Wieferich primes

Zeta-Flux · 2014-07-10, 14:32

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 post-processing/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 mis-installation, 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.

pinhodecarlos · 2014-07-14, 21:33

Do you have a windows 64-bit 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

Zeta-Flux · 2014-07-14, 21:53

I don't have a 64-bit 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.

Mathew · 2014-07-16, 21:29

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 = 1.241497e-07

Base 97

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 = 1.241486e-07

Zeta-Flux · 2014-07-17, 02:23

Thanks Mathew, that was exactly what I needed. Sadly, it does appear that my output is missing some entries!

TheCount · 2015-02-01, 11:57

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 Zeta-Flux search boundary (4*10^17).

Next milestones are:
- 1*10^18
- 2.3*10^18 (Pervushin's Mersenne number 2^61-1)
- 9.2*10^18 (the upper-bound our current software can search to i.e. 2^63)

pinhodecarlos · 2015-02-01, 12:00

Now we need an update from Zeta-Flux.

2014-07-10, 14:32	#1
Zeta-Flux May 2003 1547₁₀ 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 post-processing/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 mis-installation, 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 310^6...410^6 for any acceptable base should be sufficient.

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2014-07-14, 21:33	#2
pinhodecarlos "Carlos Pinho" Oct 2011 Milton Keynes, UK 7·733 Posts	Do you have a windows 64-bit 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

2014-07-14, 21:53	#3
Zeta-Flux May 2003 7×13×17 Posts	I don't have a 64-bit 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.

2014-07-17, 02:23	#5
Zeta-Flux 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!

2015-02-01, 11:57	#6
TheCount Sep 2013 Perth, Au. 2·7² Posts	The Primegrid PRPNet September 2014 Wieferich Challenge (one month long) pushed the leading edge of our search from 1.510^17 to 3.1710^17. The January 2015 Challenge (one week long) pushed the leading edge from 3.310^17 to 4.1410^17. So we're now past the end of Zeta-Flux search boundary (410^17). Next milestones are: - 110^18 - 2.310^18 (Pervushin's Mersenne number 2^61-1) - 9.210^18 (the upper-bound our current software can search to i.e. 2^63)

2015-02-01, 12:00	#7
pinhodecarlos "Carlos Pinho" Oct 2011 Milton Keynes, UK 7×733 Posts	Now we need an update from Zeta-Flux.