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Dear all,
A recent Wall-Sun-Sun (WSS) find from DeleteNull (double checker wwwwww): 2569278229005192557 is a WallSunSun special instance (+0 +12 p)
If you use the natural measure |A|/p to see how close it is to being a WSS, you get:|A|/p = 12/2569278229005192557 = 4.67*10^{-18} This is smaller than for any other known prime!
I keep a list of such records at OEIS A339855 where the new entry will soon appear as #47 in the Link Jeppe Stig Nielsen, Table of n, a(n).
(Last time PrimeGrid found a WSS record of this kind was in June 2015 on PRPNet when user zunewantan found 104868559750360787 (0 +1 p), so |A|/p = 9.54*10^{-18}.)
/JeppeSN |
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Congratulutions!
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Congrats DeleteNull ! |
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Congratulations, DeleteNull !
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"Accidit in puncto, quod non contingit in anno."
Something that does not occur in a year may, perchance, happen in a moment. |
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Thank you all. Who will find a smaller A?
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DeleteNull |
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Thank you all. Who will find a smaller A?
This would be an 'a' :)
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"Accidit in puncto, quod non contingit in anno."
Something that does not occur in a year may, perchance, happen in a moment. |
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 Dave 
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Joined: 13 Feb 12
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Thank you all. Who will find a smaller A?
This would be an 'a' :)
a
I win. |
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BurVolunteer tester
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Why is |A| divided by p?
The remainder r is already divided by p to yield |A| if I'm not mistaken. So why do we divide the remainder by p²?
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000 |
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Why is |A| divided by p?
The remainder r is already divided by p to yield |A| if I'm not mistaken. So why do we divide the remainder by p²?
In a way, |A|/p is like a "random" number between 0 and 0.5.
Consider first a prime near 1 million, say 1'000'003. The A of this one could be any integer from the list -500'001, -500'000, -499'999, ..., -2, -1, 0, +1, +2, ..., +500'001. For such a number to get an A with |A| <= 1000 corresponds to a "probability" (in quotes) of about 0.2%. In fact, we have:1'000'003 is a WallSunSun special instance (+0 -343'227 p)
Now, think of a prime near 1 billion, namely 1'000'000'007. Now A is from -500'000'003 through +500'000'003. So the probability that this should have an |A| <= 1000 is only 0.0002%. In this case:1'000'000'007 is a WallSunSun special instance (+0 -72'187'555 p)
In fact, the second example is more "lucky", in a sense. Even though its |A| is much higher.
The measure |A|/p is clearly about 0.34 for the first one (bad). But for the second one, |A|/p is quite good, 0.07.
For comparison, the one DeleteNull found had |A|/p equal to:
0.00000000000000000467
Not sure if this explains it?
/JeppeSN |
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May be we should add badges for small |A|, so people would have more understanding about the difficulty to find such small.
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DeleteNull |
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All we have are badges for A=0, namely:
 World First Wall-Sun-Sun prime
(there is no World First for Wieferichs because Waldemar Meißner found the the first Wieferich prime by hand in 1913)
And:
 a Wall-Sun-Sun prime
 a Wieferich prime
Maybe these badges will never be awarded.
/JeppeSN |
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All we have are badges for A=0, namely:
World First Wall-Sun-Sun prime
(there is no World First for Wieferichs because Waldemar Meißner found the the first Wieferich prime by hand in 1913)
And:
a Wall-Sun-Sun prime
a Wieferich prime
Maybe these badges will never be awarded.
/JeppeSN
hopefully, the will !!!
regards,
Grzegorz Roman Granowski
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Kind of interesting would be a badge, which goes to the current world record holder. And maybe a badge if you had the badge once...
So not a fix badge, but kind of "travelling" badge...
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"MiauiKatze" is german and means as much as "mewing cat"!
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Michael GoetzVolunteer moderator
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Kind of interesting would be a badge, which goes to the current world record holder. And maybe a badge if you had the badge once...
So not a fix badge, but kind of "travelling" badge...
That probably won't happen while my lungs draw breath. I'm very much against awards that get taken away from users.
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My lucky number is 75898524288+1 |
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Kind of interesting would be a badge, which goes to the current world record holder. And maybe a badge if you had the badge once...
So not a fix badge, but kind of "travelling" badge...
That probably won't happen while my lungs draw breath. I'm very much against awards that get taken away from users.
Ok, I haven't seen that this way...
You are completely right!
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"MiauiKatze" is german and means as much as "mewing cat"!
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That record did not stand long!
Rick Reynolds (with double checker sakage@otoge) found: 3071294187877470251 is a WallSunSun special instance (+0 +14 p)
This gives:|A|/p = 14/3071294187877470251 = 4.56*10^{-18} which is smaller (i.e. nearer) than DeleteNull's record from earlier this month.
Congratulations. I will update OEIS A339855 again.
/JeppeSN |
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Congrats Rick!
Progress seems very fast from 25... to 30...
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DeleteNull |
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Congrats Rick!
Progress seems very fast from 25... to 30...
Thanks didn’t even realize until now. Bet it won’t last long!
Cheers |
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compositeVolunteer tester
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I'd better get on the bandwagon before it's gone.
Except that my GTX 760 takes 20 times longer to run a task than my wingman.
(I came equipped for this gumfight. Oh! he said GUNfight. LOL)
EDIT:
I uninstalled the NVidia driver (418.181.07) that comes from Debian's nonfree section and installed the latest (460.67) that I could get from nvidia.com and I see a whopping 20% improvement in WW runtimes. Is this for real or just the natural variation in task runtimes?
It is probably for real. The GPU utilization went up, from 83% to 97%.
WAITAMINUTE. I went from 1 thread per task to 2 threads per task. This would account for the higher GPU utilization. But I expected the CPU time to double, instead of dropping by 1/3 to 1/2. So it could yet be the driver. |
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Congrats, RR !
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"Accidit in puncto, quod non contingit in anno."
Something that does not occur in a year may, perchance, happen in a moment. |
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Congrats, RR !
Thank you! |
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compositeVolunteer tester
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The change of driver configuration has a minor contribution to the speedup.
It shaves 20 seconds (2.2%) from PPS sieve.
This is understandable. I had the whole gamut of management interfaces hooked into the driver installed from the Debian repo, whereas I have none of that when I installed the driver downloaded from NVidia. |
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Again congrats! And with Wieferich (+1) with a<10!
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Again congrats! And with Wieferich (+1) with a<10!
Yes, really nice! Maybe deserves a separate thread because it is not a Wall-Sun-Sun. /JeppeSN |
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That record did not stand long!
Rick Reynolds (with double checker sakage@otoge) found:3071294187877470251 is a WallSunSun special instance (+0 +14 p)
This gives:|A|/p = 14/3071294187877470251 = 4.56*10^{-18} which is smaller (i.e. nearer) than DeleteNull's record from earlier this month.
Congratulations. I will update OEIS A339855 again.
/JeppeSN
Beaten by an A=-1 find. Finder GregCinAZ, and DC'er vanos0512. See the separate thread about it.
|A|/p = 1/7665762181374748069 = 0.13*10^{-18}
/JeppeSN |
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World First Wall-Sun-Sun prime
a Wall-Sun-Sun prime
a Wieferich prime
