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rogueVolunteer developer
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Would it be possible to load all remaining work for PPS (for decimal length < 1 million digits) the next time work is loaded? Maybe a thread could be started for people to guesstimate when all of those tasks will be completed. |
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I have always assumed that PPS will continue and just begin searching the range where PPS-Mega stopped before it was expanded to include k>1200.
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rogueVolunteer developer
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I have always assumed that PPS will continue and just begin searching the range where PPS-Mega stopped before it was expanded to include k>1200.
Possibly, but the point is that PrimeGrid has a known number of work units to find all sub-mega PPS primes for k < 1200. PPS Mega is open-ended. |
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And the convention at this point is to terminate the non-MEGA suffixed project when it catches up to the project that was intended to leapfrog up to mega primes (GFN-17 low stopped while GFN-17 mega continued). I don't think that makes sense though. Consider the terminal state, eventually PrimeGrid will only be searching for mega primes (on most if not all prime finding projects), so it won't make sense to have projects specifically named to clarify that they are searching for mega primes.
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 mikey
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Would it be possible to load all remaining work for PPS (for decimal length < 1 million digits) the next time work is loaded? Maybe a thread could be started for people to guesstimate when all of those tasks will be completed.
Is this all of the PPS tasks or just the Sive kind or just the LLR kind? |
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The naming conventions were made back when Mega was a lot less likely. The issue is that there are statistics sites that take into effect the name of the projects and create statistics per name. Renaming them afterward throws all those stats out the door. So keeping the names, as is, will most likely be the way things work. PPS itself will go away and PPS Mega will continue on.
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streamVolunteer moderator
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Would it be possible to load all remaining work for PPS (for decimal length < 1 million digits) the next time work is loaded? Maybe a thread could be started for people to guesstimate when all of those tasks will be completed.
I'll not load all this work now, but I could say that we have 724203 tests not loaded yet. Add "Available tasks" (underlined) from front page and you'll get total number of untested candidates.
The discussion is still ongoing, but it's most possible that PPS will became "low K, high N" project. I.e. it'll will leapfrog to 3,64M for few small k's. Details on which range and k should be tested are still under development.
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[...] PPS itself will go away and PPS Mega will continue on.
If PPS were to go away, then PPS DIV would need to revive.
It would not make sense to have no subprojects for 4<k<1200, and two subprojects for k>1200.
But stream's prospect of few small k sounds nice.
/JeppeSN |
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streamVolunteer moderator
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One of two remaining files with PPS candidates is loaded. Now we have 339058 candidates in remaining file plus plus number of loaded candidates visible on front page left.
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pawgSend message
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Can PPS Mega test full width of k's? In that scenario we will have only two PPS subprojects, Extended with small tasks and Mega with large ones. One day when PPSE will reach 1M mark there will be only one PPS subproject left. |
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One day when PPSE will reach 1M mark there will be only one PPS subproject left.
PPSE is currently gaining ~426 digits/week (see here)
at this rate PPSE will reach 1M on June 3rd 2044. |
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By then, I'll be 83 yo :)
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Nick 
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By then, I'll be 83 yo :)
I will be trying to work out the technicalities of pants. |
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mikey
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By then, I'll be 83 yo :)
I will be trying to work out the technicalities of pants.
LOL!! |
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streamVolunteer moderator
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Below is a tentative final plan for PPS transition
For overview of currently tested and untested ranges, check my page http://boincvm.proxyma.ru:30080/test4vm/public/pps_dc_status.php
We'll switch to concept of "optimal testing depth". It's based on "weight" of a prime - https://primes.utm.edu/top20/page.php?id=8#weighted which is the ratio of computational effort to probability of success for a GFN divisor. A simplified meaning of this formula is: it makes sense to test small k higher.
We're going to test k >= 51. Using k=49, N=9M as a starting point, Yves Gallot calculated optimal testing depth for all k's. These values were rounded up with 0.5M step. Finally, it gives following optimal test ranges for each k:
51-57 9,0M
59-69 8,5M
71-83 8,0M
85-103 7,5M
105-129 7,0M
131-165 6,5M
167-213 6,0M
215-285 5,5M
287-391 5,0M
393-557 4,5M
559-739 4,0M
I.e. first we'll test k=51-739 for N=3,64M-4,0M. Next, number of k's will be reduced and we'll test k=51-557 for N=4,0M-4,5M. And so on. k >= 741 will be not tested at all, their optimal depth is below 3,64M (they'll be eventually merged with PPS-MEGA).
k < 51 should be tested higher than 9M, but we don't have a good sieving for this range yet. Anyway, it'll take a while to get there and sieving should be ready at that point.
Additionally, we'll test k=9, 27, 121 up to 9M (regardless of optimal depth) to double-check PrpNet tests (k=27, 121) and finish untested candidates remaining from DIV project (k=9). |
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Great. I like the tentative plan a lot!
It is going to be a bit like filling a closed upside-down funnel with water. Or should we say a conical flask.
It will take a while to fill this flask. After that, we'll see if sieving for tiny k (4<k<50) has been accomplished.
/JeppeSN |
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What determines the optimal depth? What will need to happen for some of these ranges to be pushed farther?
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Yves GallotVolunteer developer
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What determines the optimal depth? What will need to happen for some of these ranges to be pushed farther?
The optimal depth is infinite but for each fixed amount of work (of Cobblestones on PrimeGrid) a list of numbers of the form k·2n + 1 can be tested. However k and n are not independent and an optimal "contour line" can be calculated.
Let N = k·2n + 1 and lN = log N.
The time complexity of performing one multiplication is O(lN log lN). A primality test is O(lN) multiplications. The likelihood that N is prime is 1/lN then the complexity for one prime is O(lN3 log lN). log lN is almost constant for PPS then O(lN3) provides a good estimate. Since k << 2n this is O(n3).
The divisibility of a Fermat or a GF number is a desired property and we know that the probability is about 1/k for N prime.
Then the contour lines are defined by the relation k · n3 = constant.
For example, if the limit for k = 51 is n = 9M then for k ~ 500 we have nmax ~ (51 · 9M3 / 500)1/3 ~ 4.2M and for k ~ 5000: nmax ~ 2M. |
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Very good. The k * n^3 = constant idea was also discussed three years ago. Someone (theAy) made a post with a nice (k,n) plot with the various PPS projects back then. But this was before our PPS-DIV project (which was conceived after discussions of this sort), and the plot also does not show the move of PPS-MEGA to 1200<k<10000. /JeppeSN |
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rogueVolunteer developer
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It looks the rest of the PPS takes for k <1200 that are less than 1e6 digits have been loaded. This would be a good time of everyone to guess when the last task (not a double-check) will be handed out. |
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Very good. The k * n^3 = constant idea was also discussed three years ago. Someone (theAy) made a post with a nice (k,n) plot with the various PPS projects back then. But this was before our PPS-DIV project (which was conceived after discussions of this sort), and the plot also does not show the move of PPS-MEGA to 1200<k<10000. /JeppeSN
That is a very descriptive plot; where is theAy as I believe they can add considerably to this tread?
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New megaprime tasks are now being sent out on "regular" PPS! /JeppeSN |
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New megaprime tasks are now being sent out on "regular" PPS! /JeppeSN
Cool !
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rogueVolunteer developer
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I'm surprised that the current challenge has wiped out the remaining candidates < 1M digits so quickly, although many of those tests are not completed yet. |
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Such a new PPS-regular megaprime 295*2^3642206+1 can be seen now at https://www.primegrid.com/primes/primes.php?project=PPS&factors=XGF&sortby=date. /JeppeSN |
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Last PPS workunit for n < 3,32M returned today.
"Old PPS" if officially finished. Now all k's are testing new ranges.
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