

[quote=appeldorff;197263]An update on my Sierp255 reservation:

I am currently at the halfway mark (n=15000). 208 primes found and proven so far. I've attached them to this post.

Also, it appears there is a small typo regarding Sierp base 255. It says there are 547 k's remaining yet there are 548 k's listed.

208 down, 340 to go[/quote]

Thanks for the primes. Nice progress! :smile: Technically you're closer to 1/4th done due to the increased testing times for n=15K-25K...just thought I'd give you an idea of what is left.

My apologies for the mistake on the pages. In doing a rebalancing with k's to search vs. k's remaining, it appears that the # of k's remaining at n=5100 is correct. I accidently left one k remaining that should have been removed; k=87036. 87036*255^4784+1 is prime.

You can remove k=87036 from your testing. I checked your primes file for a prime for k=87036 and there was none. This means that there are 339 k's remaining at n=15K.


Gary

Mini-Geek 2009-12-05 14:16

I'll take Riesel base 298 (5 k's) from 10K to 25K. I'll sieve n=10K through 100K to my optimal depth for 25K (300G) and post that sieve file now, (should only take a day or so) but probably wait until I'm done with Riesel base 24 to start the PFGW work.

Mini-Geek 2009-12-06 13:31

1 Attachment(s)
[quote=Mini-Geek;197907]I'll take Riesel base 298 (5 k's) from 10K to 25K. I'll sieve n=10K through 100K to my optimal depth for 25K (300G) and post that sieve file now, (should only take a day or so)[/quote]
Sieve file attached. (NewPGen format)

Mini-Geek 2009-12-08 03:08

1 Attachment(s)
[quote=Mini-Geek;197907]I'll take Riesel base 298 (5 k's) from 10K to 25K. ... but probably wait until I'm done with Riesel base 24 to start the PFGW work.[/quote]
I changed my mind and finished it to n=25K. :smile:
One prime: (verified)
[code]30*298^10338-1[/code]The results for 10K-25K and a new sieve file with k=30 and n=10K-25K removed (i.e. now it's the four remaining k's from 25K-100K sieved to 300G) are attached.

Mini-Geek 2009-12-09 15:09

Reserving and starting Sierp base 300 (conj. k is 85) to n=2500.

Mini-Geek 2009-12-09 15:16

Sierpinski Base 300
Conjectured k = 85

Found Primes:[code]2*300^1+1
3*300^2+1
4*300^1+1
5*300^2+1
6*300^1+1
7*300^5+1
8*300^26+1
9*300^20+1
10*300^1+1
11*300^1+1
13*300^5+1
14*300^1+1
15*300^2+1
16*300^1+1
17*300^1+1
18*300^2+1
19*300^1+1
20*300^11+1
21*300^1+1
23*300^3+1
24*300^2+1
26*300^2+1
27*300^1+1
28*300^44+1
29*300^672+1
30*300^1+1
31*300^2+1
32*300^1+1
33*300^1+1
34*300^13+1
35*300^1+1
36*300^24+1
37*300^4+1
39*300^1+1
40*300^2+1
41*300^1+1
42*300^1+1
43*300^2+1
44*300^8+1
46*300^2+1
47*300^6+1
48*300^1+1
49*300^25+1
50*300^146+1
52*300^1+1
53*300^1+1
54*300^8+1
55*300^2251+1
56*300^3+1
57*300^2+1
58*300^1+1
59*300^11+1
60*300^2+1
61*300^1+1
62*300^3+1
63*300^163+1
65*300^1+1
66*300^1+1
67*300^1+1
69*300^3+1
70*300^1+1
71*300^2+1
72*300^1+1
73*300^2+1
74*300^6+1
75*300^1+1
76*300^3+1
78*300^10+1
79*300^2+1
80*300^1+1
81*300^2+1
82*300^15+1
83*300^275+1
84*300^13+1[/code]

Trivial Factor Eliminations:
12
22
25
38
45
51
64
68
77

GFN Eliminations:
1

Conjecture Proven

Mini-Geek 2009-12-12 04:35

Reserving Riesel base 300. I already started. k=81 alone remains at n=2500. I'll post the full statuses once I find a prime for k=81 proving the conjecture, or it gets too large and I give up on it.

Mini-Geek 2009-12-12 14:51

[quote=Mini-Geek;198594]Reserving Riesel base 300. I already started. k=81 alone remains at n=2500. I'll post the full statuses once I find a prime for k=81 proving the conjecture, or it gets too large and I give up on it.[/quote]
Despite expecting under 1 prime in n=2500-25K, I found a prime for this at n=12793! :smile: The conjecture is now proven.

Riesel Base 300
Conjectured k = 85

Found Primes:[code]2*300^1-1
3*300^26-1
4*300^3-1
5*300^1-1
6*300^96-1
7*300^1-1
8*300^1-1
9*300^1-1
10*300^1-1
11*300^1-1
12*300^2-1
13*300^98-1
15*300^25-1
16*300^1-1
17*300^1-1
18*300^1-1
19*300^2-1
20*300^2-1
21*300^1-1
22*300^1-1
23*300^1-1
25*300^1-1
26*300^4-1
28*300^3-1
29*300^1-1
30*300^1-1
31*300^7-1
32*300^2-1
33*300^29-1
34*300^8-1
35*300^1-1
36*300^1-1
37*300^2-1
38*300^1-1
39*300^1-1
41*300^10-1
42*300^516-1
43*300^1-1
44*300^5-1
45*300^1-1
46*300^1-1
48*300^18-1
49*300^1-1
50*300^3-1
51*300^1-1
52*300^2-1
54*300^2-1
55*300^6-1
56*300^2-1
57*300^1-1
58*300^5-1
59*300^2-1
60*300^20-1
61*300^2-1
62*300^52-1
63*300^1-1
64*300^11-1
65*300^11-1
67*300^4-1
68*300^1-1
69*300^8-1
71*300^3-1
72*300^1-1
73*300^2-1
74*300^106-1
75*300^174-1
76*300^18-1
77*300^1-1
78*300^1-1
80*300^13-1
81*300^12793-1
82*300^3-1
83*300^624-1
84*300^2-1
[/code]Trivial Factor Eliminations:
1
14
24
27
40
47
53
66
70
79

Conjecture Proven

MyDogBuster 2009-12-16 05:18

Sierp Base 300
 
Sierp Base 300
Conjectured k = 85
Covering Set = 7,43
Trivial Factors k == 12 mod 13(13) and k == 22 mod 23(23)

Found Primes: 74k's File attached

Trivial Factor Eliminations:
12
22
25
38
45
51
64
68
77

Conjecture Proven


All times are UTC. The time now is 08:18.

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.