20140710, 14:32  #1 
May 2003
1547_{10} Posts 
Wieferich primes
As some of you might know, I spent quite a bit of time running a Wieferich prime search on the supercomputers at BYU. I've been doing the postprocessing/statistics with a coauthor, and we noticed that the number of primes with given Fermat quotient was significantly low.
I'd like to make sure that this undercount is not an error due to either my hardware or a misinstallation, or anything like that. So I was hoping someone here would download the software (available at http://www.math.cornell.edu/~dorais/...?page=software), run it on a small segment that overlaps with my computations, and send me the output file so I can compare it to what I obtained. I'd guess this should only take a day or two on a decent personal computer. Running the program on a range like 3*10^6...4*10^6 for any acceptable base should be sufficient. 
20140714, 21:33  #2 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
7·733 Posts 
Do you have a windows 64bit binary?
Also I would like your opinion/comment about this http://www.primegrid.com/forum_threa...rap=true#45945 and this http://www.elmath.org/ Best regards, Carlos 
20140714, 21:53  #3 
May 2003
7×13×17 Posts 
I don't have a 64bit windows binary.
Regarding those other searches, my search went to 4*10^{17}, which is significantly further than any of their counts. However, some of the results make me question whether my results are valid, and so I'm checking some of the obvious places for errors. It appears I may be missing upwards of 20% of the near misses. 
20140716, 21:29  #4 
Nov 2009
350_{10} Posts 
Base 53
Code:
WIEFERICH BASE 53 WIEFERICH RANGE 3000000 .. 4000000 WIEFERICH BOUND 16777216 21102532269939173 2825534 21677796312992873 6033216 20018122387202993 5612970 24670497579688013 +6194444 20408479370749523 8293710 22860173915689163 15915409 24723904494509273 5435934 22568777561860583 9016870 25176661633553483 12321603 21757326332261573 +12975434 21284162624915243 898461 20887017204973973 +6918581 25741565291081693 2126647 25208410796579063 10377937 24198623432733803 6749465 25273835299052393 +622719 25459198239785363 107141 21227216385855533 12139967 22544233198927493 +12384124 20015992002486533 +5275214 25596807531815573 +2842292 WIEFERICH TIME 22025.168487/177408177408 = 1.241497e07 Code:
WIEFERICH BASE 97 WIEFERICH RANGE 3000000 .. 4000000 WIEFERICH BOUND 16777216 20158257756827287 3544638 19996307105294617 +2979598 23021375390643727 +8435504 25235933105993707 3217725 22339344871233487 +12111240 25443827576026957 +712337 20202459108721987 12844158 25087371430141117 +2087398 20201176241986837 10477728 19751207945018647 +7690683 21797797965843997 2303074 22112713777204147 +15557003 20061322068177487 +13620664 20210735819274097 +14676396 21424829077822267 +4498114 21813538897280227 +4946913 25046885578765147 +14341602 WIEFERICH TIME 22024.984475/177408177408 = 1.241486e07 
20140717, 02:23  #5 
May 2003
7×13×17 Posts 
Thanks Mathew, that was exactly what I needed. Sadly, it does appear that my output is missing some entries!

20150201, 11:57  #6 
Sep 2013
Perth, Au.
2·7^{2} Posts 
The Primegrid PRPNet September 2014 Wieferich Challenge (one month long) pushed the leading edge of our search from 1.5*10^17 to 3.17*10^17.
The January 2015 Challenge (one week long) pushed the leading edge from 3.3*10^17 to 4.14*10^17. So we're now past the end of ZetaFlux search boundary (4*10^17). Next milestones are:  1*10^18  2.3*10^18 (Pervushin's Mersenne number 2^611)  9.2*10^18 (the upperbound our current software can search to i.e. 2^63) 
20150201, 12:00  #7 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
7×733 Posts 
Now we need an update from ZetaFlux.

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