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John
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Message 8333 - Posted: 27 Feb 2008 | 5:30:40 UTC
Last modified: 7 Sep 2008 | 3:59:51 UTC

Over the past nine months, six new projects (4 primality and 2 sieves) have been added to PrimeGrid. As mentioned in this post, \"the primary focus was on simplicity...how easily could a new sub-project be implemented within PrimeGrid and BOINC.\"

We will soon be adding three new projects...all primality testing (LLR). Simplicity of implementation is still a driving factor right now. However, we may explore adding other primality programs in the future and add prime searches with increasing variety.

Sieving was conducted over the past several months and has been completed for the first project and ongoing for the other two projects.

• Sophie Germain Prime Search
A prime number p is called a Sophie Germain prime if 2p + 1 is also prime. For example, 5 is a Sophie Germain prime because it is prime and 2 × 5 + 1 = 11, is also prime. They are named after Marie-Sophie Germain, an extraordinary French mathematician.

We\'ll be searching the form k*2^n-1. If it is prime, then we\'ll check k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1. We are able to do this because a quad sieve was performed for this search. This sieve ensured that k*2^n-1, k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1 do not have any small prime divisors.

As you can see, a twin prime is also possible from this search although we expect to find a Sophie Germain prime first. Here are some stats for the search:

k range: 1<k<41T
n=666666
sieve depth: p=200T
candidates remaining: 34,190,344

Probability of one or more significant pair = 80.1%
Probability of one or more SG = 66.7%
Probability of one or more Twin = 42.3%

Approximate WU length:
Athlon64 2.1Ghz - ~2000 secs (~33.3 minutes)
C2D 2.1 Ghz - ~1015 secs (~16.9 minutes) per core
C2Q 2.4 GHz - ~880 secs (~14.7 minutes) per core

Primes found in this search will enter the Top 5000 Primes database ranked about 600.

For more information about Sophie Germain primes, please visit these links:
http://primes.utm.edu/glossary/page.php?sort=SophieGermainPrime
http://mathworld.wolfram.com/SophieGermainPrime.html
http://en.wikipedia.org/wiki/Sophie_Germain_prime

For more infomation about Marie-Sophie Germain, please visit these links:
http://en.wikipedia.org/wiki/Sophie_Germain
http://www.pbs.org/wgbh/nova/proof/germain.html

• 3*2^n+1
This will be a sister project to the already established 3*2^n-1 project. We hope to eventually have both projects at the same n value. We have reserved k=3 from the ProthSearch site. Our initial goal will be like 3*2^n-1, tested up to n=5M. However, sieving is currently being conducted beyond that.

Here are some stats for the search:

k=3
sieved n range: 1<n<5M
sieve depth: p=500T (ongoing)

3*2^n+1 will be a double check effort for even n up to ~1.8M and for odd n up to ~2.6M. Beyond that will be new primes, although there may be a small chance of a missed prime in the lower ranges.

• +1 Prime Search
This search will be looking for primes in the form of k*2^n+1. With the condition 2^n > k, these are often called the Proth primes. We will be coordinating our effort through the ProthSearch site. This project will also have the added bonus of possibly finding Generalized Fermat Numbers (GFN) factors. Each k*2^n+1 prime found may be a GFN factor. As this requires PrimeFormGW (PFGW) (a primality-testing program), once PrimeGrid finds a prime, it will then be manually tested outside of BOINC for GFN divisibility.

Our initial goal will be to double check all previous work up to n=300K for k<1200 and to fill in any gaps that were missed. Primes found in this range will not make it into the Top 5000 Primes database (currently n>333333). However, the work is still important as it may lead to new GFN or "classical" Fermat number factors. While there are many GFN factors, currently there are only about 270 "classical" Fermat number factors known.

Here are some stats for the search:

k range: 4<k<1200
n range: 1<n<5M
sieve depth: currently at p=10T (ongoing)

Once the initial goal is reached, we\'ll advance to n<400K and then n<500K. Afterwards, we\'ll turn our focus to smaller k values and higher n values. For example, k<32 complete to n=2M, k<64 complete to n=1M and so on. Primes found in these ranges will definitely make it into the Top 5000 Primes database.

For more information about \"Proth\" primes, please visit these links:
http://primes.utm.edu/glossary/page.php?sort=ProthPrime
http://mathworld.wolfram.com/ProthPrime.html
http://en.wikipedia.org/wiki/Proth_number

EDIT: 7 Sept 2008 - Updated "classical" Fermat number factors information.

Other suggestions for future projects

Generalized Cullen/Woodall Search: This is similar to our current Cullen/Woodall search except a base other than 2 will be selected. The form of these primes are as follows:

Generalized Cullen: n*b^n+1
Generalized Woodall: n*b^n-1

One base in particular, b=13, is interesting as no prime has yet to be found although it has been tested up to n=250K.

There are ongoing efforts here:
Steven Harvey\'s Generalized Woodall number Search
Günter Löh\'s Generalized Cullen Search for 3 <= b <= 100
Daniel Hermle\'s Generalized Cullen Search for 101 <= b <= 200

Hyper Cullen/Woodall: Again, similar to our current Cullen/Woodall search. The form of these primes are as follows:

HyperCullen: k^n*n^k+1, k>n
HyperWoodall: k^n*n^k-1, k>n

There is an ongoing effort here: Steven Harvey\'s Generalized Woodall number Search

Generalized Fermat Prime Search: This searches for primes in the form b^2^n+1. A previous project has already completed a substantial amount of work. It can be found here: Generalized Fermat Prime Search. We may be able to double check all completed work and then help the previous project extend their search.

Wieferich prime: There is now an established effort for this search which can be found here: http://www.elmath.org/

Octoproth Search: There was an effort, but it is now on hiatus due to lack of interest. It can be found here: http://mersenneforum.org/forumdisplay.php?f=63

Riesel and Sierpinski conjectures: There are two well known projects already established...Riesel Sieve and Seventeen or Bust. There is now an established effort for bases other than 2 which can be found here: http://mersenneforum.org/showthread.php?t=9738
____________

gemery

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Message 8334 - Posted: 27 Feb 2008 | 14:01:41 UTC

In speed terms per work unit, I can do a LLR (TPS) work unit in about 11 minutes, what times per work unit for some of these other projects?

Emma Laurijssens

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Message 8335 - Posted: 27 Feb 2008 | 14:51:03 UTC

Another thought: will participation in these projects require selecting each project individually in our account settings each time it is added? Maybe I\'d like to accept new projects by default and unselect them whenever necessary. This would be just a checkbox on the web page. OTOH it is yet another checkbox, which doesn\'t necessarily mean an improvement.
____________
?SYNTAX ERROR
READY.

Rytis
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Message 8336 - Posted: 27 Feb 2008 | 17:56:05 UTC - in response to Message 8335.

Maybe I\'d like to accept new projects by default and unselect them whenever necessary. This would be just a checkbox on the web page.

Sadly, this is not possible with the current BOINC implementation. You can either select no projects (which would send you work from any of available ones), or you can select the ones you\'d like.
____________

John
Honorary cruncher

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Message 8337 - Posted: 27 Feb 2008 | 18:43:18 UTC - in response to Message 8334.

In speed terms per work unit, I can do a LLR (TPS) work unit in about 11 minutes, what times per work unit for some of these other projects?

The first post will be updated as sample timings are gathered. The Sophie Germain Prime Search already has approximate WU times listed.
____________

gemery

Joined: 12 May 07
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Message 8338 - Posted: 27 Feb 2008 | 19:19:36 UTC - in response to Message 8337.

In speed terms per work unit, I can do a LLR (TPS) work unit in about 11 minutes, what times per work unit for some of these other projects?

The first post will be updated as sample timings are gathered. The Sophie Germain Prime Search already has approximate WU times listed.

Short times.. That is better than the 15-20 hours my machines take for the others :)

bring it on

John
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Message 8339 - Posted: 29 Feb 2008 | 3:54:17 UTC

I decided to create a separate post for timings.

Unlike the SG project, n will increase for the 3*2^n+1 project. Here are some approximate WU times:

[u]n C2Q 2.4 GHz C2D 2.1GHz Athlon64 2.1GHz[/u] 100000 11 seconds 12 seconds 23 seconds 150000 20 seconds 23 seconds 50 seconds 200000 43 seconds 49 seconds 1.4 minutes 250000 1.1 minutes 1.3 minutes 2.3 minutes 300000 1.3 minutes 1.6 minutes 2.8 minutes 400000 2.9 minutes 3.5 minutes 5.8 minutes 500000 4.8 minutes 5.8 minutes 10.2 minutes 750000 11.4 minutes 13.5 minutes 24.4 minutes 1000000 20.3 minutes 23.5 minutes 45.9 minutes 1250000 25.3 minutes 30.1 minutes 57.4 minutes 1500000 50.5 minutes 59.6 minutes 1 hour 19 minutes 1750000 58.9 minutes 1 hour 9 minutes 2 hours 6 minutes 2000000 1 hour 27 minutes 1 hour 43 minutes 3 hours 27 minutes 2250000 1 hour 38 minutes 1 hour 59 minutes 3 hours 53 minutes 2500000 1 hour 48 minutes 2 hours 9 minutes 7 hours 41 minutes 3000000 3 hours 18 minutes 3 hours 58 minutes 8 hours 31 minutes 3500000 3 hours 51 minutes 4 hours 37 minutes 10 hours 33 minutes 4000000 5 hours 50 minutes 7 hours 9 minutes 13 hours 45 minutes 4500000 6 hours 34 minutes 8 hours 3 minutes 15 hours 0 minutes 5000000 11 hours 25 minutes 14 hours 3 minutes 25 hours 41 minutes

____________

parabol

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Message 34199 - Posted: 16 Mar 2011 | 1:21:00 UTC

Hi all

would it be possible to deleate all entries older than 2 years from the forum ??

???? why not ????

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