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-   -   Wilson-prime search practicalities (https://www.mersenneforum.org/showthread.php?t=16028)

MrRepunit 2011-10-31 20:53

I finished my range 360e9 to 400e9, nothing found, not even a near wilson prime.

[QUOTE]
If you don't look, you won't find.

However, if you do look, you probably still won't find. C'est la vie.

Paul [/QUOTE]
Exactly my thoughts!

Mathew 2011-11-01 11:19

[QUOTE=wblipp;276498]:surprised Who are you and what have done with the real RDS? The one that thinks everybody should be working on the Cunningham project, but only with factoring code they have written themselves?[/QUOTE]

wblipp,

Since I joined the forum, R.D. Silverman has recommended both the Sierpinski project and NFS@home numerous times.

Jeff Gilchrist 2011-11-21 15:09

[QUOTE=R. Gerbicz;276306]For the new code (still not finished) [/QUOTE]

Just wondering how the new code is coming along?

Jeff.

R. Gerbicz 2011-11-21 16:38

[QUOTE=Jeff Gilchrist;279388]Just wondering how the new code is coming along?

Jeff.[/QUOTE]

Now I wait only for a parallel FFT code from David Harvey, it could take 2-3 months. I have written other parts of the algorithm, using David's ideas.

maxal 2012-01-31 12:48

This is a nice search project. Do you maintain database of Wilson quotients modulo p in the search?
They would be helpful in finding other related primes such as generalized Wilson primes p of order n satisfying the congruence [tex](n-1)!(p-n)!\equiv (-1)^n\pmod{p^2}[/tex] (alternatively, the Wilson quotient [tex]((p-1)!+1)/p \equiv H_n \pmod{p}[/tex], where [tex]H_n[/tex] is the n-th harmonic number).
See sequences A128666, A079853, A152413 in the OEIS.

maxal 2012-01-31 16:09

[QUOTE=maxal;287875]alternatively, the Wilson quotient [tex]((p-1)!+1)/p \equiv H_n \pmod{p}[/tex][/QUOTE]
should be [tex]((p-1)!+1)/p \equiv H_{n-1} \pmod{p}[/tex] for the order n generalized Wilson prime. So order 1 generalized Wilson primes are conventional Wilson primes, order 2 generalized Wilson primes are near-Wilson primes p with Wilson quotient modulo p equal 1. However, order n>2 generalized Wilson primes are not near-Wilson primes.

MrRepunit 2012-10-10 21:09

Hi.
Is there any news related to the code improvement?
Danilo

MrRepunit 2012-10-10 22:42

Hi Robert.
I just found and read the paper you co-authored. Nice work. I really liked the algorithmic improvements. My math level is restricted to theoretical physics stuff, so I could not follow every detail.

Is it still possible that you publish the source code?

For the interested readers:
[URL]http://arxiv.org/pdf/1209.3436[/URL]
For the impatient readers: The search is now complete up to 10[SUP]13[/SUP], no new Wilson prime was found.

Dubslow 2012-10-11 05:25

[QUOTE=MrRepunit;314203]Hi Robert.
I just found and read the paper you co-authored. Nice work. I really liked the algorithmic improvements. My math level is restricted to theoretical physics stuff, so I could not follow every detail.

Is it still possible that you publish the source code?

For the interested readers:
[URL]http://arxiv.org/pdf/1209.3436[/URL]
For the impatient readers: The search is now complete up to 10[SUP]13[/SUP], no new Wilson prime was found.[/QUOTE]

Very interesting, it seems to me to be a well-written and in depth research paper, besides the obvious "practical" (massive) improvements. I would also like to see some source, because I would like to help extend the search bound even further. (My number theory class covered Wilson's theorem last week. :smile:)

R. Gerbicz 2012-11-02 03:21

[QUOTE=MrRepunit;314203]Hi Robert.
I just found and read the paper you co-authored. Nice work. I really liked the algorithmic improvements. My math level is restricted to theoretical physics stuff, so I could not follow every detail.

Is it still possible that you publish the source code?

For the interested readers:
[URL]http://arxiv.org/pdf/1209.3436[/URL]
For the impatient readers: The search is now complete up to 10[SUP]13[/SUP], no new Wilson prime was found.[/QUOTE]

Sorry for my late answer. See the updated paper: [url]http://arxiv.org/abs/1209.3436[/url]
The search is complete up to 2*10^13. I will see if I could release the code, a not small part of the code is from David Harvey. The idea to use larger e>6 values is completely comes from them, I have coded it.

Jeff Gilchrist 2012-11-07 17:55

[QUOTE=R. Gerbicz;316710]Sorry for my late answer. See the updated paper: [url]http://arxiv.org/abs/1209.3436[/url]
The search is complete up to 2*10^13. I will see if I could release the code, a not small part of the code is from David Harvey. The idea to use larger e>6 values is completely comes from them, I have coded it.[/QUOTE]

Thanks for the update. Does this new code support multiple cores like you were talking about before? I wouldn't mind playing with your new code if you are able to release it.


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