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Message boards :
Wieferich and Wall-Sun-Sun Prime Search :
Which near-finds are shown?
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I am not sure I understand which near-Wieferich and near-Wall-Sun-Sun primes are actually shown. In WW by the numbers it is stated "For numbers between 1e9 and the end of our PRPNet search, special instances with |A| <= 100 are shown". Doesn't this mean that, from the pages here and here, say 3411159925463651, to pick a random example, should be reported? Or is that sentence to be read "For numbers between 1e9 and the end of our PRPNet search, special instances with |A| <= 100 that were previously missed are shown"? If not, why are those primes not listed at the WW Statistics page? Or was that range part of the "very beginning of the current search (completed in the first day)" mentioned in the WW by the numbers thread? Thanks for any insight into this. | |
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 Michael Goetz Volunteer moderator
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I am not sure I understand which near-Wieferich and near-Wall-Sun-Sun primes are actually shown. In WW by the numbers it is stated "For numbers between 1e9 and the end of our PRPNet search, special instances with |A| <= 100 are shown". Doesn't this mean that, from the pages here and here, say 3411159925463651, to pick a random example, should be reported? Or is that sentence to be read "For numbers between 1e9 and the end of our PRPNet search, special instances with |A| <= 100 that were previously missed are shown"? If not, why are those primes not listed at the WW Statistics page? Or was that range part of the "very beginning of the current search (completed in the first day)" mentioned in the WW by the numbers thread? Thanks for any insight into this.
Correct, previously known primes (both of them) and special instances are not shown. They've already been discovered, so they're not shown as discoveries.
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My lucky number is 75898524288+1 | |
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So from /stats_ww.php we infer that we have not found any (nontrivial) missed near-finds yet. When we get out of the region that was covered by PRPNet, the distinction between "missed" and "known" near-finds will disappear, and we should start seeing more entries on that stats page. /JeppeSN | |
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BurVolunteer tester
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I hope I didn't miss something obvious, but the results page now shows a prime found by Grzegorz with A = 193.
WW by the numbers says only primes with |A|<=100 are shown for the range covered by PRP previously. That prime is at 265E15, so below the previous limit of 6E17.
Anyway, congratulations!
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000 | |
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Ravi FernandoProject administrator
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I hope I didn't miss something obvious, but the results page now shows a prime found by Grzegorz with A = 193.
WW by the numbers says only primes with |A|<=100 are shown for the range covered by PRP previously. That prime is at 265E15, so below the previous limit of 6E17.
You did miss something: this is a near-Wall-Sun-Sun prime, not a near-Wieferich, and the PRPNet WSS search didn't get as far as the Wieferich search. In fact this prime is just beyond the PRPNet search limit. | |
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Nice! Apparently, the WSS search on PRPNet did not miss any finds or near-finds, but good to be in new territory now (with Wall-Sun-Sun, that is). I verified it with my PARI function. Looks like everything is working perfectly. /JeppeSN | |
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I have speculated whether it would be relevant to consider |A| ≤ 10'000 as near-finds once the leading edge advances far enough. Of course the natural measure would be |A| / p.
/JeppeSN | |
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Michael GoetzVolunteer moderator
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Nice! Apparently, the WSS search on PRPNet did not miss any finds or near-finds, but good to be in new territory now (with Wall-Sun-Sun, that is). I verified it with my PARI function. Looks like everything is working perfectly. /JeppeSN
We were only double checking for primes, not special instances. We were skipping *all* special instances until we were past the PRPNet range. The original plan was to start the current search where PRPnet left off, but I wanted to make sure we didn't miss any actual primes. That would have been tragic.
Checking for missed special instances would have been exceptionally difficult because we don't have a definitive list of what had been discovered previously.
From this point on (in WSS), we will report everything that's found. But until now, we've only been looking for primes.
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My lucky number is 75898524288+1 | |
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So we do not know how many near-finds were "missed" by the PRPNet search?
Do you have a list of all near-finds up to 265174785950610443 (by some reasonable definition)? Some (all?) of the near-WSS found on PRPNet can be seen at http://u-g-f.de/PRPNet/findlist_adv.php?proj=WSS, right now.
I thought about constructing a sequence of all primes p such that |A|/p was smaller than for any previous prime.
/JeppeSN | |
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ReggieVolunteer moderator
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So we do not know how many near-finds were "missed" by the PRPNet search?
There were no near-finds missed by PRPNet with |A|<=100. I do not know how many were missed with 100<|A|<=1000.
Do you have a list of all near-finds up to 265174785950610443 (by some reasonable definition)? Some (all?) of the near-WSS found on PRPNet can be seen at http://u-g-f.de/PRPNet/findlist_adv.php?proj=WSS, right now.
That list is complete. I will be working on a page later today to show imported data.
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Message boards :
Wieferich and Wall-Sun-Sun Prime Search :
Which near-finds are shown? |
