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Congratulations to K Lewis for finding 19030795636403797. That's the first near Wieferich with A < 100 in a while and the first with A < 100 above 3e15 that had not already been found by Dorais and Klyve beforehand. Nice. 


RogerVolunteer developer Volunteer tester
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Yay, I got a Wieferich near find!
69397046751123461 (1 173 p). That was the hardest near find to date, requiring 37,353 tests.
The number of tests required till the next near find loosely follows an exponential curve.
Now I can relax for the PRPNet 27 Challenge.
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As many of you are probably not aware, Richard Crandall got me involved with the Wieferich search a number of years ago. Working with him led to the creation of a Wieferich search I did a few years ago and more recently prompted me to learn about OpenCL and write wwwwcl. It was his hope that another Wieferich prime would be found in his lifetime. Sadly, that didn't happen as he died on Thursday. He was very well known in the mathematics community and it was an algorithm of his, the Discrete Weight Transform, that is behind most prime searches today.
In his memory, I propose that everyone dedicate some CPU and/or GPU power to the Wieferich search for a few days. Maybe we'll get lucky. 


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R.I.P Richard Crandall :(
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92*10^^{1439761}1 NEARREPDIGIT PRIME :) :) :)
4 * 650^^{498101}1 CRUS PRIME
314187728^^{131072}+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! 


Michael GoetzVolunteer moderator Project administrator
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It is extremely sad to hear of his passing, and I'd like to offer my condolences to his family and friends. The world is a lesser place now.
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Thank you Mark for sending along the news, sad though it may be.
Gary 


HonzaVolunteer moderator Volunteer tester Project scientist Send message
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Out of curiosity, there is a mockup graph of Near Wieferich founds so far.
http://s2.postimage.org/upgl0qant/Wieferich.png
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Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 


rogueVolunteer developer
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Our of curiosity, there is a mockup graph of Near Weiferich founds so far.
http://s2.postimage.org/upgl0qant/Wieferich.png
That's interesting, but I wonder how it would look if the x axis were logarithmic. 


HonzaVolunteer moderator Volunteer tester Project scientist Send message
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That's interesting, but I wonder how it would look if the x axis were logarithmic.
Hope I got it right... http://postimage.org/image/nzdxprg7h/
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My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 



I got one today! My last one was in July. :0
82684879689553451 (1 458 p)
But look at this one found today,
MiHost 82687771042557349 (1 10 p)
WOW! Very close!
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HonzaVolunteer moderator Volunteer tester Project scientist Send message
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But look at this one found today,
MiHost 82687771042557349 (1 10 p)
WOW! Very close!
I think that's nearest one we have found so far!
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My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 


Sysadm@NbgVolunteer moderator Volunteer tester Project scientist
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But look at this one found today,
MiHost 82687771042557349 (1 10 p)
WOW! Very close!
I think that's nearest one we have found so far!
Yes
according to my list (sorted by value) the formerly nearest were
user team client value date reported
Tarmo_Ilves Aggie_The_Pew server3 3723113065138349 (1 +18 p) Saturday 31st of December 2011 04:31:52 PM
JAMC My_Way 2 5131427559624857 (+1 18 p) Tuesday 03rd of January 2012 10:51:51 PM
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I got one today! My last one was in July. :0
82684879689553451 (1 458 p)
But look at this one found today,
MiHost 82687771042557349 (1 10 p)
WOW! Very close!
Just saw this post.. CongRATS ! 


HonzaVolunteer moderator Volunteer tester Project scientist Send message
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according to my list (sorted by value) the formerly nearest were...
Can you make link to this page somewhere? Or have I missed it before? It would have been easier to make graph if I knew this link.
http://ugf.de/PRPNet/help.html may be suitable.
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 


Sysadm@NbgVolunteer moderator Volunteer tester Project scientist
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according to my list (sorted by value) the formerly nearest were...
Can you make link to this page somewhere? Or have I missed it before? It would have been easier to make graph if I knew this link.
http://ugf.de/PRPNet/help.html may be suitable.
Link is there:
starting page http://ugf.de/PRPNet/ row "WFS" column "hits"
named "findlist" (equivalent to the primelist at prime searches)
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HonzaVolunteer moderator Volunteer tester Project scientist Send message
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Link is there:
starting page http://ugf.de/PRPNet/ row "WFS" column "hits"
named "findlist" (equivalent to the primelist at prime searches)
Thanks, I've missed that one before.
Last found is encouraging.
We are doing >100k tests a month and should clear current range up to 100e15 before end of February.
____________
My stats
Badge score: 1*1 + 5*1 + 8*3 + 9*11 + 10*1 + 11*1 + 12*3 = 186 



Nice sub 100 find Scott
Scott_Brown Duke_University GT640 90845186086414511 (+1 77 p) Sunday 27th of January 2013 03:22:58 PM
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Scott BrownVolunteer moderator Project administrator Volunteer tester Project scientist
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Nice sub 100 find Scott
Scott_Brown Duke_University GT640 90845186086414511 (+1 77 p) Sunday 27th of January 2013 03:22:58 PM
Thanks. It was a good Wieferich near find day overall! ...and a double shot for you!
Scott_Brown Duke_University GT640 90845186086414511 (+1 77 p) Sunday 27th of January 2013 03:22:58 PM
Honza BOINC.SK Honza 90789964532564971 (1 +570 p) Sunday 27th of January 2013 02:02:27 PM
brinktastee Aggie_The_Pew eviltim 90556733200674001 (+1 126 p) Sunday 27th of January 2013 02:57:26 AM
brinktastee Aggie_The_Pew eviltim 90519940212656789 (1 320 p) Sunday 27th of January 2013 01:31:02 AM



RogerVolunteer developer Volunteer tester
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First time I've crunched WFS this year and after 2 days found my fourth near Wieferich!
114246519827636887 (+1 467 p)
This is the 21st near Wieferich find this year. 



First time I've crunched WFS this year and after 2 days found my fourth near Wieferich!
114246519827636887 (+1 467 p)
This is the 21st near Wieferich find this year.
Nice one Roger!
It's been a while for me. Hope to get one soon ;)
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I got one today. Pretty low too!!
WFS 115341564749415161 (+1 +34 p) Aggie_The_Pew asusi7950 Wednesday 22nd of May 2013 12:00:59 PM
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I got one today. Pretty low too!!
WFS 115341564749415161 (+1 +34 p) Aggie_The_Pew asusi7950 Wednesday 22nd of May 2013 12:00:59 PM
Congrats. That's one of the closest so far and the second closest above the range that had been searched by Dorais & Klyve. 



I got one today. Pretty low too!!
WFS 115341564749415161 (+1 +34 p) Aggie_The_Pew asusi7950 Wednesday 22nd of May 2013 12:00:59 PM
Congrats. That's one of the closest so far and the second closest above the range that had been searched by Dorais & Klyve.
Go AtP! (And yes, congratulations on the find). 


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Congrats brinktastee on your nice near find! That's 10 for you overall. Looks like your about to overtake Scott Brown on points as well to claim 2nd place. 


Scott BrownVolunteer moderator Project administrator Volunteer tester Project scientist
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Finally knocked rogue out of the top spot...Phew! that took a while.
Now let's find one of these very elusive primes!




Finally knocked rogue out of the top spot...Phew! that took a while.
Now let's find one of these very elusive primes!
I'm STILL gunning for you Scott!
I just can't quite get to you and when I do I fall back behind.
Now I'm going on vacation and will be shutting down so I will have to try even harder to get to you when I get back. :) <evil laugh>
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Scott BrownVolunteer moderator Project administrator Volunteer tester Project scientist
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Finally knocked rogue out of the top spot...Phew! that took a while.
Now let's find one of these very elusive primes!
I'm STILL gunning for you Scott!
I just can't quite get to you and when I do I fall back behind.
Now I'm going on vacation and will be shutting down so I will have to try even harder to get to you when I get back. :) <evil laugh>
Oh, you'll get me I think. I am moving over to WallSunSun to catch that project back up from the application error work...and I will be on vacation in about 5 weeks, so you'll probably catch me then.
Have a good and safe vacation. 


RogerVolunteer developer Volunteer tester
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Yay! I got a Wieferich near find. My 5th so far.
124594134536762119 (+1 +850 p)
That one took us 39,733 tests to find. At this p level I would expect an average of one every 10,000 tests.
The biggest gap so far was 60,094 tests. The test required will only increase.
Maybe we need a message in the software telling us how close we got for each test, even if it wasn't near, so we know its working.
My record time for one Wieferich test is now 44.54 seconds! I've got the screen shot to prove it.
I can average 49 seconds per test, so about 6 days full crunching till the next near find. 



Maybe we need a message in the software telling us how close we got for each test, even if it wasn't near, so we know its working.
That's already possible via the s parameter in wwww and wwwwcl, which currently seems to be used with s1000. I suspect that this value for s is configured on the server side and passed to wwww as parameter when it processes a range received from the port.
Note that the value of the s parameter corresponds to the A value in the congruence
2^((p−1)/2) ≡ ±1 + Ap (mod p^2)
That A exists for any prime p. The closeness you are asking for is thus exactly measured by the size of A. I think having the software report that value for every prime isn't particularly useful.
When p is large, A will also be quite large most of the time. 



I got a near today.
145172216558999221 (1 +26 p)
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RogerVolunteer developer Volunteer tester
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I got a near today.
145172216558999221 (1 +26 p)
Well done brinktastee! That's the 5th nearest find on PRPNet so far. 



I got a near today.
145172216558999221 (1 +26 p)
Well done brinktastee! That's the 5th nearest find on PRPNet so far.
If instead we use A/p as our measure of being "nearly" Wieferich (so calculate 26/145172216558999221 in this case), the find of yesterday appears to be the secondnearest, at 1.79e16.
Well done indeed.
Of course one can argue that the measure A is more relevant.
/JeppeSN 



Grabbed another one today! :)
147348089501325541 (1 360 p)
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Grabbed another one today! :)
147348089501325541 (1 360 p)
:thumbup: Grats!
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Today zzuupp found the sixth nearWieferich of 2014, p = 149648763777446677.
The last four nearWieferichs have all been congruent to 5 (or 3) modulo 8.
/JeppeSN 



User brinktastee found 152898977773687601 (+1 +241 p). This time a "+1" prime (p == 601 == 1 (mod 8)).
The value A/p = 241/152898977773687601 = 1.5762e15 measures the "nearness".
/JeppeSN 



User brinktastee found 152898977773687601 (+1 +241 p). This time a "+1" prime (p == 601 == 1 (mod 8)).
The value A/p = 241/152898977773687601 = 1.5762e15 measures the "nearness".
/JeppeSN
Congrats B!!! 



Now 1998golfer found his first nearWieferich, 155993139654086299 (1 +714 p). With p == 299 == 3 (mod 8), and 714/155993139654086299 = 4.6e15.
Now eight nearWieferichs in 2014 (which is less than eight months old). Since we have a challenge in September, we will probably find more.
When a nearWieferich is defined as one where A is between 1000 and +1000, and a true Wieferich has A=0, we expect approx. one proper Wieferich for each 2000 nearWieferichs (with usual asumptions that A behaves "uniformly"). Since the start, PRPNet has found 229 nearWieferichs. So if we do ten times as much work as we ever did, our chances are fair to find a Wieferich.
/JeppeSN 


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Now 1998golfer found his first nearWieferich, 155993139654086299 (1 +714 p). With p == 299 == 3 (mod 8), and 714/155993139654086299 = 4.6e15.
Now eight nearWieferichs in 2014 (which is less than eight months old). Since we have a challenge in September, we will probably find more.
When a nearWieferich is defined as one where A is between 1000 and +1000, and a true Wieferich has A=0, we expect approx. one proper Wieferich for each 2000 nearWieferichs (with usual asumptions that A behaves "uniformly"). Since the start, PRPNet has found 229 nearWieferichs. So if we do ten times as much work as we ever did, our chances are fair to find a Wieferich.
/JeppeSN
Oooh cool. Didn't even notice. I didn't get an email for this, nor for my nearWSS a while back.
Thanks for posting!
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275*2^3585539+1 is prime!!! (1079358 digits)
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HonzaVolunteer moderator Volunteer tester Project scientist Send message
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When a nearWieferich is defined as one where A is between 1000 and +1000, and a true Wieferich has A=0, we expect approx. one proper Wieferich for each 2000 nearWieferichs (with usual asumptions that A behaves "uniformly"). Since the start, PRPNet has found 229 nearWieferichs. So if we do ten times as much work as we ever did, our chances are fair to find a Wieferich.
How are we doing on WSS using similar metric?
____________
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When a nearWieferich is defined as one where A is between 1000 and +1000, and a true Wieferich has A=0, we expect approx. one proper Wieferich for each 2000 nearWieferichs (with usual asumptions that A behaves "uniformly"). Since the start, PRPNet has found 229 nearWieferichs. So if we do ten times as much work as we ever did, our chances are fair to find a Wieferich.
How are we doing on WSS using similar metric?
That is more or less the same!
Again we calculate some value modulo p^2, again we know what it will be (0) mod p, so mod p^2 we have 0 + A*p. That A could be any integer between p/2 and +p/2. When A is between 1000 and +1000, we call that "near". When A=0, that is a WallSūnSūn.
So the probability of a nearWallSūnSūn is 2000 times the probability of a real WallSūnSūn.
PRPNet has found 218 nearWSS. We expect to find 2000 nearWSS for each WSS on average, in the long run.
(Our expectations could be wrong, of course, since there is no mathematical proof that the asymptotic behaviors is as conjectured.)
/JeppeSN 



When a nearWieferich is defined as one where A is between 1000 and +1000, and a true Wieferich has A=0, we expect approx. one proper Wieferich for each 2000 nearWieferichs (with usual asumptions that A behaves "uniformly"). Since the start, PRPNet has found 229 nearWieferichs. So if we do ten times as much work as we ever did, our chances are fair to find a Wieferich.
How are we doing on WSS using similar metric?
That is more or less the same!
Again we calculate some value modulo p^2, again we know what it will be (0) mod p, so mod p^2 we have 0 + A*p. That A could be any integer between p/2 and +p/2. When A is between 1000 and +1000, we call that "near". When A=0, that is a WallSūnSūn.
So the probability of a nearWallSūnSūn is 2000 times the probability of a real WallSūnSūn.
PRPNet has found 218 nearWSS. We expect to find 2000 nearWSS for each WSS on average, in the long run.
(Our expectations could be wrong, of course, since there is no mathematical proof that the asymptotic behaviors is as conjectured.)
/JeppeSN
Addition: This could be too naïve for WallSūnSūn, though. For example Klaška's paper (free) says it is unlikely to find any WallSūnSūns ending in 3 or 7 (i.e. with p == ±2 (mod 5)). So that gives only half the chance, namely primes ending in 1 or 9 (so p == ±1 (mod 5)). /JeppeSN 


HonzaVolunteer moderator Volunteer tester Project scientist Send message
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Addition: This could be too naïve for WallSūnSūn, though. For example Klaška's paper (free) says it is unlikely to find any WallSūnSūns ending in 3 or 7 (i.e. with p == ±2 (mod 5)). So that gives only half the chance, namely primes ending in 1 or 9 (so p == ±1 (mod 5)). /JeppeSN
Thanks for your thoughts and reference.
Anyone searching for a FibonacciWieferich prime using a computer is facing
an immediate problem of completing the search of the interval [2 x 10^14,10^15]. By
(9), theoretically, there should be about 0.02 FibonacciWieferich primes within
this interval ending with 1 or 9. In the following interval [10^15,10^16] then, there
should be about 0.03 primes. Even though the odds are not much favourable, there
is still hope that a FibonacciWieferich prime will be discovered.
Well, I don't know how much this is encouraging but I'll give it a try again on my GTX580.
btw, it reminds me there is (semi)active nonBOINC Czech project on this subject.
http://www.elmath.org/.
Their CPU client wasn't optimized and due to lack of response from project stuff we have decided (Czech BOINC community] not to promote it.
Perhaps they have some theoretical papers on this subject as well.
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Multiply the 0.02 or 0.03 from that quote by 2000, and you get the number of nearWSS ending in 1 or 9 we expect to find in the same intervals, I guess. /JeppeSN 


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Fear not. There is a WSS challenge straight after the Wieferich Challenge.
Anyway, to get this thread back on track below is the full email reply to my query from François Dorais:
Dear Roger,
I just realized that you are not ZetaFlux and that just made me read your message in a different light. I don't know who ZetaFlux is so I can neither confirm nor deny the claim. He appears to have used an older version of WPSE but it wasn't buggy so I don't know why he is missing some data.
Anyway, I had a look at Primegrid which I now understand is not what ZetaFlux was running. This is a great project! I checked your data against mine and I can confirm that your finding agree with ours up to 6.7e15.
I was a little puzzled by this remark:
Although the search for Wieferich primes reached an upper bound of 6.7e15, PrimeGrid's search will begin at 3e15. The reason for this is that Dorais and Klyve redefined what a "near" Wieferich prime was. Therefore, they did not search for "classical" "near" Wieferich primes. We do not expect to find any Wieferich primes between 3e15 and 6.7e15, but we do expect some "near" Wieferich primes. [EDIT  It appears that Dorais' and Klyve's definition did catch some "classical" "near" Wieferich primes but not all. We're searching for A < = 1000] <http://www.primegrid.com/forum_thread.php?id=3008&nowrap=true#45945>
I wish you had contacted us then to ask about this. It is true that we looked at different notions of near misses in our paper, but that doesn't mean we didn't search for "classical" near misses. In fact, since we were interested in the distribution of Fermat quotients, we had collected a very vast amount of data and we had a list of "classical" near misses for A <= 600000. The reason we "redefined" near misses is that the relative size version gives more accurate results for measuring distribution.
There is one important difference in that we used "full" Fermat quotients, i.e. A such that 2^{p1} = 1 + pA (mod p^2), rather than "half" Fermat quotients, i.e. 2^{(p1)/2} = (+/)1 + pA (mod p^2). Fortunately, since ((+/)1 + pA)^2 = 1 +/ 2pA (mod p^2), it's straightforward to recover the list of small "half" Fermat quotients from the list of small "full" Fermat quotients. I did that to check my list with yours and I'm happy to report that our lists agree on the overlap.
By the way, it would be nice if your data was available in plain CSV format. It was a bit of a pain to manually check against your PDF file. I also couldn't find a link to your code. Is it available?
Best wishes,
François
You'll be pleased to know we've fixed up the Primegrid reference François is mentioning. 



Roger,
Note that the Wikipedia section was recently updated to describe the relation between the "A" in our project, related to 2^{(p1)/2}, and the "A" belonging to the square of that, 2^{p1}. This relation is trivial, one doubling modulo p.
When the first "A" is close to zero numerically, so is its "double" mod p. However, when the nonclassical "A" is close to zero in this way, its "half" may be very far from zero, depending on whether the nonclassical "A" was odd or even.
/JeppeSN 



Regarding the absolute size A and the relative A/p, note that I have started to calculate A/p for finds, in this thread. Because "we" (PRPNet's WFS project) stick to A <= 1000 no matter how big p gets, we will get very few nearWieferichs.
A relative size requirement like A/p < 10^{14} should in theory keep producing a "constant" flux of nearWieferichs (by that altered definition).
/JeppeSN 


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Regarding the absolute size A and the relative A/p, note that I have started to calculate A/p for finds, in this thread. Because "we" (PRPNet's WFS project) stick to A <= 1000 no matter how big p gets, we will get very few nearWieferichs.
A relative size requirement like A/p < 10^{14} should in theory keep producing a "constant" flux of nearWieferichs (by that altered definition).
/JeppeSN
Using the definition of near as A/p < 10^{14}
With the lead currently at 1.587e17, A would have to be < 1587 to be "near".
That sounds reasonable.
92.000e17 is the upperbound that the current software can search to.
At that level A would have to be < 92000 to be "near".
That sounds reasonable as well.
Near finds are getting far apart, but we don't want to devalue them.
If rogue can modify wwww to support this it would have my support. 


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A crude way to implement this change is to just to add the following lines into the wwww/WWWW.cpp function:
void WWWW::Validate(void)
...
if (ii_SearchType == 1 && !memcmp(line, "wieferich_special=", 18))
ii_SpecialThreshold = atoi(line+18);
...
Compile the app then just add the following to the wwww.ini file that's read at run time:
wieferich_special=1559 // current completed 155,912,600,000,000,000
There are other ways to do this but this one is configurable by the PRPNet user. Whether the Wieferich PRPNet Server would accept a special value above 1000 is another question. That value is hard coded.
Even without this change you can have fun testing the effect of changing the limit "s switch" for determining special instances:
>wwwwcl p0e4 P1e4 TWieferich s100 v 



Regarding the absolute size A and the relative A/p, note that I have started to calculate A/p for finds, in this thread. Because "we" (PRPNet's WFS project) stick to A <= 1000 no matter how big p gets, we will get very few nearWieferichs.
A relative size requirement like A/p < 10^{14} should in theory keep producing a "constant" flux of nearWieferichs (by that altered definition).
/JeppeSN
Using the definition of near as A/p < 10^{14}
With the lead currently at 1.587e17, A would have to be < 1587 to be "near".
That sounds reasonable.
92.000e17 is the upperbound that the current software can search to.
At that level A would have to be < 92000 to be "near".
That sounds reasonable as well.
Near finds are getting far apart, but we don't want to devalue them.
If rogue can modify wwww to support this it would have my support.
Dorais and Klyve in their Table 4 (top of page 11) actually list all with A/p < 10^{13}, so that is ten times as many. (As I said earlier, their "A" corresponds to 2^{p1}, not 2^{(p1)/2}.)
/JeppeSN 


RogerVolunteer developer Volunteer tester
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Dorais and Klyve in their Table 4 (top of page 11) actually list all with A/p < 10^{13}, so that is ten times as many. (As I said earlier, their "A" corresponds to 2^{p1}, not 2^{(p1)/2}.)
/JeppeSN
Dorais and Klyve were trying to create statistics on Near Finds for analysis, we're not doing that so A/p < 10^{14} is enough.
Note that the Wikipedia section was recently updated to describe the relation between the "A" in our project, related to 2^{(p1)/2}, and the "A" belonging to the square of that, 2^{p1}. This relation is trivial, one doubling modulo p.
When the first "A" is close to zero numerically, so is its "double" mod p. However, when the nonclassical "A" is close to zero in this way, its "half" may be very far from zero, depending on whether the nonclassical "A" was odd or even.
So when we have a Near Find using "half" Fermat quotients it is also a Near Find using "full" Fermat quotients, such as Dorais and Klyve used, however the reverse is not always true. If that's correct then I am thinking that it would be better to search using "full" Fermat quotients so you don't miss anything interesting. 



[...]
So when we have a Near Find using "half" Fermat quotients it is also a Near Find using "full" Fermat quotients, such as Dorais and Klyve used, however the reverse is not always true. If that's correct then I am thinking that it would be better to search using "full" Fermat quotients so you don't miss anything interesting.
Absolutely correct, as far as I know. /JeppeSN 



Many finds right now, just before the challenge starts this Monday.
brinktastee found 159941928418171813 (1 775 p). With p == 813 == 5 (mod 8), and A/p = 775/159941928418171813 = 4.8e15.
/JeppeSN 



Scott_Brown found 160388140707579713 (+1 +850 p); with p == 713 == 1 (mod 8), and 850/160388140707579713 = 5.3e15.
When the around the wwwworld challenge runs (entire September 2014), I will not report individual nearWieferichs in this thread.
/JeppeSN 



Scott_Brown found 160388140707579713 (+1 +850 p); with p == 713 == 1 (mod 8), and 850/160388140707579713 = 5.3e15.
When the around the wwwworld challenge runs (entire September 2014), I will not report individual nearWieferichs in this thread.
/JeppeSN
That challenge found 31 nearWieferichs, the smallest being 170164210886417897 and the largest 317133503989986679.
It found one false positive, 214714110964439699 (1 +12113703224047600 p), erroneously given as 214714110964439699 (+16384 29001 p).
/JeppeSN 



Many finds right now, just before the challenge starts this Monday.
brinktastee found 159941928418171813 (1 775 p). With p == 813 == 5 (mod 8), and A/p = 775/159941928418171813 = 4.8e15.
/JeppeSN
Did this nearfind get found during the challenge?
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Many finds right now, just before the challenge starts this Monday.
brinktastee found 159941928418171813 (1 775 p). With p == 813 == 5 (mod 8), and A/p = 775/159941928418171813 = 4.8e15.
/JeppeSN
Did this nearfind get found during the challenge?
sorry, no! if you check the whole findlist you will find a reporting date "Saturday 30th of August 2014 06:00:11 PM" and this is not in September ;)
____________
Sysadm@Nbg
my current lucky number: 113856050^65536 + 1
PSAPRPNetStatsURL: http://ugf.de/PRPNet/




Many finds right now, just before the challenge starts this Monday.
brinktastee found 159941928418171813 (1 775 p). With p == 813 == 5 (mod 8), and A/p = 775/159941928418171813 = 4.8e15.
/JeppeSN
Did this nearfind get found during the challenge?
sorry, no! if you check the whole findlist you will find a reporting date "Saturday 30th of August 2014 06:00:11 PM" and this is not in September ;)
Also, the post (by me) being quoted is from August, and I am not able to predict which finds will be done in the future, and by whom ;) No posts to this thread were done in September (UTC).
/JeppeSN 



user team client value ▾ date reported
MiHost AMD_Users Farscape2 82687771042557349 (1 10 p) Tuesday 15th of January 2013 04:49:41 PM
JAMC My_Way 2 5131427559624857 (+1 18 p) Tuesday 03rd of January 2012 10:51:51 PM
Tarmo_Ilves Aggie_The_Pew server3 3723113065138349 (1 +18 p) Saturday 31st of December 2011 04:31:52 PM
[DPC]Pyrus Dutch_Power_Cows genghis 4150209531584437 (1 24 p) Monday 02nd of January 2012 12:21:06 AM
brinktastee Aggie_The_Pew ASUS_I7_950 145172216558999221 (1 +26 p) Monday 14th of July 2014 02:19:30 PM
all findings are pretty old still
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wbr, Me. Dead J. Dona




Death[Kiev], it is easier for the absolute value of A to be small when p is small. /JeppeSN 



User composite found 325347156897384571 (1 +361 p). His second nearWieferich, and the greatest one ever found. It is 571 == 3 (mod 8). A/p = 361/325347156897384571 = 1.1e15. /JeppeSN 



If you use PARI/GP, you can check our Wieferich finds very easily with this function:
checkWieferich(p) = {
if(!isprime(p)p==2,return("no, p is not an odd prime"));
plusOrMinus = kronecker(2,p);
result = centerlift(Mod(2,p^2)^((p1)/2));
result = (resultplusOrMinus)/p;
Strprintf("%d (%+d %+d p)", p, plusOrMinus, result)
}
I posted similar code in the September 2014 challenge thread.
If you use this to check huge numbers, consider using ispseudoprime method instead of isprime, in the top of the function "body".
/JeppeSN 


RogerVolunteer developer Volunteer tester
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Looks like I just found 494997492935398501 (1 +470 p). With p == 501 == 5 (mod 8), and A/p = 470/494997492935398501 = 9.495e16.
This is my 8th near find and best A/p so far!
A good finish to Wieferich season for me. 



Congratulations. /JeppeSN 

