Wilson-prime search practicalities - Page 11

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

Exactly my thoughts!

Mathew · 2011-11-01, 11:19

Quote:

Originally Posted by wblipp

: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?

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:

Originally Posted by R. Gerbicz

For the new code (still not finished)

Just wondering how the new code is coming along?

Jeff.

R. Gerbicz · 2011-11-21, 16:38

Quote:

Originally Posted by Jeff Gilchrist

Just wondering how the new code is coming along?

Jeff.

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 $(n-1)!(p-n)!\equiv (-1)^n\pmod{p^2}$ (alternatively, the Wilson quotient $((p-1)!+1)/p \equiv H_n \pmod{p}$ , where $H_n$ is the n-th harmonic number).
See sequences A128666, A079853, A152413 in the OEIS.

maxal · 2012-01-31, 16:09

Quote:

Originally Posted by maxal

alternatively, the Wilson quotient $((p-1)!+1)/p \equiv H_n \pmod{p}$

should be $((p-1)!+1)/p \equiv H_{n-1} \pmod{p}$ 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:
http://arxiv.org/pdf/1209.3436
For the impatient readers: The search is now complete up to 10¹³, no new Wilson prime was found.

Dubslow · 2012-10-11, 05:25

Quote:

Originally Posted by MrRepunit

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:
http://arxiv.org/pdf/1209.3436
For the impatient readers: The search is now complete up to 10¹³, no new Wilson prime was found.

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.

)

R. Gerbicz · 2012-11-02, 03:21

Quote:

Originally Posted by MrRepunit

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:
http://arxiv.org/pdf/1209.3436
For the impatient readers: The search is now complete up to 10¹³, no new Wilson prime was found.

Sorry for my late answer. See the updated paper: http://arxiv.org/abs/1209.3436
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:

Originally Posted by R. Gerbicz

Sorry for my late answer. See the updated paper: http://arxiv.org/abs/1209.3436
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.

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.

2012-01-31, 12:48	#115
maxal Feb 2005 2²·3²·7 Posts	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 $(n-1)!(p-n)!\equiv (-1)^n\pmod{p^2}$ (alternatively, the Wilson quotient $((p-1)!+1)/p \equiv H_n \pmod{p}$ , where $H_n$ is the n-th harmonic number). See sequences A128666, A079853, A152413 in the OEIS. Last fiddled with by maxal on 2012-01-31 at 12:49

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2012-10-10, 21:09	#117
MrRepunit Mar 2011 Germany 2³·11 Posts	Hi. Is there any news related to the code improvement? Danilo

2012-10-10, 22:42	#118
MrRepunit Mar 2011 Germany 2³·11 Posts	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: http://arxiv.org/pdf/1209.3436 For the impatient readers: The search is now complete up to 10¹³, no new Wilson prime was found.