Wieferich primes - searching on www.elmath.org

New prime numbers discovered by prime-finding projects.

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Wieferich primes - searching on www.elmath.org

Postby miroslavkures » Thu Jan 03, 2008 9:18 am

You can participate in the project Wieferich@home aimed at searching for Wieferich primes.

Download free application on www.elmath.org.

Wieferich primes satisfy
2^(p?1) ? 1 (mod p^2)
and only two Wieferich primes are known up to now: 1093 and 3511.
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Re: Wieferich primes - searching on www.elmath.org

Postby kpearson » Wed Jan 09, 2008 5:21 pm

miroslavkures wrote:You can participate in the project Wieferich@home aimed at searching for Wieferich primes.

Download free application on www.elmath.org.

Wieferich primes satisfy
2^(p−1) ≡ 1 (mod p^2)
and only two Wieferich primes are known up to now: 1093 and 3511.


Thanks Miroslav! I have added an entry for this project on the main site.
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Postby miroslavkures » Tue Feb 05, 2008 1:14 pm

The notably increasing speed of searching and additional innovations are in Version 2. More than 200 users ? participate!
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Postby rogue » Wed Feb 06, 2008 1:27 am

Out of curiosity, how fast is the client? For example, if I run the client on a Core 2 Duo for primes in the range of 2e15, how many tests can it do per second?
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Postby miroslavkures » Mon Feb 11, 2008 3:41 pm

Please, download and run the client application. Your speed will be displayed on the screen. You may use both cores with multicore launcher. Thanks for resulting comments.
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Postby rogue » Wed Feb 13, 2008 12:24 am

miroslavkures wrote:Please, download and run the client application. Your speed will be displayed on the screen. You may use both cores with multicore launcher. Thanks for resulting comments.


I don't intend to d/l and run your app. I have plenty of other projects to which I dedicate my CPU. I was asking because I wrote a program (on PPC) and had extended the search to 3e15 and was curious to know how comparable the speed is, in tests per second. The results are not published. In case you don't believe me, one near Wieferich is for p = 2276306935816523 and there are three others between your last near Wieferich and the one I listed here.
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Postby miroslavkures » Thu Feb 14, 2008 3:54 pm

Very nice. So, we use two tests parallelly: the complete test and the periodic test. The complete one tests cca 300-700 primes per second. Simultaneously, the periodic test implements the conjecture that binary expressions of Wieferich primes are periodic. The speed is multiplied by number of cores. As to Your testing: unpublished results are suspicious - although Your near W.p. is OK. Nevertheless, our strategy is not a linear searching; we search already for primes greater than 6*10^15 in one of four ranges. More on www.elmath.org.

If You have more questions or even want cooperate, You can also use my e-mail kures@fme.vutbr.cz.
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Postby rogue » Thu Feb 14, 2008 10:58 pm

miroslavkures wrote:Very nice. So, we use two tests parallelly: the complete test and the periodic test. The complete one tests cca 300-700 primes per second. Simultaneously, the periodic test implements the conjecture that binary expressions of Wieferich primes are periodic. The speed is multiplied by number of cores. As to Your testing: unpublished results are suspicious - although Your near W.p. is OK. Nevertheless, our strategy is not a linear searching; we search already for primes greater than 6*10^15 in one of four ranges. More on www.elmath.org.

If You have more questions or even want cooperate, You can also use my e-mail kures@fme.vutbr.cz.


The results are unpublished as I provided the software and some of the horsepower for someone else. They have the responsibility to publish the results,. which I why I won't reveal more information than what I know.

So if I understand correctly, you ignore certain primes because they do not periodic. But that is based upon an unproven conjecture. Your results are likely to be incomplete, especially WRT near Wieferichs.

300-700 tests per second? That speed seems slow to me. I would expect at least 50,000 per second per core on a Core 2 Duo at 2.4 GHz. Is the expmod written in C only or is it written in assembler?
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Postby miroslavkures » Fri Feb 15, 2008 6:33 am

rogue wrote:So if I understand correctly, you ignore certain primes because they do not periodic. But that is based upon an unproven conjecture. Your results are likely to be incomplete, especially WRT near Wieferichs.

No. We use two tests. The first one ("complete") tests every prime. The second one tests only periodic primes (simultaneously and independently) up to the bit length 3500. The speed is related to the complete test.

If You have quicker algorithm, You can explain it :D
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Postby rogue » Fri Feb 15, 2008 11:03 pm

miroslavkures wrote:
rogue wrote:So if I understand correctly, you ignore certain primes because they do not periodic. But that is based upon an unproven conjecture. Your results are likely to be incomplete, especially WRT near Wieferichs.

No. We use two tests. The first one ("complete") tests every prime. The second one tests only periodic primes (simultaneously and independently) up to the bit length 3500. The speed is related to the complete test.

If You have quicker algorithm, You can explain it :D


I just realized that there was an error in the x86 code I tested with as it performed mod p, not p^2. Of note, my original code was run on PPC and could do over 300,000 tests per second at 1e15. It has the distinct advantage that PPC has 32 registers to work with. I'll putz more with some x86 code and see what I can do with it.
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