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JohnHonorary cruncher
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PPS (LLR) Milestones, Goals, and Progress
This thread will be a general continuation of this previous effort: Getting k < 1200 to n=1M before Challenge. We are attempting to fulfill our original intentions with the Proth Prime Search which are twofold: 1) find primes for k < 10000; 2) push lower k's higher. The effort will now search lower k's to higher n's intermixed with the 1200<k<10000 range from 670K towards 700K. The current groups are as follows:
k<10 to 3M (note k=3 is excluded since it's part of the 321 Prime Search)
10<k<32 to 2.5M
32<k<100 to 2M
100<k<500 to 1.5M
500<k<1200 to 1.3M
1200<k<4000 to 800K
4000<k<10000 to 700K
Note: Lower k's provide better opportunities to find primes with (x)GFN divisibilities and even an elusive Fermat Number divisor. We are also doing our best to balance both the SGS (LLR) and PPS (LLR) projects as they have a direct impact on each other in regards to the Top 5000 primes list. Please see this post for more details.
The current status is: The leading edge for PPS (LLR) k=5,7,9 has reached n=2.48M (that's 150k in the last 24 hours). Testing times now are ~4.9x's longer than they were at n=1M. They will continue to increase. There are 46k candidates remaining to reach 3M.
Regular updates will be posted to this thread.
____________



JohnHonorary cruncher
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Progress Update
The leading edge for PPS (LLR) has reached n=2.6M (that's 120k in the last 24 hours). Testing times now are ~5.2x's longer than they were at n=1M. They will continue to increase. There are 36k candidates remaining to reach 3M.
The first success in this extended effort: 9*2^1807574+1 (544135 digits  ranked 111th) found by Reuben Gathright (Reuben Gathright) of the SETI.USA team. A top 30 prime at PrimeGrid. :)
[EDIT] WOW!!! The second success quickly followed: 9*2^2543551+1 (765687 digits  ranked 57th) found by Scott Brown (Scott Brown) of the Duke University team. A top 20 prime at PrimeGrid. :)
Can we bump it back up to 200k/day to finish this off in the next couple of days? Afterwards, our first intermixing will occur as 1200<k<10000 for 670k<n<672k will be inserted.
____________




Throwing 3 cores at the task (after trashing 24 WUs because I forgot to make the binaries executable after copying them into the project directory and modifying my app_info.xml). One core is reserved for the GPU.
____________



JohnHonorary cruncher
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Prime Fermat Divisor
Scott finds one of those "elusive" prime Fermat divisors. As hoped, searching the lower k's to higher n's has paid off. After further testing of Scott's k=9 prime, it was shown to divide F2543548. See news post for more info. Testing is complete:
9*2^2543551+1 Divides F2543548
9*2^2543551+1 Divides GF(2543549,3)
9*2^2543551+1 Divides xGF(2543549,3,2)
9*2^2543551+1 Divides xGF(2543549 ,4,3)
9*2^2543551+1 Divides GF(2543549,6)
9*2^2543551+1 Divides xGF(2543549 ,8,3)
9*2^2543551+1 Divides xGF(2543542 ,9,2)
9*2^2543551+1 Divides xGF(2543547 ,9,8)
9*2^2543551+1 Divides GF(2543550,11)
9*2^2543551+1 Divides xGF(2543550,11,2)
9*2^2543551+1 Divides xGF(2543550,11,3)
9*2^2543551+1 Divides xGF(2543550,11,4)
9*2^2543551+1 Divides xGF(2543550,11,6)
9*2^2543551+1 Divides xGF(2543550,11,8)
9*2^2543551+1 Divides xGF(2543550,11,9)
9*2^2543551+1 Divides GF(2543549 ,12)
9*2^2543551+1 Divides xGF(2543550,12,11) This is not only a success for Scott but for everyone else participating as well. Congratulations to you all!!!
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Congratulations to the discoverer (Scott Brown) and to the PrimeGrid team (John, Lennart and Rytis) for the discovery.
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Prime Fermat Divisor
Scott finds one of those "elusive" prime Fermat divisors. As hoped, searching the lower k's to higher n's has paid off. After further testing of Scott's k=9 prime, it was shown to divide F2543548. See news post for more info. Testing is not complete, but we do know the following:
9*2^2543551+1 Divides F2543548
9*2^2543551+1 Divides GF(2543549,3)
9*2^2543551+1 Divides xGF(2543549,3,2)
9*2^2543551+1 Divides xGF(2543550? ,4,3)
9*2^2543551+1 Divides GF(2543549,6)
9*2^2543551+1 Divides xGF(2543550? ,8,3)
9*2^2543551+1 Divides xGF(2543550? ,9,2)
9*2^2543551+1 Divides xGF(2543550? ,9,8)
9*2^2543551+1 Divides GF(2543550,11)
9*2^2543551+1 Divides xGF(2543550,11,2)
9*2^2543551+1 Divides xGF(2543550,11,3)
9*2^2543551+1 Divides xGF(2543550,11,4)
9*2^2543551+1 Divides xGF(2543550,11,6)
9*2^2543551+1 Divides xGF(2543550,11,8)
9*2^2543551+1 Divides xGF(2543550,11,9)
9*2^2543551+1 Divides GF(2543550? ,12)
9*2^2543551+1 Divides xGF(2543550,12,11)
? will be updated once testing is complete. This is not only a success for Scott but for everyone else participating as well. Congratulations to you all!!!
I am somewhat aware of what Fermat numbers are, but what do the notations GF(a,b) and xGF(a,b,c) mean?
____________
Thanks,
Jim



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I am somewhat aware of what Fermat numbers are, but what do the notations GF(a,b) and xGF(a,b,c) mean?
GF(a,b) is the Generalized Fermat number b^2^a + 1.
xGF(a,b,c) is the extended Generalized Fermat number b^2^a + c^2^a.
____________




I am somewhat aware of what Fermat numbers are, but what do the notations GF(a,b) and xGF(a,b,c) mean?
GF(a,b) is the Generalized Fermat number b^2^a + 1.
xGF(a,b,c) is the extended Generalized Fermat number b^2^a + c^2^a.
Ahh...
____________
Thanks,
Jim




Congratulations guys =D
____________
My Top 5000 Primes:
110059!+1 is prime! (FPS)
14493618614235*2^6666661 is prime! (SGS) 


JohnHonorary cruncher
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Progress Update
The leading edge for PPS (LLR) has reached n=2.75M (that's 150k in the last 24 hours). Testing times now are ~8.1x's longer than they were at n=1M. They will continue to increase. There are 22k candidates remaining to reach 3M.
A lot can happen in 24 hours. Two primes and a World Record Prime Fermat divisor. Congratulations to everyone for this success. While we didn't bump it back up to 200k/day, 150k/day is quite respectable considering testing times continue to increase.
Note: Next range will be 1200<k<10000 for 670k<n<672k.
____________



HonzaVolunteer moderator Volunteer tester Project scientist Send message
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[EDIT] WOW!!! The second success quickly followed: 9*2^2543551+1 (765687 digits  ranked 57th) found by Scott Brown (Scott Brown) of the Duke University team. A top 20 prime at PrimeGrid. :)
Congrats Scott.
I think I'm doublechecker. It there a link to computer reported this WU, how long it took etc.?
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 



Congrats to both of you!
____________
@AggieThePew




At http://www.prothsearch.com/fermat.html, I noticed that a Fermat divisor was found on March 12th within PrimeGrid: 7333 Â· 2^138560 + 1 divides F138557.
What's the story behind this discovery? Was a mistake made back in March? 


JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2875 ID: 2449 Credit: 2,681,934 RAC: 0

At http://www.prothsearch.com/fermat.html, I noticed that a Fermat divisor was found on March 12th within PrimeGrid: 7333 Â· 2^138560 + 1 divides F138557.
What's the story behind this discovery? Was a mistake made back in March?
In short, it was discovered on 12 March 2011 but was not realized until a double check effort of all Proth primes n<210k revealed it had been overlooked. Please see news post for more info.
____________



HonzaVolunteer moderator Volunteer tester Project scientist Send message
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Congrats Scott.
I think I'm doublechecker. Is there a link to computer reported this WU, how long it took etc.?
Found it  http://www.primegrid.com/workunit.php?wuid=191438931
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 


JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2875 ID: 2449 Credit: 2,681,934 RAC: 0

Progress Update
The leading edge for PPS (LLR) has reached n=2.99M (that's 240k in the last 48 hours). Testing times now are ~8.2x's longer than they were at n=1M. They will continue to increase. There are 1.7k candidates remaining to reach 3M.
We'll complete the last of the 3M work today and enter the next range of 1200<k<10000 for 670k<n<672k. There are 262k WU's in this range.
Thanks for all the help as we begin this new phase of the search. We'll return to low k work (10<k<100 for 1M<n<1.5M) probably in a few weeks.
[EDIT] As of this edit, new work is now going out.
____________




Testing times increasing pretty fast. 



Testing times increasing pretty fast.
Not now



HonzaVolunteer moderator Volunteer tester Project scientist Send message
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I switched to PSP for the time being (ie. ruby badge), all tasks in high priority (duration correction factor above 20). Let's see how long until it settles down...
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 



I did the same thing Honza. I may set my grid back to PPS though if the PSPs aren't gonna run well on my older chips. If the PPS runtimes increase too, I suppose credits will as well? As I recall, PPS never game a ton of credits but it's got a great chance of finding (or in this case, rediscovering) primes.
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JohnHonorary cruncher
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Progress Update
All work for k=5,7,9 up to n=3M is out. Current work is being drawn from the 1200<k<10000 for 670k<n<672k range so testing times have returned to "normal". We'll use n=1M as the base testing time. These WU's are almost 2x's faster than tests at n=1M. Depending on completion rates, n may be increased to n=675k.
Thanks for all the help as we begin this new phase of the search. We'll return to low k work (10<k<100 for 1M<n<1.5M) once the current range is out.
FYI, k<1200 for n<1M is complete. This is a major accomplishment! Congratulations everyone!!!
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JohnHonorary cruncher
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Progress Update
All work is out for 1200<k<10000 for 670k<n<675k range. Yes, the range went quickly so it was increased to 675k.
We have returned to low k work (10<k<100 for 1M<n<1.5M). Testing times are back up to the 1M baseline. In fact, we are already at 1.14M so times are about 1.3x's that at 1M. These will continue to increase as n increases.
A lot of the work up to 1.2M will be double check work from previous efforts. A bit more first pass will open up from 1.2M1.4M. Afterwards, over half the range will be first pass.
Thanks again for all your help and support.
____________



JohnHonorary cruncher
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Progress Update
k=5, 7, 9 for 1M<n<3M is COMPLETE!
1200<k<10000 for 670k<n<675k is COMPLETE!
EXCELLENT work!!! Well done everyone.
10<k<100 for 1M<n<2M is the current range. Progress now is at n=1375289. Testing times are about 1.8x's that at 1M. These will continue to increase as n increases.
Our double check work is getting less and less as you can see here:
31% first pass at 1.2M
44% first pass at 1.3M
62% first pass at 1.4M
69% first pass at 1.5M
78% first pass at 1.6M
87% first pass at 1.8M
91% first pass at 2.0M
96% first pass at 2.5M At n=2M, we'll pause again and complete a PPSE range of 1200<k<10000 for 675k<n<680k or 685k. Afterwards, we are looking at 10<k<32 to n=2.5M.
Thanks again for all your help and support.
____________




Looks like progress of 10<k<100 is near n=2M...
Is the plan still to work on 1200<k<10000 afterwards..? 



I have a lot of PPS work units that are being given to me without a wing man. Will those be double checked eventually?
And...
Looks like progress of 10<k<100 is near n=2M...
Is the plan still to work on 1200<k<10000 afterwards..?
I am also interested in the answer to this.
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I have a lot of PPS work units that are being given to me without a wing man. Will those be double checked eventually?
PPS and SGS (and I think one other) have adaptive handout. If your machine proves itself for a set amount of period it can be considered good enough to do work without a wingperson. It will get dual jobs and most of the time you will be the second receiver to a person who's not been deemed good enough to work on their own.
Enjoy the pleasures of getting work that is immediately validated.




I have a lot of PPS work units that are being given to me without a wing man. Will those be double checked eventually?
No, SGS (LLR), PPS (LLR), and TRP (LLR) use Adaptive replication. That's why sometimes you see a minimum quorum of 1. 



I *think* that any WU where the result is a prime is doublechecked, even if the initial replication is 1.
Gary 


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I guess the question is more to do with if there is doublechecking eventually for the candidates where adaptive replication only sent out one WU and it was reported as composite. There could be missing primes in there. If you're just looking for top 5000 primes, it doesn't matter too much per se, but it does mean that recording the limits of the search are more complex. It does matter a lot more for conjecture proving, and also as n increases the error rates get higher.
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I guess the question is more to do with if there is doublechecking eventually for the candidates where adaptive replication only sent out one WU and it was reported as composite.
This was my question.
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Hi all crunchers :)
We only have ~13k numbers left on PPS (n=1M2M) so all help is needed to finish them.
If you can ? please switch to PPS LLR to get all wu's out there done.
I will raise buffer on frontpage to 10k That way you can see progress.
When it get close to zero I will load PPS n= 675k680k.
Why ? We have a challenge soon :) We need to try to get all 1M2M done
before the challenge
Thanks
Lennart




I've got it chugging along on PPS LLR, I should hit silver on it by the end of the challenge.
____________




Thanks for all help.
We are now down below 10k
Lennart 



What range is the next stage going to be?
____________




First we will do n=675k680k (maybe higher)
After that we follow the plan k= 100500 up to n=1.5M
Lennart 



I'm pretty new to this whole thing. Will the crunching times go up with the increase in k, or is the amount of actual work done in a WU the same? (that should show my ignorance of the math behind it)...
Just trying to figure out if it is the size of "n" or the size of "k" which has the most impact on crunching times...
Thx
Edit: I said "size" when I really meant "k" 



I'm pretty new to this whole thing. Will the crunching times go up with the increase in k, or is the amount of actual work done in a WU the same? (that should show my ignorance of the math behind it)...
Just trying to figure out if it is the size of "n" or the size of "k" which has the most impact on crunching times...
Thx
Edit: I said "size" when I really meant "k"
It is the size of n that increase time. There is a little increase when k's get bigger but nothing you will notice here on pps.
The range we will start now (675k680k) is much faster then those we are running now ( n=1M2M)
Lennart 



I'm pretty new to this whole thing. Will the crunching times go up with the increase in k, or is the amount of actual work done in a WU the same? (that should show my ignorance of the math behind it)...
Just trying to figure out if it is the size of "n" or the size of "k" which has the most impact on crunching times...
Thx
Edit: I said "size" when I really meant "k"
Short answer: just the n. The k's effect is essentially negligible.
Long answer:
It's mostly the n that makes the difference in crunching time. Think of it this way: if you have two sequences of numbers, like this:
1*2=2; 2*2=4; 3*2=6; 4*2=8; 5*2=10
versus
2^1=2; 2^2=4; 2^3=8; 2^4=16; 2^5=32
the latter increases in size much more quickly, being an exponential sequence instead of a linear one. The numbers being tested in the Proth Prime Search are defined by the sequence k*2^n+1. Since n is an exponent and k merely a multiplier, the n will have a much greater effect on the size of the number, particularly as we generalize this to large values of k and n. The k does still have an effect, but it is minuscule compared to that of the n. And since crunching time is proportional to the size of the number (read: number of digits), it is by extension affected primarily by the n.
Even longer answer (continuing from the long answer): :)
Note that the k does have a secondary effect which can make a more significant difference in crunching time. For calculations of this type, the most efficient way to run them on a computer is to use what's called a Fast Fourier Transform (FFT). The full details of such an algorithm are, needless to say, very complicated, but the part relevant to this discussion is that computers are programmed to handle FFTs in such a way that their sizes increase in a stepwise manner. It's somewhat like gears in a car with a manual transmission, where (for instance) first gear is good for everything up to 15 MPH, second gear up to 2025 MPH, third gear up to 3540 MPH, and so on. You can drive at 40 MPH in first gear, but you'll waste a lot of gas and probably ruin your engine; the reverse, however, is not true, for you'll stall the car if you drive at 10 MPH in third gear. With FFTs, you can safely use too big an FFT (at the expense of additional crunching time), but using too small an FFT will produce an inaccurate result. The trick is to find the lowest FFT that you can use safely. The LLR code at the core of PrimeGrid's worker application does this automatically, and makes its decision by looking at the k and n and comparing them with a hardcoded table of what's safe to run with what FFT. So the k does have some effect on the crunching time, though still not so great an effect as the n; and the difference still evens out to an exponential progression as n increases with k held constant. For this reason, the lowest k's are considered the most desirable, because you can find primes of the same size with less work. That said, the difference isn't huge until the size of k increases greatly (for instance, k=500 will not take much longer to test than k=10, but k=100000 will take noticeably longer).
Hope this helps! :) 



Actually both answers were helpful. Thanks to you both! My trade is as a systems administrator and starter programmer, not as a scientist (or mathematician more accurately). Wikipedia is woefully full of too much information on primes in general to grasp in one go (and generally terrible at describing the different search algos from a computing perspective) :)
Any suggestions on what subproject could benefit most from an additional 336 2.6Ghz Nehalem cores crunching on them (That's sort of tongue in cheek since I'm posting to the PPS LLR status thread)? I've got an (actual) small server farm to burnin which comes online within the next couple of weeks if I do my job right :p . Most of the project status posts (and the preferences pages) seem to be out of date.
The good news, is that the administration of the server farm is under my control (including whether or not it runs primegrid after business hours :D).
Thanks 



First we will do n=675k680k (maybe higher)
After that we follow the plan k= 100500 up to n=1.5M
Lennart
We're already at 680K, so John's suggested 685K looks
likely if we're going to have any of these left for the Challenge?
I've been running TRP LLR's on the 32bit blade cluster
(looking for "gold"), but am planning on finishing those
before/during the Challenge, to get mostly PPS LLR's.
Bruce* 



Thank you all :)
All wu's pps 1M2M is done
Lennart
____________




First we will do n=675k680k (maybe higher)
After that we follow the plan k= 100500 up to n=1.5M
Lennart
I though that you were referring to n=680k685k (which
John had previously mentioned), but I'm seeing valid tasks
from 682k already. Any chance "maybe higher" might stretch
to 690k?
Nothing wrong with some portion of the contest running in
"k= 100500 up to n=1.5M", but I can certainly confirm that
these n < 700k are giving a lot more hits (of the type appealing
to people dropping in for the contest) than the larger n's we
were running just before. Bruce* 



First we will do n=675k680k (maybe higher)
After that we follow the plan k= 100500 up to n=1.5M
Lennart
I though that you were referring to n=680k685k (which
John had previously mentioned), but I'm seeing valid tasks
from 682k already. Any chance "maybe higher" might stretch
to 690k?
Nothing wrong with some portion of the contest running in
"k= 100500 up to n=1.5M", but I can certainly confirm that
these n < 700k are giving a lot more hits (of the type appealing
to people dropping in for the contest) than the larger n's we
were running just before. Bruce*
We will continue to at least 690K or 695k :)
Lennart 



First we will do n=675k680k (maybe higher)
After that we follow the plan k= 100500 up to n=1.5M
Lennart
I though that you were referring to n=680k685k (which
John had previously mentioned), but I'm seeing valid tasks
from 682k already. Any chance "maybe higher" might stretch
to 690k?
Nothing wrong with some portion of the contest running in
"k= 100500 up to n=1.5M", but I can certainly confirm that
these n < 700k are giving a lot more hits (of the type appealing
to people dropping in for the contest) than the larger n's we
were running just before. Bruce*
We will continue to at least 690K or 695k :)
Lennart
Hi all PPS freak :)
We did load all up to 700k.
After 700k ther are 23 options. We will decide after the challenge what will come after 700k.
Happy crunching...
Lennart
____________



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Hi all PPS freak :)
We did load all up to 700k.
After 700k ther are 23 options. We will decide after the challenge what will come after 700k.
Apparently the decision was already made as I see tasks for n>700000 going out for k>1200. What was that decision? 



After 700k ther are 23 options. We will decide after the challenge what will come after 700k.
Apparently the decision was already made as I see tasks for n>700000 going out for k>1200. What was that decision?
This doesn't sound like the previously mentioned
"After that we follow the plan k= 100500 up to n=1.5M"
looks more like
"1200<k<4000 to 800K". Bruce* 


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Apparently the decision was already made as I see tasks for n>700000 going out for k>1200. What was that decision?
This doesn't sound like the previously mentioned
"After that we follow the plan k= 100500 up to n=1.5M"
looks more like
"1200<k<4000 to 800K". Bruce*[/quote]
Lennart let me know via PM that he had to load up to n=710000 to ensure that the server wouldn't run out of work during the challenge. 



...
Lennart let me know via PM that he had to load up to n=710000 to ensure that the server wouldn't run out of work during the challenge.
Thanks; so I can stop counting 9's to find when the next range
starts arriving. That's n=690xxx, n=6990xx, n=69990x that I've
been seeing in my valid task list, PPS LLR. Bruce 



I was looking for an explanation why my PPS LLR units suddenly increase from a 9 minute runtime to 80 minutes runtime.
I guess this has something to do with it?
____________




I was looking for an explanation why my PPS LLR units suddenly increase from a 9 minute runtime to 80 minutes runtime.
I guess this has something to do with it?
Yes and no. Yes it is because of the larger n's, but not the ones mentioned here if I'm not mistaken. I guess you're getting pps_llr instead of pps_llr_extended, like me and some of other power cows on our own forum? If you look at the results you'll see that _extended is with n's in the range of 700k  7??k, but the non extended are for n's over 2M. This apparently costs a lot more time. 



More time, more credits: so it looks fair enough :)
____________
92*10^^{1439761}1 NEARREPDIGIT PRIME :) :) :)
4â€Š*â€Š650^^{498101}1 CRUS PRIME
314187728^^{131072}+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! 



Credit is not the most important for me on LLR, I am more interested in finding primes, so just wanted to know what the impact is of these longer WU's for finding a prime.
If the chance prime/not prime stays the same, then the chance of finding a prime has decreased (ie. 9 times smaller).
____________




I am with Arjant2 :D just wanna find primes :) 



TheDawgz are frequently fuzzy on these type of things so please correct us if we are wrong ... but
It looks like we have moved into a range that John had mentioned back in July consisting of low k's and n's > 2M.
If so, then this should be mostly 1st pass work and the primes should make the Top 100 with digit counts >600k.
____________
There's someone in our head but it's not us. 



TheDawgz are frequently fuzzy on these type of things so please correct us if we are wrong ... but
It looks like we have moved into a range that John had mentioned back in July consisting of low k's and n's > 2M.
If so, then this should be mostly 1st pass work and the primes should make the Top 100 with digit counts >600k.
Looks like a mixture of ranges on my end. I've got wu's running between 15 minutes and 1:30 hours on the same machine. So, here's hoping to find one of the "big" primes. 


JohnHonorary cruncher
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I was looking for an explanation why my PPS LLR units suddenly increase from a 9 minute runtime to 80 minutes runtime.
I guess this has something to do with it?
Our apologies. The tasks were from our next range: 10<k<32 from 2M<n<2.5M The work was uploaded yesterday and the WU generator started sending them out prematurely. There's still ~100k tasks remaining in the 709k710k range. The issue has been resolved and the work has returned to that range.
Here's an update to the remaining PPS ranges on the todo list:
10<k<32 from 2M<n<2.5M
100<k<500 from 1M<n<1.5M
500<k<1200 from 1M<n<1.3M
1200<k<4000 from 710k<n<800k
Additionally, we are looking at splitting out the single digit k's to achieve the following levels:
3 @ 7M (321 Prime Search  ongoing effort)
5 @ 5M
7 @ 4M
9 @ 3M (already at 3M)
So basically, it's only 5 & 7 that would increase. Our effort remains to search lower k's to higher n's intermixed with work from the 1200<k<10000 lower n ranges.
____________




Thanx John for clarifying.
____________



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Additionally, we are looking at splitting out the single digit k's to achieve the following levels:
3 @ 7M (321 Prime Search  ongoing effort)
5 @ 5M
7 @ 4M
9 @ 3M (already at 3M)
As I maintain prothsearch.com, I recommend taking 5, 7, and 9 to 5M. 



Have we moved into the newer ranges now? I notice most of my wu's are now taking much longer to run. 



Just because you add or subtract 1 from a given number, you do not necessarily end up with a prime number.
But in my guess it could be either even or odd.
If they are even, they should not be prime numbers.
What about this example number: 8867383 .
Put that number into a formula and try deduce whether it is prime or not.
Anyway, I just put it together a little bit and wrote 37*49*67*73 into my calculator.
Only 49 (7*7) is not a prime, the other three numbers are.
So, if a given number happens to possibly return a factor in it, that number is not prime, but what about any number in it (like 73)? They could be prime numbers on their own.
The fundamental theorem of arithmetic says that every integer greater than one can be written as a unique product (up to ordering) of primes. So the prime factorization of the number you gave is 7*7*37*67*73.
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Have we moved into the newer ranges now? I notice most of my wu's are now taking much longer to run.
Yes. 10<k<32 from 2M<n<2.5M is now in the queue. It will be followed by 500<k<1200 from 1M<n<1.3M and then an n range in 1200<k<4000 from 710k<n<800k.
____________




Just because you add or subtract 1 from a given number, you do not necessarily end up with a prime number.
But in my guess it could be either even or odd.
[...].
The number they add or subtract 1 to/from is always even, because it is a multiple of 2. Therefor every number tested must be odd, exactly because every even number other than 2 can not be prime.
____________
PrimeGrid Challenge Overall standings  Last update: From Pi to Paddy (2016)




Have we moved into the newer ranges now? I notice most of my wu's are now taking much longer to run.
Yes. 10<k<32 from 2M<n<2.5M is now in the queue. It will be followed by 500<k<1200 from 1M<n<1.3M and then an n range in 1200<k<4000 from 710k<n<800k.
Great, thanks for the update. 


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Progress Update
Progress through the 10<k<32 for 2M<n<2.5M range has been surprisingly quick. We are currently at 2.375M after only a couple of days. At this rate, we should reach 2.5M in 34 days. That is quite IMPRESSIVE!!!
Next up is the 500<k<1200 for 1M<n<1.3M range. We are skipping over the 100<k<500 for 1M<n<1.5M range (for now) to give participants at the Proth Search Site time to complete their reservations. Afterwards, we'll complete a section of the 1200<k<4000 to 800K range.
Proth Prime Search Update
k=3 to 25M is ongoing in the 321 Prime Search (currently at n=7457987)
k=5 to 5M (currently at n=3M)
k=7 to 4M (currently at n=3M)
k=9 to 3M (currently at n=3M)
10<k<32 to 2.5M is ongoing (currently at n=2004074)
32<k<100 to 2M (currently at n=2M)
100<k<500 to 1.5M (currently at n=1M)
500<k<1200 to 1.3M (currently at n=1M)
1200<k<4000 to 800K is ongoing (currently at n=691891)
4000<k<10000 to 700K is ongoing (currently at n=691891)
____________



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Progress Update
Faster than expected, work for the 10<k<32 for 2M<n<2.5M range has been emptied. We are now in the 500<k<1200 for 1M<n<1.3M range. Next up we'll complete a section of the 1200<k<4000 to 800K range...most likely 710k725k, more if necessary.
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Hi all,
I have some questions concerning PPS:
When i look at the range statistics page, I wonder why there are only 1186 tasks completed for k=4801 when 21210 are done for k=4785 ?
On the 5, 000 largest known prime list, I read for instance that 27*2^2218064+1 is prime and it was found in 2009, but it is in the n=22.5M range we just finished to check. So, my first question is what project found this prime in 2009 ? The second is how do you take this former discovery into account ?
Fab
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HonzaVolunteer moderator Volunteer tester Project scientist Send message
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I found mentioned prime on PRPNET (27121 Prime Search subproject: k=27 & 121 for k*2^n+1 for n<10M)
This particular range of k=27 (now n~3,77M) was already covered, same apply for k=121 (now n~4.39M)
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JohnHonorary cruncher
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When i look at the range statistics page, I wonder why there are only 1186 tasks completed for k=4801 when 21210 are done for k=4785 ?
The k's have different densities. After sieving, k's have a different number of candidates remaining. In this case, k=4785 has a great deal more candidates remaining than k=4801.
Nash weights are typically used to compare remaining candidate densities between k's. Chris Nash created the Nash Sieve. From this, in collaboration with Paul Jobling, came psieve. psieve offered an option that would calculate the Nash weight of k's. This is simply the count of those n remaining after applying the Nash sieve. The standard Nash weight is calculated over the range 100000 < n < 110000.
Another comparison tool is Jack Brennen's Proth Weight applet. If you input 4785 to 4801 with step 2, you'll see for that range that k=4785 is the highest weight and 4801 is the lowest weight.
Note that these are general comparison tools.
On the 5, 000 largest known prime list, I read for instance that 27*2^2218064+1 is prime and it was found in 2009, but it is in the n=22.5M range we just finished to check. So, my first question is what project found this prime in 2009 ? The second is how do you take this former discovery into account ?
As Honza points out, 27*2^2218064+1 was found in a previous PrimeGrid effort in PRPNet. When new work is loaded, we mark all known primes so they are not tested again.
Additionally, there are individual searchers who are prime finding on their own. We invite all individual searchers to upload their residues to save PrimeGrid time in (double) checking their ranges.
____________




When new work is loaded, we mark all known primes so they are not tested again.
Most of the time. There are those few that sneak through every so often. Take it from someone who had one :)




Merci :)
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Progress Update
Progress through the 500<k<1200 for 1M<n<1.3M range has been trudging along. Today we have reached n=1.1M. At that rate, we have AT LEAST 24 more days to reach 1.3M.
Next up is the 1200<k<4000 to 800K range (710k725k). It is probably while we're in this range that we'll see the end to SGS single primes making it into the Top 5000 list. :(
Proth Prime Search Update
k=3 to 25M is ongoing in the 321 Prime Search (currently at n=7505609)
k=5 to 5M (currently at n=3M)
k=7 to 4M (currently at n=3M)
k=9 to 3M (currently at n=3M)
10<k<32 to 2.5M (currently at n=2.5M)
32<k<100 to 2M (currently at n=2M)
100<k<500 to 1.5M (currently at n=1M)
500<k<1200 to 1.3M is ongoing (currently at n=1.1M)
1200<k<4000 to 800K (currently at n=710k)
4000<k<10000 to 700K (currently at n=710k)
FYI, as of this post, n entry levels in the Top 5000 list:
350th  n=1338620
400th  n=1269198
500th  n=1168975
600th  n=1086798
____________




Hi,
Proth Prime Search (LLR)
The beta cuda is ready ???
OpenCL is used ??
thanks 


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Please have a look in the thread llrCUDA testing.
____________
Best wishes. Knowledge is power. by jjwhalen




The leading edge is now at n=1280000 close to the 1,3M edge.
If the suspension of PPS prime reporting continues, may I suggest PPS continues at k=5 (and/or 7) instead of 1200<k<4000 since there are fewer primes in the higher n range (lower k)... 



The leading edge is now at n=1296000, hours away from the 1,3M cut.
Since the PPS prime reporting halt is still ongoing, i'd like to revisit my suggestion below to continue with lower k's (5 and/or 7) instead of 1200<k<4000....
Any thoughts/comments...? 



...
Here's an update to the remaining PPS ranges on the todo list:
10<k<32 from 2M<n<2.5M
100<k<500 from 1M<n<1.5M
500<k<1200 from 1M<n<1.3M
1200<k<4000 from 710k<n<800k
Additionally, we are looking at splitting out the single digit k's to achieve the following levels:
3 @ 7M (321 Prime Search  ongoing effort)
5 @ 5M
7 @ 4M
9 @ 3M (already at 3M)
So basically, it's only 5 & 7 that would increase. Our effort remains to search lower k's to higher n's intermixed with work from the 1200<k<10000 lower n ranges.
Alternatively, if 5 & 7 were split out, people could switch from PPS LLR to the
5split or 7split projects. I might run some of each; keeping an eye on the top20
list (by number, not by score! tied at twelve, but with enough backlog for 11th).
Meanwhile, the return of electric here has produced a SGS hit; my first since April 14.
Bruce* 



well now the cue is empty...
are we now to believe that PPS is on hold completely until the end of SGS primes to top5000 ?! 



well now the cue is empty...
are we now to believe that PPS is on hold completely until the end of SGS primes to top5000 ?!
The queue is filled again  not sure what with, but something. One
of my managers was reporting no tasks for c. 5 hours. Bruce*
(Two SGS hits ... These don't seem to be getting reported either;
nothing from PrimeGrid in the past 48 hours  only one,
"11/2/2011 21:20:06 CDT", West Tennessee time.) 



It was filled with 1200<k<4000...
I guess our suggestions were ignored and not even honored with a reply... 



It was filled with 1200<k<4000...
I guess our suggestions were ignored and not even honored with a reply...
Yes, looks like
3061*2^710016+1 is not prime.
Given that not even SGS primes are being reported, looks like
our Admins are busy elsewhere. If one compares SGS and the
present PPS LLR range, n = 710000 is going to be well above
the lower edge of the Top5000, for a while, at least.
Regards, Bruce* 



well now the cue is empty...
are we now to believe that PPS is on hold completely until the end of SGS primes to top5000 ?!
It was filled with 1200<k<4000...
I guess our suggestions were ignored and not even honored with a reply...
With my apologies to the Admins and the other 45,568 other registered users here at PrimeGrid ..
Please loose the attitude.
____________
There's someone in our head but it's not us. 



excuse me?!
I mean no disrespect to the admins.
I think they do a fantastical job running PG.
But the PPSreportinghalt is a mess (in my opinion, which my dear TheDawgz I hope I still may have) of their own making... 


JohnHonorary cruncher
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Alternatively, if 5 & 7 were split out, people could switch from PPS LLR to the
5split or 7split projects.
I apologize for the miscommunication. I should have said "singled out within the PPS (LLR) project" instead of splitting out. k=5 & 7 will remain within the PPS (LLR) project. There are currently no plans on separating them out like k=3 which btw was a collaboration with the 321 Search project. :)
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But the PPSreportinghalt is a mess
Yes, the lack of prime submissions external to PrimeGrid has caught us by surprise...meaning that PPS primes will have to wait a little bit longer before submission is resumed. However we view this as a positive as it allows more users searching SGS to submit their primes into the Top 5000 list.
PPS prime submission will continue to be suspended until SGS falls out of the Top 5000 list. The bottom 50 can be viewed here. Current PPS primes awaiting to be submitted will enter at position ~330th to 690th. Their expected lifespan in the Top 5000 list is upwards of a decade. Therefore, there's no concern of them falling out any time soon.
The 710k725k primes will enter at position ~3260th. Again, no concern of falling out any time soon.
Thank you for your patience as we navigate through SGS's end to the Top 5000 list.
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...meaning that PPS primes will have to wait a little bit longer before submission is resumed. However we view this as a positive as it allows more users searching SGS to submit their primes into the Top 5000 list.
Might I suggest that at this point, all that is being accomplished is delaying the inevitable, at the cost of artificially withholding submissions that by all rights aught to have already been submitted.
Although I consider it unlikely, it is conceivable that someone other than PrimeGrid might also submit the prime to the top 5k list. I don't think you want to be in the position of defending the nonsubmission to the prime finder if someone jumps ahead of him/her and submits it manually while the primes are being withheld.
My opinion, for what it's worth, is that more harm than good is being done right now.
____________
My lucky number is 75898^{524288}+1 



I think the idea is that no one will do SGS if they do not get into the top 5000.
I think it is rubbish, consider that many happily do Sieves and SOB with no chance of finding a prime (SOB = very little chance with only 5 left to find and 17 for the whole project).
I agree that admins should let nature take its course. I have no personal gain in ths as I have not got any primes (not even waiting ones).
____________
Member team AUSTRALIA
My lucky number is 9291*2^1085585+1 


JohnHonorary cruncher
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I think the idea is that no one will do SGS if they do not get into the top 5000.
No, that is not the case. It's simply to optimize the end of SGS on the Top 5000 list. BTW, TPS continued quite well after it fell from the Top 5000 list and eventually, the twin was found.
____________




I think the idea is that no one will do SGS if they do not get into the top 5000.
No, that is not the case. It's simply to optimize the end of SGS on the Top 5000 list. BTW, TPS continued quite well after it fell from the Top 5000 list and eventually, the twin was found.
That would be the pair with n = 333333, 8/13/2009. Sounds like
n = 333333 fell off of the top5000 in 2009, with n = 666666 falling
off in 2011. Would a plausible extrapolation be that n = 999999
will fall off some time in 2013? If so, n < 1M lasts only two years.
That's a longer timeframe than the next couple of weeks, to one
month, maybe for PPS LLR reporting to be unfrozen. My first result
in distributed computing was c. 1/3 of the sieving for breaking RSA120
in June 1993. I'm starting to wonder whether the next two years
of PPS LLR might merit a higher priority than weeks 3 and 4 of keeping
SGS in the top5000; which would suggest a hard deadline of
Nov 21. My current backlog of 20 hits (18 PPS, 2 SGS) is a moderate
career'sworth. My most recent was 10/14; next week will be a month's
worth of computing with no feedback on results. Just wondering ...
Bruce* 


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Progress Update
We are well into 1200<k<4000 to 800K range (710k725k). SGS has officially dropped out of the Top 5000 list and the backlog of PPS primes have been submitted.
Next up is the 100<k<500 to 1.5M range. We expect to enter that range within the next two weeks.
Proth Prime Search Update
k=3 to 25M is ongoing in the 321 Prime Search (currently at n=7505609)
k=5 to 5M (currently at n=3M)
k=7 to 4M (currently at n=3M)
k=9 to 3M (currently at n=3M)
10<k<32 to 2.5M (currently at n=2.5M)
32<k<100 to 2M (currently at n=2M)
100<k<500 to 1.5M (currently at n=1M)
500<k<1200 to 1.3M (currently at n=1.3M)
1200<k<4000 to 800K ongoing (currently at n=710k)
4000<k<10000 to 725K ongoing (currently at n=710k)
____________




Progress Update
We are well into 1200<k<4000 to 800K range (710k725k). SGS has officially dropped out of the Top 5000 list and the backlog of PPS primes have been submitted.
Next up is the 100<k<500 to 1.5M range. We expect to enter that range within the next two weeks.
...
Looks like these are starting early, n=1M, before the finish to 725k  likely
to keep traffic down for the duration of the Challenge?
I'm still seeing a mixture of the two, but the earlier range is still in
n = 722k, so perhaps the two weeks worth is being deferred.
Looking to get my gold on 321 during or soon after the Challenge,
then maybe work on TRP. Bruce* 


JohnHonorary cruncher
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Looks like these are starting early, n=1M, before the finish to 725k  likely
to keep traffic down for the duration of the Challenge?
It's the nature of the WU generator. When both PPS (4<k<1200) and PPSE (1200<k<10000) work is in the queue, both will go out together. Otherwise, it's typically by n.
At the rate PPSE (1200<k<10000 for 710k<n<725k) was going out, we were going to be empty in a day or two.
____________




No PPS LLR WUs available?
____________
35 x 2^3587843+1 is prime! 


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Progress Update
Currently, the active range is 100<k<500 to 1.5M.
Proth Prime Search Update
k=3 to 25M is ongoing in the 321 Prime Search (trailing edge n=7620569; leading edge n=8180124)
k=5 to 5M (currently at n=3M)
k=7 to 4M (currently at n=3M)
k=9 to 3M (currently at n=3M)
10<k<32 to 2.5M (currently at n=2.5M)
32<k<100 to 2M (currently at n=2M)
100<k<500 to 1.5M ongoing (trailing edge n=1005938; leading edge n=1103385)
500<k<1200 to 1.3M (currently at n=1.3M)
1200<k<4000 to 800K ongoing (trailing edge n=724010; leading edge n=725k)
4000<k<10000 to 725K ongoing (trailing edge n=723984; leading edge n=725k)
Green is completed goal. :)
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Here is a milestone of sorts  My first prime I got since coming back to PG in July 2011 is now ranked 5035  It entered the top 5000 ranked 3513 in August 2011
5035  2337 Â· 2^678383 + 1  204218  L2522  Aug 2011
We are moving at a fast pace it seems
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Member of AtP
Shown here is an Australian native rat (Ratus Kickarsus) 


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Progress Update
The March to the Solstice has made good progress towards accomplishing these goals.
NOTE: A snafu in loading the next range allowed k=7 to also be included. Therefore, we'll be taking both k=5 & 7 to 5M. This will weaken our chances of finishing the goals by the end of the year.
Currently, the active range is k=5 & 7 from 3M to 5M.
Proth Prime Search Update
k=3 to 25M is ongoing in the 321 Prime Search (trailing edge n=7673589; leading edge n=8192966)
k=5 to 5M ongoing (trailing edge n=3000949; leading edge n=4246999)
k=7 to 5M ongoing (trailing edge n=3000104; leading edge n=4246816)
k=9 to 3M (currently at n=3M)
10<k<32 to 2.5M (currently at n=2.5M)
32<k<100 to 2M (currently at n=2M)
100<k<500 to 1.5M ongoing (trailing edge n=1187833; leading edge n=1.2M)
500<k<1200 to 1.3M (currently at n=1.3M)
1200<k<4000 to 800K ongoing (trailing edge n=739038; leading edge n=775k)
4000<k<10000 to 725K (currently at n=725k)
Green is completed goal. :)
____________



HonzaVolunteer moderator Volunteer tester Project scientist Send message
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John, how many candidates are there for active range is k=5 & 7 from 3M to 5M?
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My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 


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John, how many candidates are there for active range is k=5 & 7 from 3M to 5M?
k=5: 29,519 total
k=7: 71,585 total
____________




My upmost appolgy to PG and the wing man..For some reason my PPS.llr than ran for 15 minutes turned into 3:30 to 4:30 hours. Even tho my cach is a day on all..well I had to abort quit a bit of wu's because of time dead lines. Sorry..
____________
My first Prime
20208428036625*2^6666661 (SGS)
PROUD MEMBER OF TEAM CARL SAGAN 


JohnHonorary cruncher
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The End of 2011
Here are the numbers for the end of 2011. Looks like a good starting point for 2012! :)
May 2012 be a healthy and prosperous year for all!
Proth Prime Search Update
k=3 to 25M is ongoing in the 321 Prime Search (trailing edge n=7743792; leading edge n=8192966) excluded from year end goals ;)
k=5 to 5M ongoing (trailing edge n=3377139; leading edge n=5M)
k=7 to 5M ongoing (trailing edge n=3307796; leading edge n=5M)
k=9 to 3M (currently at n=3M)
10<k<32 to 2.5M (currently at n=2.5M)
32<k<100 to 2M (currently at n=2M)
100<k<500 to 1.5M ongoing (trailing edge n=1.2M; leading edge n=1223663)
500<k<1200 to 1.3M (currently at n=1.3M)
1200<k<4000 to 800K (currently at n=775k)
4000<k<10000 to 725K (currently at n=725k)
Green is completed goal. :)
____________



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I see that 500<k<1200 has been loaded with workunits over 1.3M. When can we expect goals for 2012? 


JohnHonorary cruncher
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2012 Goals
Here are the new goals for 2012. Yes, they are much more aggressive than last year. However, with the promise of the new AVX builds available for Sandy Bridges, we have confidence that these goals are attainable.
Proth Prime Search Update
k=3 to 9M  ongoing in the 321 Prime Search (trailing edge n=7841640; leading edge n=8192966)
k=5 to 7M  (currently at n=5M)
k=7 to 6M  (currently at n=5M)
k=9 to 4M  (currently at n=3M)
10<k<32 to 3M  (currently at n=2.5M)
32<k<100 to 2.5M  (currently at n=2M)
100<k<500 to 2M  ongoing (trailing edge n=1245850; leading edge n=1373125)
500<k<1200 to 1.5M  ongoing (trailing edge n=1.3M; leading edge n=1303923)
1200<k<4000 to 1.25M  (currently at n=775k)
4000<k<10000 to 1M  (currently at n=725k)
Green is completed goal. :)
____________



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2012 Goals  Progress update
The Year of the Dragon completed a huge chunk of work. We are very close to achieving the first goal of the year. One month down, 11 to go. :)
Thank you to everyone for participating. Once n=1.5M has been reach for both 100<k<500 and 500<k<1200, we'll move to lower n's at 4000<k<10000.
Proth Prime Search Update
k=3 to 9M  ongoing in the 321 Prime Search (trailing edge n=7981182; leading edge n=8192966)
k=5 to 7M  (currently at n=5M)
k=7 to 6M  (currently at n=5M)
k=9 to 4M  (currently at n=3M)
10<k<32 to 3M  (currently at n=2.5M)
32<k<100 to 2.5M  (currently at n=2M)
100<k<500 to 2M  ongoing (trailing edge n=1406274; leading edge n=1484139)
500<k<1200 to 1.5M  ongoing (trailing edge n=1320383; leading edge n=1484139)
1200<k<4000 to 1.25M  (currently at n=775k)
4000<k<10000 to 1M  (currently at n=725k)
Green is completed goal. :)
____________



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2012 Goals  Progress update
The 4000<k<10000 range has made some GREAT strides over the past week going from n=725k to n~747k. That's pretty AMAZING!!! And just as expected, producing a lot of primes for the Tour. BTW, the effort to get to 1.5M resulted in completing the first goal of 2012. Congratulations to all!
Thank you to everyone for participating. Should we reach n=775k next week, the 1200<k<4000 range will be added and both will be loaded up to n=800k. That should definitely last through the end of the Tour.
Proth Prime Search Update
k=3 to 9M  ongoing in the 321 Prime Search (trailing edge n=8037764; leading edge n=8192966)
k=5 to 7M  (currently at n=5M)
k=7 to 6M  (currently at n=5M)
k=9 to 4M  (currently at n=3M)
10<k<32 to 3M  (currently at n=2.5M)
32<k<100 to 2.5M  (currently at n=2M)
100<k<500 to 2M  (currently at n=1.5M)
500<k<1200 to 1.5M  (currently at n=1.5M)
1200<k<4000 to 1.25M  (currently at n=775k)
4000<k<10000 to 1M  ongoing (trailing edge n=728077; leading edge n=746811)
Green represents a completed goal. :)
____________



rogueVolunteer developer
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k=5 to 7M  (currently at n=5M)
k=7 to 6M  (currently at n=5M)
k=9 to 4M  (currently at n=3M)
Would you consider testing all of these (or just 5 and 7) to the same n? 



Will there ever be an expansion above k=10,000?
I like seeing discoveries of Fermat divisors, and there are probably some low n primes in the 10000<k<50000 range. 



Top 5 Fermat factors with k>10000:
71007 * 2^49490 + 1
177795 * 2^38969 + 1
121531 * 2^30260 + 1
13323 * 2^19220 + 1
17217 * 2^14530 + 1
Those are some pretty low n values! 



Perhaps a separate project dedicated to high k value Fermat divisors would be more appropriate though. I doubt we'd find many top 5000 primes, if any. 


rogueVolunteer developer
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Will there ever be an expansion above k=10,000?
I like seeing discoveries of Fermat divisors, and there are probably some low n primes in the 10000<k<50000 range.
There is already a project that has a search, although it isn't coordinated with a client/server app. Go over to fermatsearch.org. 


JohnHonorary cruncher
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Perhaps a separate project dedicated to high k value Fermat divisors would be more appropriate though. I doubt we'd find many top 5000 primes, if any.
As rogue mentions, F E R M A T S E A R C H . O R G offers what you're looking for. Additionally, in their news section, you'll see PG's last two Fermat primes. :)
Also, if you take a look at Prime factors k Â· 2^n + 1 of Fermat numbers F(m) and complete factoring status compiled by Wilfrid Keller, you see at the bottom of the page Known search limits. In the 10000<k<50000 range you mention, here are the following limits:
up to k=10000 has been searched to n=210000 (actually, latest PRPNet progress shows n=313065)
up to k=20000 has been searched to n=77000
up to k=50000 has been searched to n=61000
____________



JohnHonorary cruncher
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k=5 to 7M  (currently at n=5M)
k=7 to 6M  (currently at n=5M)
k=9 to 4M  (currently at n=3M)
Would you consider testing all of these (or just 5 and 7) to the same n?
Once all the goals have been met for the year, this would certainly be considered. Note that k=5 is such a low weight that getting it to 7M would only take a week or so. However, k=7 & 9 are heavy weights and would take quite a bit longer. Even just getting k=9 to 5M will take some time.
____________



rogueVolunteer developer
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k=5 to 7M  (currently at n=5M)
k=7 to 6M  (currently at n=5M)
k=9 to 4M  (currently at n=3M)
Would you consider testing all of these (or just 5 and 7) to the same n?
Once all the goals have been met for the year, this would certainly be considered. Note that k=5 is such a low weight that getting it to 7M would only take a week or so. However, k=7 & 9 are heavy weights and would take quite a bit longer. Even just getting k=9 to 5M will take some time.
That just means more opportunities for mega primes! 


JohnHonorary cruncher
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Joined: 21 Feb 06 Posts: 2875 ID: 2449 Credit: 2,681,934 RAC: 0

k=5 to 7M  (currently at n=5M)
k=7 to 6M  (currently at n=5M)
k=9 to 4M  (currently at n=3M)
Would you consider testing all of these (or just 5 and 7) to the same n?
Once all the goals have been met for the year, this would certainly be considered. Note that k=5 is such a low weight that getting it to 7M would only take a week or so. However, k=7 & 9 are heavy weights and would take quite a bit longer. Even just getting k=9 to 5M will take some time.
That just means more opportunities for mega primes!
An optimist! I like it!!! :D
____________




What's the plan after n=800k has been reached for the current range? Will the next range of n's be loaded for 1200<k<10000 or will we be switching back to lower k's/higher n's?
____________
PrimeGrid Challenge Overall standings  Last update: From Pi to Paddy (2016)



HonzaVolunteer moderator Volunteer tester Project scientist Send message
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I think n>800k can be loaded for whole 1200<k<10000.
500<k<1200 to 1.5M  (currently at n=1.5M)
1200<k<4000 to 1.25M  (currently at n=775k)
4000<k<10000 to 1M  ongoing (trailing edge n=728077; leading edge n=746811)
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 


JohnHonorary cruncher
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2012 Goals  Progress update
The Tour de Primes has really done a nice job advancing PPS (LLR) towards its 2012 goals. Well done everyone!!!
Work will continue for the 120010000 ranges up to n=800k. Afterwards, a decision will be made where to go next. Most likely the search will stay at this level and push towards n=850k or even 900k. It all depends on progress. The past 3 weeks have just been incredible moving through a 55k n range. If the pace continued, 850k could be reached by the end of March.
As for other ranges, there's definitely plenty of work to do. The path forward will be to "cherry pick" some of the easier goals to achieve. It's nice to see bold green in the list. ;) Expect a pattern of venturing off to another range and then back to 120010000. This will be repeated over and over for the rest of the year.
Thank you again to everyone helping out with this effort. :)
Proth Prime Search Update
k=3 to 9M  ongoing in the 321 Prime Search (trailing edge n=8077245; leading edge n=8202120)
k=5 to 7M  (currently at n=5M)
k=7 to 6M  (currently at n=5M)
k=9 to 4M  (currently at n=3M)
10<k<32 to 3M  (currently at n=2.5M)
32<k<100 to 2.5M  (currently at n=2M)
100<k<500 to 2M  (currently at n=1.5M)
500<k<1200 to 1.5M  (currently at n=1.5M)
1200<k<4000 to 1.25M  ongoing (trailing edge n=775000; leading edge n=780000)
4000<k<10000 to 1M  ongoing (trailing edge n=763032; leading edge n=780733)
Green represents a completed goal. :)
____________



HonzaVolunteer moderator Volunteer tester Project scientist Send message
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Work will continue for the 120010000 ranges up to n=800k. Afterwards, a decision will be made where to go next. Most likely the search will stay at this level and push towards n=850k or even 900k.
We are now at 799k territory.
Since now further annoucement was made, I assume we will simply continue in most likely scenario.
FFT length: 64K
I wonder when it gets increased?
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 



Work will continue for the 120010000 ranges up to n=800k. Afterwards, a decision will be made where to go next. Most likely the search will stay at this level and push towards n=850k or even 900k.
We are now at 799k territory.
Since now further annoucement was made, I assume we will simply continue in most likely scenario.
FFT length: 64K
I wonder when it gets increased?
Hi
800k810k is loaded and I think we will go to at least 900k first and then we can discuss further directions.
Lennart
____________




All I ask is that Primegrid hold off on k=63 & k=87. I have been independently crunching those k values for n>2,000,000. Once I'm finished, I'll gladly share the results.
I have been crunching these two k values, even at lower n, for quite some time.
(edit): Please hold off on "32<k<100 to 2.5M  (currently at n=2M)"
____________
15547296^32768 + 1 is prime!
63 Â· 2^1356980 + 1 is prime!
63 Â· 2^1356980 + 1 divides xGF(1356973,11,4)! 



any update?
____________
wbr, Me. Dead J. Dona




You can check the progress here also: http://www.primegrid.com/stats_pps_llr.php
It looks like we are sitting at 856K complete for the 1200<k<4000 and 4000<k<10000 ranges. So we completed about 100,000 n for each k in the last two months. I think we can definitely accomplish these goals by the end of the year if we keep making that kind of progress.
____________




PPSE 1200<k<4000 and 4000<k<10000 is loaded to 870k now.
Leading edge is at 859k now.
Lennart 



PPSE 1200<k<4000 and 4000<k<10000 is loaded to 870k now.
Leading edge is at 859k now.
I was mentioning passing Buster for 7th over on the credit milestone
thread; but perhaps it's worth noting that credit here on PPS (LLR) is
pretty good. I blew past both Buster and Mumps (who hasn't been
moving) into 6th  my RAC took a dip while running some TRPs during
the Challenge, but it's gone back up after switching back.
With a clear field up to 870k in view (and perhaps somewhat further
after that, towards 900k), I starting to contemplate the nearly unthinkable.
Another 1000 points to catch Lennart!
(This is on the Primegrid "Top Prime Finders" (by score) listing.)
Lennart



HonzaVolunteer moderator Volunteer tester Project scientist Send message
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I was mentioning passing Buster for 7th over on the credit milestone
thread; but perhaps it's worth noting that credit here on PPS (LLR) is
pretty good. I blew past both Buster and Mumps (who hasn't been
moving) into 6th  my RAC took a dip while running some TRPs during
the Challenge, but it's gone back up after switching back.
...
Another 1000 points to catch Lennart!
Actually, I like this stats. It is a long way run and doesn't involve GPUs...yet.
I hope to get 10th (by score) soon. 5th by total prime count...it will not last long, will it?
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 



PPSE 1200<k<4000 and 4000<k<10000 is loaded to 870k now.
Leading edge is at 859k now.
Lennart
This evening's email says
the following prime was submitted on your behalf:
107045 : 4341*2^870079+1 (261924 digits)
so perhaps the next range has been loaded ... if so,
how far? John's leapday post mentions 900k as possible;
as well as 2012 yearend targets of 1.25M and 1M split
at k = 4000.
Regards, bdodson* 



PPSE 1200<k<4000 and 4000<k<10000 is loaded to 870k now.
Leading edge is at 859k now.
Lennart
This evening's email says
the following prime was submitted on your behalf:
107045 : 4341*2^870079+1 (261924 digits)
so perhaps the next range has been loaded ... if so,
how far? John's leapday post mentions 900k as possible;
as well as 2012 yearend targets of 1.25M and 1M split
at k = 4000.
Regards, bdodson*
We are definitely zipping through quite quickly.
____________




At what n are we going to transition to a different k range?
____________




At what n are we going to transition to a different k range?
We're getting real close to n=900K
7821*2^889737+1 is not prime.
2447*2^889707+1 is not prime.
6041*2^889705+1 is not prime.
The options appear to be to staying with these k = 1200,4000;
k = 4000,10000 perhaps heading towards n=1M or switching
to one of the smaller k ranges. Judging by the above we may
know soon what Lennart et.al. have decided.
(Well, fairly close.)
bdodson*
Currently 3rd on the PrimePages Top20 by number of primes;
two behind Broadhurst for 2nd (actually 1+ epsilon). 



It appears that we have transitioned to a different range.
____________




Edit to my previous post, I thought we had transitioned ranges because my computer was now taking 7+ hours to do a PPS LLR, but it turns out some WU I had aborted didn't end their processes and were hogging up all my CPU resources. D'oh.
____________




I am working on a new SGS range now so We will go up to 1M before we start on lower pps k's.
Lennart 



Thanks for telling us the plan. Hopefully we make it there soon, and complete these goals by the end of the year.
____________




2012 Goals  Progress update
Good progress is being made in advancing PPS (LLR) towards its 2012 goals. Let's keep up the good work!!!
Work will continue for the 120010000 ranges up to n=1M. SGS is actively being sieved and we want to make sure PPS is high enough to remain on the Top 5000 when SGS starts.
After n=1M has been reached for 120010000, the path forward will be to "cherry pick" some of the easier goals to achieve. It's nice to see bold green in the list. ;) We will then return to 12004000 to push it to n=1.25M.
Thank you again to everyone helping out with this effort. :)
Proth Prime Search Update
k=3 to 9M  ongoing in the 321 Prime Search (trailing edge n=8374043; leading edge n=8399706)
k=5 to 7M  (currently at n=5M)
k=7 to 6M  (currently at n=5M)
k=9 to 4M  (currently at n=3M)
10<k<32 to 3M  (currently at n=2.5M)
32<k<100 to 2.5M  (currently at n=2M)
100<k<500 to 2M  (currently at n=1.5M)
500<k<1200 to 1.5M  (currently at n=1.5M)
1200<k<4000 to 1.25M  ongoing (trailing edge n=881184; leading edge n=891369)
4000<k<10000 to 1M  ongoing (trailing edge n=881974; leading edge n=891369)
Green represents a completed goal.
Lennart 



Awesome! Looking good there.
____________




2012 Goals  Progress update
Good progress is being made in advancing PPS (LLR) towards its 2012 goals. Let's keep up the good work!!!
Work will continue for the 120010000 ranges up to n=1M. SGS is actively being sieved and we want to make sure PPS is high enough to remain on the Top 5000 when SGS starts.
...
Thank you again to everyone helping out with this effort. :)
Proth Prime Search Update
...
100<k<500 to 2M  (currently at n=1.5M)
500<k<1200 to 1.5M  (currently at n=1.5M)
1200<k<4000 to 1.25M  ongoing (trailing edge n=881184; leading edge n=891369)
4000<k<10000 to 1M  ongoing (trailing edge n=881974; leading edge n=891369)
Green represents a completed goal.
Lennart
Some of the SGS timings appeared focused on n=1.29M with large k.
Is that the range of the new SGS/twin llr search? In a few years that
would bump all of 4000 < k < 10000 for sure, looks like all of
1200 < k < 4000 as well. Of course, all primes below 1000000digits
will be bumped from the top5K eventually, presuming that we keep at this,
and a SGS search that far above 2^1M will find primes at a slower
rate than we're enjoying here below 2^1M.
To rephrase the question, with the previous SGS search at
200700digits, what's the new threshold? Looks like n=1.29M
suggests somewhere above 370000digits, perhaps a round
400000digits?
Best Regards, Bruce*
(currently 2nd on the PrimePages list by number of primes
on the top5K list) 


j.sheridanVolunteer tester Send message
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SGS is actively being sieved
where? can we join in? 



SGS is actively being sieved
where? can we join in?
You don't have to ! The first range will be done in ~15 days.
Lennart 



Does the first range being done mean that SGS will start again, or will you go further into the sieve before the project is started again? And what n level is it this time?
____________



HonzaVolunteer moderator Volunteer tester Project scientist Send message
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So, leading edge (and primes reported) are in >900k territory, well done.
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 


HonzaVolunteer moderator Volunteer tester Project scientist Send message
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Leading edge is almost ~915k and FFT size of 72K is stating to kick in with higher k's.
Expect some WUs with longer processing time of ~20%.
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 



That will slow down our progress a bit, but hopefully it doesn't make too big of a dent in our progress to 1mil.
____________




Progress is quite good, we have increased the leading edge by about 35K since Lennart's update at the beginning of the month.
____________




Progress is quite good, we have increased the leading edge by about 35K since Lennart's update at the beginning of the month.
As nice round number today,
5385*2^925000+1, 278457 (decimal)
75K n's to go. 



We are going at the pace of about 1000 n per day, so we should get to 1mil before mid September.
____________




The pace slowed, it looks like we won't hit 1mil until late September/possibly early October, regardless, we should finish off <1mil before the challenge which will mean we should be able to destroy the next range during the challenge (I'm guessing that will be the 1200<k<4000 range to 1.25mil goal that we will work on during the challenge since they would have the shortest times of the remaining goals. Although Lennart did say:
After n=1M has been reached for 120010000, the path forward will be to "cherry pick" some of the easier goals to achieve. It's nice to see bold green in the list. ;) We will then return to 12004000 to push it to n=1.25M. Perhaps we will finally have a PPS challenge that won't challenge the servers?
____________




The pace slowed, it looks like we won't hit 1mil until late September/possibly early October, regardless, we should finish off <1mil before the challenge which will
mean ...
Here's another week's progress (of a sort)
Added 109143 : 9071*2^983279+1 (296001 digits)
296Kdigits, with another c. 17K bits left to go to k=1M.
bdodson*
(rapidly dropping from 200 primes on the top5000,
down to 180 primes; and down from 2nd to 4th
place by number of primes)
(255Kdigit Proth primes from April/May 2011  April/May 2012
dropping out of the top5000 more quickly than I'm
finding new 296Kdigit primes ...) 


HonzaVolunteer moderator Volunteer tester Project scientist Send message
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We will enter TOP2000 with PPS primes very soon...
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 



Leading edge just passed 999000, we should hit the goal by the end of Monday. Does anyone know what the next range will be and if it will loaded immediately upon completing this range?
____________




I asked Lennart about this when posting the challenge announcement. This was his answer:
We have to finish all up to 1M first so we might load 1M+ if we need more in the challenge and change to lower k's after the challenge. If we finish 1M before the challenge we might start on a lower k.
Seeing how we have a challenge that will only last 1 day I would think it's most interesting to load 1200<k<4000 to 1.25M is most interesting, as this will allow most people to participate.
____________
PrimeGrid Challenge Overall standings  Last update: From Pi to Paddy (2016)




I agree with you. I also don't think it will take too terribly long to finish off that range.
____________



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Good News Everyone! Leading edge is over 1M. But why 4000<k<10000 is also loaded over 1M? I thought we'll focus on 1200<k<4000 after we reach 1M. 



I'm guessing code on the server needs to be updated in order for a new range to be sent out.
____________




So, any idea on when we are going to move onto a new range rather than keep plugging away past the previous goal?
____________




Good News Everyone! Leading edge is over 1M. But why 4000<k<10000 is also loaded over 1M? I thought we'll focus on 1200<k<4000 after we reach 1M.
Lennart's June 2012 Update gives 1M as the target for the year
on 4000 < k < 10000. Of the recent Proth's above 1M, three have
k < 4000 (mine's 3791*2^1001609+1 (301518 digits)), while there
are fourteen with 4000 < k < 10000. (That's relative to the Prime
Pages window of 72 hours.)
Seems like a majority of our current effort is focused off of the annual
targets, which includes 1200 < k < 4000 to 1.25M. There's also the
usual odds for a Proth prime to be a Fermat divisor of 1/k, which favors
k < 4000; although searching k > 4000 gets credit (on the 'Pages)
for larger difficulty.
Bruce* 



Good News Everyone! Leading edge is over 1M. But why 4000<k<10000 is also loaded over 1M? I thought we'll focus on 1200<k<4000 after we reach 1M.
Lennart's June 2012 Update gives 1M as the target for the year
on 4000 < k < 10000. Of the recent Proth's above 1M, three have
k < 4000 (mine's 3791*2^1001609+1 (301518 digits)), while there
are fourteen with 4000 < k < 10000. (That's relative to the Prime
Pages window of 72 hours.)
Seems like a majority of our current effort is focused off of the annual
targets, which includes 1200 < k < 4000 to 1.25M. There's also the
usual odds for a Proth prime to be a Fermat divisor of 1/k, which favors
k < 4000; although searching k > 4000 gets credit (on the 'Pages)
for larger difficulty.
Bruce*
The leading edge is the same for 1200<k<4000 and 4000<k<10000, they aren't favoring either.
____________




2012 Goals  Progress update
Good progress is being made in advancing PPS (LLR) towards its 2012 goals. Let's keep up the good work!!!
Work will continue for the 120010000 ranges up to n=1.1M. SGS is online and we want to make sure PPS is high enough to remain on the Top 5000.
Thank you again to everyone helping out with this effort. :)
Proth Prime Search Update
k=3 to 9M  ongoing in the 321 Prime Search (trailing edge n=8.5M; leading edge n=8.62M)
k=5 to 6M  (currently at n=5M) (*)
k=7 to 6M  (currently at n=5M)
k=9 to 4M  (currently at n=3M)
10<k<32 to 2.5M  (currently at n=2.5M)
32<k<100 to 2.2M  (currently at n=2M)
100<k<500 to 2.2M  (currently at n=2M)
500<k<1200 to 2.2M  (currently at n=1.5M)
1200<k<10000 to 1.03M  ongoing (trailing edge n=998493; leading edge n=1.005M)
Green represents a completed goal.
Lennart 



Good to know, but this makes me unsure of whether or not we will be able to hit all the goals for this year if we are pushing 1200<k<10000 that far, oh well. It amounts to less low range work for next year.
____________




... Of the recent Proth's above 1M, three have
k < 4000 ..., while there are fourteen with 4000 < k < 10000. ...
The leading edge is the same for 1200<k<4000 and 4000<k<10000, they aren't favoring either.
They? I'm suggesting two counting questions. three vs fourteen?
is one. The other is 4000  1200 = 2800 k's vs 10000  4000 =
6000 k's. There are waymore k's in the 2nd range being sent out,
and that "favors" the larger k range by 28to60. More candidates
submitted to LLR and more primes found. Substantially.
But, of course, Lennart's right. For a short term 1.0M  1.1M we
can tolerate a few extra early 2013 primes; I think we were wondering
about 1.0M  1.25M, but that isn't happening. OK?
bdodson* (@Lennart: thanks for the update!)




We should have changed to a smaller k but I will keep the low n in the challenge.
It is only 24hr.
Lennart 



We should have changed to a smaller k but I will keep the low n in the challenge.
It is only 24hr.
Lennart
Uhm; that's "low n" meaning large k, and continuing with
1200<k<10000 to 1.03M  ongoing (trailing edge n=998493; leading edge n=1.005M)
if I'm reading correctly. The smaller k's have n at/above 2M.
I'm seeing
7555*2^1010048+1 is not prime.
4869*2^1010097+1 is not prime.
for tasks that have just been sent, as in
4 Oct 2012  13:30:46 UTC 4 Oct 2012  13:47:48 UTC
With c. 27 hours to the start of the challenge, looks like
we'll be competing in n=1.01. Bruce* 



...
I'm seeing
7555*2^1010048+1 is not prime.
4869*2^1010097+1 is not prime.
for tasks that have just been sent, as in
4 Oct 2012  13:30:46 UTC 4 Oct 2012  13:47:48 UTC
With c. 27 hours to the start of the challenge, looks like
we'll be competing in n=1.01. Bruce*
Looks like the leading edge at/near the end of the challenge
was in 1.017M
Is prime? 9125*2^1017239+1 is not prime.
...
413603656 290601 6 Oct 2012  15:17:36 UTC 6 Oct 2012  17:53:22 UTC Aborted by user 0.00 0.00  PPS (LLR) v1.01
413848949 187389 6 Oct 2012  17:56:38 UTC 7 Oct 2012  2:53:40 UTC Completed and validated 8,374.76 8,323.37 11.41 PPS (LLR) v6.13
shows 1.017239M sent at 15:17, then resent at 17:56, just short of
the 18:00 UTC close. And for one just past the close
Is prime? 6699*2^1017827+1 is not prime.
...
413686351 291102 6 Oct 2012  18:27:50 UTC 6 Oct 2012  22:23:40 UTC Aborted by user 0.00 0.00  PPS (LLR) v6.13
413853911 187389 6 Oct 2012  18:28:12 UTC 7 Oct 2012  5:11:13 UTC Completed and validated 8,568.37 8,507.76 9.89 PPS (LLR) v6.13
413872377 239220 6 Oct 2012  22:23:56 UTC 7 Oct 2012  0:37:04 UTC Completed and validated 551.37 456.55 9.89 PPS (LLR) v1.01
with quorum 2, sent at 18:27 UTC, for 1.0178M
Server seems to have gotten past the load from the contest; I'm
seeing 180 tasks to be validated now, under 100 a few minutes ago;
and "primes found" back up (rather than "down for contest").
Bruce* (@peppert*: nice cores!)




2012 Goals  Progress update
Good progress is being made in advancing PPS (LLR) towards its 2012 goals. Let's keep up the good work!!!
Work will continue for the 120010000 ranges up to n=1.1M. SGS is online and we want to make sure PPS is high enough to remain on the Top 5000.
Thank you again to everyone helping out with this effort. :)
Proth Prime Search Update
k=3 to 9M  ongoing in the 321 Prime Search (trailing edge n=8.62M; leading edge n=8.68M)
k=5 to 6M  (currently at n=5.55M)
k=7 to 6M  (currently at n=5.55M)
k=9 to 4M  (currently at n=4M)
10<k<32 to 2.5M  (currently at n=2.5M)
32<k<100 to 2.2M  (currently at n=2M)
100<k<500 to 2.2M  (currently at n=2M)
500<k<1200 to 2.2M  (currently at n=1.5M)
1200<k<10000 to 1.03M  ongoing leading edge n=1.03M)
Lennart
Updated 20121023 00:30 UTC 



FYI, the PPS goals in the LLR priorities thread are outdated.
____________




k=3,5,7 have all met or exceeded their goals.
____________




2012 Goals  Progress update
Good progress is being made in advancing PPS (LLR) towards its 2012 goals.
Only about one month left. Let's keep up the good work!!!
Work will continue for the 120010000 ranges up to n=1.1M. SGS is online and we want to make sure PPS is high enough to remain on the Top 5000.
Thank you again to everyone helping out with this effort. :)
Proth Prime Search Update
k=3 to 9M  ongoing in the 321 Prime Search (trailing edge n=8.99M; leading edge n=8.68M)
k=5 to 6M  (currently at n=6M) DONE
k=7 to 6M  (currently at n=6M) DONE
k=9 to 4M  (currently at n=4M) DONE
10<k<32 to 2.5M  (currently at n=2.5M) DONE
32<k<100 to 2.2M  (currently at n=2M)
100<k<500 to 2.2M  (currently at n=1.5M)
500<k<1200 to 2.2M  (currently at n~1.6M)
1200<k<10000 to 1.03M  ongoing leading edge n=1.03M) DONE
Lennart
Updated 20121128 02:30 UTC 


