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321 Prime Search :
More than 60 hours to find a factor?
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 Bur Volunteer tester
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Joined: 25 Feb 20
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I was looking through my stats and from a little over 3000 sieve tasks I found 55 factors or one in 63 tasks. Since each task now takes more than one hour that's 63 hours to eliminate one candidate.
321 LLR takes 8 hours on average, so I could have done 350 or more LLR tests instead of finding 55 composites.
I know the n-range of the sieve is much larger, but still it seems a waste of time to me. When LLR will reach the current n values of the sieve computers will be faster as well, so will they take 63 hours to LLR the same number?
Or am I missing something? I'm quite sure you guys have a good reason to keep the sieve running even now, but could someone please explain? :)
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000 | |
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Michael GoetzVolunteer moderator
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I was looking through my stats and from a little over 3000 sieve tasks I found 55 factors or one in 63 tasks. Since each task now takes more than one hour that's 63 hours to eliminate one candidate.
321 LLR takes 8 hours on average, so I could have done 350 or more LLR tests instead of finding 55 composites.
I know the n-range of the sieve is much larger, but still it seems a waste of time to me. When LLR will reach the current n values of the sieve computers will be faster as well, so will they take 63 hours to LLR the same number?
Or am I missing something? I'm quite sure you guys have a good reason to keep the sieve running even now, but could someone please explain? :)
You answered your own question: We're not just sieving the candidates we're testing now, but also the candidates we'll be testing with LLR years from now. 321 is currently in the n=16M range, and we're sieving up to n=50M. Those tasks will take about 10 times as long to run on LLR as the current tasks.
So, yes, you found 55 factors, but by the end of the sieve file, you would be able to only 35 tasks on LLR rather than the 350 you could do today.
That being said, we just switched to fast double checks, which either makes LLR twice as fast, or the sieve twice as slow. When this is taken into account, we may already be at the point where it's time to stop sieving 321. More information on this aspect will be forthcoming once we decide what we're going to do.
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My lucky number is 75898524288+1 | |
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robishVolunteer moderator
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That being said, we just switched to fast double checks, which either makes LLR twice as fast, or the sieve twice as slow. When this is taken into account, we may already be at the point where it's time to stop sieving 321. More information on this aspect will be forthcoming once we decide what we're going to do.
Wow I completely missed that. That's a nice dilemma to ponder :)
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My lucky numbers 10590941048576+1 and 224584605939537911+81292139*23#*n for n=0..26 | |
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That being said, we just switched to fast double checks, which either makes LLR twice as fast, or the sieve twice as slow. When this is taken into account, we may already be at the point where it's time to stop sieving 321. More information on this aspect will be forthcoming once we decide what we're going to do.
Wow I completely missed that. That's a nice dilemma to ponder :)
GOSH! I missed that too!
*starts sieving immediately*
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My lucky number is 6219*2^3374198+1
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BurVolunteer tester
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So, yes, you found 55 factors, but by the end of the sieve file, you would be able to only 35 tasks on LLR rather than the 350 you could do today. I see, this doesn't take increasing computational speed into account though. I don't know when those candidates will be LLR checked and how strong speed increases, but since even 35 is close to 55 and 321 sieve now is actually slower than 1 h (I saw many 5000 s WUs) it might be a problem?
And leaps in efficiency such as LLR2 might occur again. To me it feels like a lot of CPU time is used for something now that if circumstances change slightly could be a waste. And since sieving is so far ahead of LLR, why not pause?
(once again, I have little experience in this matter, so don't take it as condescending, I'm merely curious)
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000 | |
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Michael GoetzVolunteer moderator
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...this doesn't take increasing computational speed into account...
You're ignoring the fact that CPU speed will also affect sieves. If we run the sieve in the future, it will be running on those same, super fast 100-th generation Intel or Zen-99 CPUs, or whatever we're running at that point. The ratio of the sieve to the CPU will presumably stay the same. There's no advantage to deferring the sieving.
On the other hand, starting and stopping projects involves a lot of administrative work, and disruption for users. We'd much prefer to get the entire thing done in one shot that to keep starting and stopping it. The only reason we've started and then restarted sieves is because we never imagined we'd need further sieving, not because we thought it was better to defer it to the future.
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My lucky number is 75898524288+1 | |
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BurVolunteer tester
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Ok, I didn't think about that. If there's a breakthrough in LLR similar to LLR2 though, then sieving time might have been wasted. If LLR2 had hit 2 years from now for example.
But I understand that it's a big effort from administrative point of view.
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000 | |
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Michael GoetzVolunteer moderator
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Ok, I didn't think about that. If there's a breakthrough in LLR similar to LLR2 though, then sieving time might have been wasted. If LLR2 had hit 2 years from now for example.
You can't make decisions based upon what magical hardware or software advances might suddenly appear -- or not appear -- in the indefinite future.
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My lucky number is 75898524288+1 | |
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Ok, I didn't think about that. If there's a breakthrough in LLR similar to LLR2 though, then sieving time might have been wasted. If LLR2 had hit 2 years from now for example.
You can't make decisions based upon what magical hardware or software advances might suddenly appear -- or not appear -- in the indefinite future.
Think quantum, maybe?
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My lucky number is 6219*2^3374198+1
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mikey
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Ok, I didn't think about that. If there's a breakthrough in LLR similar to LLR2 though, then sieving time might have been wasted. If LLR2 had hit 2 years from now for example.
You can't make decisions based upon what magical hardware or software advances might suddenly appear -- or not appear -- in the indefinite future.
Think quantum, maybe?
Is that 1 NM die size? | |
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321 Prime Search :
More than 60 hours to find a factor? |
