**Prime Sierpinski Problem Sieve**

Einstellungen kann man in den Preferences vornehmen.

Primegrid wird größer und größer, jetzt mit neuem Unterprojekt:

**Prime Sierpinski Problem Sieve**

Einstellungen kann man in den Preferences vornehmen.

Einstellungen kann man in den Preferences vornehmen.

2008-02-15: PrimeGrid - End of the life cycle of primegen application

We are inserting the final batches of work for our oldest available application, primegen. While primegen has proved very useful

in the early project stages for infrastructure testing, it has served it's purpose and it's time to make way for newer, more

efficient applications. Once the final batches are completed the cleanup will be executed, finally removing old stuck workunits.

We suggest participants running primegen exclusively also select an additional subproject for future processing. Sieve subprojects

are very similar to primegen in size, so it is probably a good choice. Once there are no more primegen work to send, we will

update project for such participants to select sieve subprojects.

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 ... rmainPrime

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 factors. Currently there are only about 250 such 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

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

Primegrid hofft, an einem Tag den Bereich bis p=2500T für PSP Sieve abzudecken.2008-03-08:

PrimeGrid is offering a one day challenge to support the Prime Sierpinski Sieve. This sieve benefits both the Prime Sierpinski Project as well as Seventeen or Bust. To participate, please select only the PSP sieve in your PrimeGrid preferences section. The challenge willbegin 15 March 2008 00:00 UTCandend 16 March 2008 00:00 UTC. Application builds are available for Linux 32 & 64 bit and Windows 32 & 64 bit.

This is a project wide effort to complete 50,000 WU's in a 24 hour period and bring the sieve depth to p=2500T (current depth is ~2400T). Not only will this be a GREAT milestone for the PSP and SoB projects, but it will also give a small stress test to PrimeGrid's servers. As PrimeGrid continues to grow, this will be a good indication as to the loads it will be able to handle in the near future.

Please come join the challenge and help PSP and SoB reach a GREAT milestone. Scores will be kept for individuals and teams. Only WU's that are issued and credit granted within the 24 hours will be counted.

Team und Userstats sind hier zu finden:

Challenge endet am 16.03. um 01:00 bei uns.

Rebirther Platz 74

BOINC Confederation Platz 26: 5 Punkte

http://primegrid.com/challenge/top_teams_24.html

2008-05-09 01:40 UTC The Drive for Five Challenge

PrimeGrid's Challenge series continues. Please come join our effort to reach n=5 million in the 321 Prime Search (3*2^n-1). The Challenge will begin 00:00 UTC, 15 May 2008. For more information, please see this forum thread.

http://www.primegrid.com/forum_thread.php?id=928

ImThe next Challenge is tentatively set for mid August. Also tentative is that the project will be on a new prime search (LLR application) – Sophie Germain. Additionally, we have already come up with few more changes to help with the start of the Challenge. Please check back at the end of July for more details.

Die PSP Sieve Challenges machen sich echt bezahlt.2008-07-27: PrimeGrid - PSP finds Mega Prime

The Prime Sierpinski Project has discovered their second mega prime: 258317*2^5450519+1. It is 1640776 digits long and will rank as the 12th largest known prime. The project has now found 17 primes total. There are only 12 primes left to solve the Prime Sierpinski Problem. For more information, please see this forum post.

August Challenge update

After much discussion, it was deemed in the best interest of PrimeGrid to change the August Challenge from Sophie Germain LLR to 321 LLR. Here's an explanation why...

PrimeGrid's current hardware reached its limit during the Lunar Landing Challenge. Even after increasing the WU size twice, the amount of activity was still almost too much for the server. This is WONDERFUL news for PrimeGrid, but no so good news for the server. ;)

The server MUST be upgraded if PrimeGrid wishes to continue the Challenges Series. We were hoping for corporate sponsorship to help build the new server but that has yet to materialize. A line item was added to the Donation page but as of this post, only 15.6% has been achieved.

Since we do not yet have a new server, a compromise was reached to continue the Challenges but not on projects that would stress the old server too much. Therefore, the original August Challenge for Sophie Germain LLR was exchanged for 321 Prime Search LLR since the WU's for Sophie Germain were too short.

Until PrimeGrid can upgrade its server, only the following projects will be available for Challenges: Cullen LLR, Woodall LLR, PSP LLR, and 321 LLR. Projects NOT available are GCW sieve and PSP sieve. Also, the addition of future projects Sophie Germain LLR and Proth Prime Search LLR will be put on hold.

BTW, SG LLR and PSP LLR will produce a lot of primes for entry into The Largest Known Primes Database. The sooner PrimeGrid can upgrade its server, the sooner everyone can start enjoying the thrill of finding primes again. :D

If you haven't done so already, please consider visiting the Donation page. We are always VERY GREATFUL for everyone's participation in PrimeGrid and appreciate everything y'all have done to make it a success.

The August Challenge is: The Dog Days of Summer

Good Luck and thank you very much for your support!

p.s. By the Numbers...to put it in perspective, 1331 users participated in the last Challenge. If 1/4 (~333) give 6 euros each or 1/2 (~666) give 3 euros each or ALL give 2 euros each, the new server would be a reality. :)

In a review yesterday of the Cullen/Woodall Project status, it was determined that we are at "optimal" sieve depth...actually, a little beyond it. Therefore, we are stopping the 32 bit and 64 bit Cullen/Woodall Sieve applications and archiving the sieve. Cullen/Woodall LLR will remain active up to n=10M.

Mit dem neuen Server folgen auch neue Unterprojekte.2008-10-23: PrimeGrid - Scheduled downtime - new server installation!

We are planning a scheduled downtime of several hours on Monday, October 27. We will be relocating PrimeGrid and BOINCstats servers to the new rack, and will add a new server for PrimeGrid, which has been purchased using funds from the recent donation drive.