The Prime Time Challenge

2008-11-14 21:00 UTC

The Prime Time Challenge has been canceled. While the server is fine, we are having issues that we are not yet able to resolve. We sincerely apologize for this. More information to come when we have it

## Primegrid

2008-12-26 07:00 UTC

PrimeGrid has added a new prime search project, thePrimorial Prime Search. These primes are of the forms p#+1 and p#-1. It enters the Project Staging Area first as a manual sieving effort. Once sufficient depth has been reached, a primality testing effort will begin.

In order to define a primorial prime, we must first define primorial. The primorial pn# is defined as the product of the first n primes. For example,

p5# = 2*3*5*7*11 = 2310

This can also be notated as p#, the product of all primes less than or equal to prime p. The above p5# would be 11#, the product of all primes less than or equal to prime 11.

Primorial primes are prime numbers of the form p#± 1. Using the example above, we would look to see if 11#+1 and 11#-1 are prime.

11# = 2*3*5*7*11 = 2310

11#+1 = 2311 is prime

11#-1 = 2309 is prime

Therefore, 11#+1 and 11#-1 are both primorial primes. Using another example, 7#:

7# = 2*3*5*7 = 210

7#+1 = 211 is prime

7#-1 = 209 is not prime

Therefore, only 7#+1 is a primorial prime.

To date, the largest known primorial prime is 392113#+1 with 169966 digits, found in 2001 by Daniel Heuer. 392113#+1 = 2*3*5*7*...*392099*392101*392111*392113 + 1

p#+1 is prime for the primes p=2, 3, 5, 7, 11, 31, 379, 1019, 1021, 2657, 3229, 4547, 4787, 11549, 13649, 18523, 23801, 24029, and 42209, 145823, 366439 and 392113 (169966 digits).

p#-1 is prime for primes p=3, 5, 11, 13, 41, 89, 317, 337, 991, 1873, 2053, 2377, 4093, 4297, 4583, 6569, 13033, and 15877 (6845 digits).

A list of the top 20 primorial primes can be found at The Prime Pages: The Top 20

Mark Rodenkirch's (in collaboration with Geoff Reynolds) psieve program will be used to sieve and Chris Nash and Jim Fougeron's PGFW program will be used to primality test.

2008-12-27: PrimeGrid - AP26 Search

PrimeGrid has added a new prime search project, anArithmetic Progression of 26 primes. An arithmetic progression of primes is a sequence of primes with a common difference between any two successive numbers in the sequence. For example 3, 7, 11 is an arithmetic progression of 3 primes with a common difference of 4.To participate, go to your PrimeGrid preferences page and select AP26 (currently only available for 64 bit Linux). For more information, please see this forum thread.

An arithmetic progression is a sequence of numbers with a common difference between any two successive numbers in the sequence. For instance, the sequence 3, 5, 7, 9, 11, 13, 15, ... is an arithmetic progression with a common difference of 2.

Therefore, an arithmetic progression of primes is a sequence of primes with a common difference between any two successive numbers in the sequence. For example 3, 7, 11 is an arithmetic progression of 3 primes with a common difference of 4.

For an arithmetic progression (AP) of primes, AP-k is k primes of the form p + d*n for some d (the common difference between the primes) and k consecutive values of n. The above AP-3 is 3 + 3*n for n=0,1,2.

n=0; 3 + 4*0 = 3 + 0 = 3

n=1; 3 + 4*1 = 3 + 4 = 7

n=2; 3 + 4*2 = 3 + 8 = 11

Another example is the AP-10 of the form 199 + 210*n for n=0..9. This produces the following sequence: 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089.

AP-k is also sometimes notated PAP-k (Primes in Arithmetic Progression).

We are searching for the longest AP, not the largest. The current record is an AP-25 discovered May 17, 2008, by Raanan Chermoni & Jaroslaw Wroblewski. For a complete list of records including longest and largest AP's, please see Jens Kruse Andersen's Primes in Arithmetic Progression Records. Also, a list of the top 20 largest AP's can be found at The Prime Pages: The Top 20

Geoff Reynolds' adaptation and implementation of Jaroslaw Wroblewski's AP code will be used for the search.

12121 Prime Search

PrimeGrid and 12121 Search are now collaborating in an effort to find a Mega Prime of the form 121*2^n-1. This is very similar to the 321 Prime Search at k=3.

12121 Search was established on 5/24/2004 to search for large primes of the form 121*2^n-1. Later, they added k=27 to their search. Their "short term" goal is to search for n up to 10M. For more information, please visit their site: 12121 Search.

As we did with 321, we are going to test the +1 form of these k's in parallel as well. Therefore, the effort will consist of the following:

121*2^n+1, 121*2^n-1

27*2^n+1, 27*2^n-1

for n<10M

First order of business is to establish a coordinated sieving effort to bring all forms to the same depth. Here's the current status:

121 -1 at p=290T for n<10M

121 +1 at p~450T for n<5M and p=1T for 5M<n<10M

27 -1 at p=130T for n<10M

27 +1 at p~450T for n<5M and p=1T for 5M<n<10M

We need two efforts but we'll only focus on one right now:

1. Primary focus - 27 -1 to bring it up to p=290T then combine with 121 to take to 450T

2. 121 & 27 +1 for 5M<n<10M to bring it up to 450T.

To participate in the manual sieve, please see 12121 Sieving Reservation.

Second order of business is to primality test 27 -1, 27 +1, and 121 +1 up to n~3.7M to combine it with 121 -1. Therefore, candidates will be available for testing in PrimeGrid's PRPNet. If you are interested in participating, please see the PRPNet thread. Port 5000 is currently loaded with 27 & 121 +1 for 600K<n<1.7M.

321 Sieve

2009-02-19 00:45 UTC

The 321 Sieve has completed its manual effort and is now available in BOINC. Current depth is p=2P for 5M < n < 25M. This is for both +1 and -1 forms. To participate, go to your PrimeGrid preferencesand select 321 Prime Search (Sieve). It's currently available for Linux64 and Windows32/64

Das ist heftig, nach ewiger Suche wurde das Teil nun wirklich gefunden !World Record Twin Primes returned

2009-08-06 16:20 UTC

The search is finally over!!! The Twin Primes have been discovered!!! Verification was quickly completed and the appropriate users are being contacted. Credit will be shared between the finder, top producer in terms of M, top producer in terms of primes found, and top siever. The Twin Primes were actually returned on the SAME!!! day as the Cullen Prime but were overlooked in the excitement of the Cullen.

Work generation has been terminated so please select another project if TPS was your only project. The project will remain active until all outstanding work has been returned and credited. Stay tuned for more details.

Nach Pre-Tests endlich verfügbar.Sophie Germain Prime Search

2009-08-16 15:55UTC

The long awaited debut of the Sophie Germain Prime Search has finally arrived. To participate, select Sophie Germain Prime Search (LLR) on your PrimeGrid preferences page. For more information, please see this forum post.

### Erfolge

So, jetzt schon im Forum offiziell...

New AP24

A new record AP24 (Arithmetic Progression of 24 primes) has been found. It is the largest known AP24. It has an ending term of 84418532426419063 surpassing the previous record of 83286253012572277 (2009, John S Morris III, PrimeGrid, AP26). The finder is Anonymous (Rebirther) of Germany. He is a member of the BOINC Confederation team.

The progression is written as 4187489431145893+15636117*23#*n for n=0..23. Credits are as follows:

Finder: Anonymous

Project: PrimeGrid

Program: AP26

Quelle/Download

Leider Schluß mit AP26, Faktor wurde gefunden.First ever AP26 Found!

2010-04-12 23:55 UTC

The search is over. A World Record AP26 (Arithmetic Progression of 26 primes) has been found. The finder is Benoãt Perichon [AF>HFR>RR] Jim PROFIT) of France. He is a member of the L'Alliance Francophone team.

The AP26 progression is written as 43142746595714191+23681770*23#*n for n=0..25. It was found by a PS3 running Linux. For more details on this find, please see this forum post.

Congratulations to everyone who participated in the AP26 Search. It has been a very challenging and rewarding project. Also, a special thanks to all the programmers who ported AP26 making it the most accessible project at PrimeGrid.

Note: there will be no more work once the queue is empty, so we would like to ask people not running for the badges to stop running AP26 subproject and give a chance for others to reach their final levels.

Primegrid geht schon wieder das Geld aus, Problem aus allen Projekten. Dafür wurde zur Spendenaktion aufgerufen, wenn nur die Multimillionäre wenigstens mal dafür sinnvoll spenden würdenPrimeGrid Donation Drive 2010 Fall

PrimeGrid is a project that is not financed by universities or commercial entities. In fact, all of our funding comes from the community, most of it through the donations page and a small amount through Google ads on the site. In the previous months donations were enough to cover all expenses running the website, however, the last few months have been particularly bad and just paying for server collocation has cut deep into our emergency funds.

It is never easy to be asking for money, but it has come to the point where we have to. We currently have money to keep the servers running for two more months. After that, we either shut down or throttle down significantly, which would be a shame having established PrimeGrid as a significant power in the prime number community, and having received uncountable hours of support from the members.

We have entered the "optimal sieve zone". Actually, we've been floating around it for some time since the last prime was found back in June. Please consider this the first notice to anyone on the cusp of their next badge level (20K, 200K, 1M, 2.5M).

It is currently unknown "exactly" when the sieve will end. However, we can guarantee another four weeks (REVISED sooner: to at least 13 Oct 2010). In the meantime, we'll be investigating to pinpoint an exact stop date. And yes, we are taking the Calendula Challenge into consideration so people won't be forced to make a choice between the two. :)

This is a major accomplishment for both the Prime Sierpinski Problem and the Seventeen or Bust projects. The PSP/SoB sieve at PrimeGrid was announced on 13 Oct 07. That date this year might be a very fitting day to end the sieve. :)

The official classification of this will be a suspension and not a termination. Should "improved" sieving methods come up in the future, this sieve will be reviewed for continuation. EDIT: And of course, should there still be k's remaining as we approach 50M, we'll need to resume sieving for n>50M. :)

We'll update everyone as soon as we know more.

John hat mal eine Zusammenfassung über die Lebenszeit der einzelnen Projekte aufgelistet.People have been asking about the "life" expectancy of the current projects. Below is a comparison of project groups. The time-frames are just references so you can compare the different groups. Take all of this with a grain of salt. :)

The conjectures in the 10+ group could easily take 100's of years if ever proven. The 5+ group could technically go on forever simply by adding more work (n max increased)

The sieves will finish before their LLR counterparts. However, they will be classified as suspended. The sieves could start back up if there are further advances in sieving efficiencies in the future or if more work is added (n max increased).

The Sophie Germain Search is by itself since a Twin and/or SG could be found at any minute. Since this is a quad sieve, there is a chance of finding both a Twin and an SG. However, should one be found at this n, another search will be started at a different n so this project would still be around.

I hope this helps.

10+ years

Prime Sierpinski Problem (LLR) will be tested to at least 50M or until all remaining k's have been proven prime.

Seventeen or Bust (LLR) will be tested to at least 50M or until all remaining k's have been proven prime.

The Riesel Problem (LLR) will be tested to at least 50M or until all remaining k's have been proven prime.

5+ years

321 Prime Search (LLR) will be tested to at least n=25M.

Cullen Prime Search (LLR) will be tested to at least n=25M.

Proth Prime Search (LLR) will be tested to at least 5M.

Woodall Prime Search (LLR) will be tested to at least n=25M.

1+ years

Cullen/Woodall (Sieve) will be sieved to optimal depth.

Proth Prime Search (Sieve) will be sieved to optimal depth.

The Riesel Problem (Sieve) will be sieved to optimal depth.

6-12 months

321 Prime Search (Sieve) will be sieved to optimal depth.

Less than a month

PSP/SoB (Sieve) will be sieved to optimal depth.

Unknown

Sophie Germain Prime Search (LLR) will be tested until a Twin and/or SG prime is found.