Active Distributed Computing Projects  Mathematics 
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Project Information  Project % Complete  Major Supported Platforms  

Mathematics  
The current largest known Mersenne prime number is
2^{43,112,609}  1 (found on August 23, 2008, and containing
almost 13 million digits). This is the largest known prime number and the 45th
Mersenne prime discovered (and the 11th Mersenne prime discovered by GIMPS).
Help find the next one in the
Great Internet Mersenne Prime Search
(GIMPS).
The 46th known Mersenne prime (and the 12th Mersenne prime discovered by GIMPS)
is 2^{37,156,667}  1 (found September 6, 2008, and containing 11.2
million digits).
The 47th known Mersenne prime (and the 13th Mersenne prime discovered by GIMPS)
is 2^{42,643,801}  1 (found April 12, 2009, and containing 12.8
million digits).
As of July 8, 2008, all exponents below 17,000,000 have been doublechecked. As of July 4, 2008, all exponents below M(20996011) have been tested at least once. Unix users can participate in GIMPS using precompiled clients or source code at Ernst Mayer's site and the manual testing forms at the PrimeNet server. Clients can be downloaded from the project's download page. Version 24.14 of the prime95 client is available for Windows 95/98/Me/NT/2000/XP as of August 9, 2005. Version 24.14 or the mprime (or statically linked sprime) client is available for Linux and FreeBSD as of August 9, 2005. Clients are also available for Windows NT/2000/XP Service, OS/2, and Windows 3.1. See a complete list of features in these versions. See the download page for information about cliens for Apple/PowerPC, StrongARM, and UNIX machines. See the project's wiki. Join a discussion forum about this project. GIMPS also has a subproject: ECM and P1 Factoring. This project is "trying to factor numbers of the form 2^{N}  1 and 2^{N} + 1 using either the P  1 method or the Elliptic Curve Method (ECM)." On September 13, 2004, this project "found a 53digit factor for M971. This was the smallest Mersenne number for which no factors were known!" 
ongoing 


Search for different kinds of prime numbers at Yves Gallot's Proth Search Page. Submit new primes to the Top 5000 Primes list. Version 7.1 of Proth is available as of July 12, 2005.

ongoing 


Help find new factors of Cunningham numbers at ECMNET.
To participate in the project, download the client (available for Windows, Linux, Solaris and various other flavors of Unix), download the Cunningham input list (see the link on the project website), then run the client and report any factors it finds through a link on the project website. Version 2.7.0 of the ECMNet client/server is available as of December 3, 2005. 
ongoing 


Find Minimal Equal
Sums of Like Powers using
Euler2000,
available on the download
page. The client automatically downloads ranges of numbers to work on. The
project celebrated its 10th anniversary on January 31, 2009.
On February 6, 2003, a project member discovered the largest (6,2,5) result above 60,000. On December 8, 2002, a project member found a new upper limit for Taxicab(6): Taxicab(6) <= 24153319581254312065344, since 24153319581254312065344 = 28906206^{3} + 582162^{3} = 28894803^{3} + 3064173^{3} = 28657487^{3} + 8519281^{3} = 27093208^{3} + 16218068^{3} = 26590452^{3} + 17492496^{3} = 26224366^{3} + 18289922^{3}. The Taxicab problem isn't a part of the Minimal Equal Sums of Like Powers project, but this is a big discovery nonetheless. Version 4.21b of the client is available as of September 30, 2002. This version handles reserved work ranges better, points to the new eulernet.org domain automatically, and on the server side, allows for simultaneous client connections. Note: you should upgrade from version 4.18 and earlier to fix a significant client bug in those versions. Note: 4.21b has a bug which prevents the client from connecting to the server if you try to reserve more than the maximum 100 ranges. Use temporary version 4.21c to fix the bug. Note: the project server was switched to a new ISP and domain, eulernet.org, as of October 15, 2002. The client should use eulernet.org when trying to connect to the project server. If your client can't connect to the project server, try pressing CtrlU, then changing the server name from eulernet.org to euler.myip.org. This may solve your problem if the DNS is incorrect. Join a discussion forum about the project. 
ongoing: Resta 3 (6,1,6): 100.0% (completed October 23, 2002) Resta 6 (6,2,5): 90.47% 


Search for factors of 2^(2^611)1, a double Mersenne number, in the MM61 project. Download and test the client, then email the project coordinator to reserve a range of numbers to test.
Note that the project website is not accessible as of October 29, 2009. If you know of a new URL for the project or if the project has ended, please let me know. 
ongoing: 18,640 ranges done, 6,360 to do 


Find 3x+1 class records in the
3x+1 Problem
project. This project attempts to find ever higher 3x+1 class records.
The client, which will work on any PC/Windows platform, and the instructions
for joining the project, are
here.
Note: the client takes about 6 weeks to finish one block on a 400MHz
CPU.
The project completed its first goal, processing 20,000 blocks, on November 19, 2002. The project found a new glide record in December, 2002. This is the first glide record found in almost a year. The record occurs at 180352,746940,718527, and the new glide is 1575, an improvement of 104 over the previous record. The project found a new Path record in March, 2003. The previous Path record was found in late 2002. The record occurs at 212581,558780,141311, (or +/ 189.2^{50}) and it reaches a maximum of 4353,436332,008631,522202,821543,171376. As of November 2, 2008, the project completed all blocks up to 67,500 and confirmed class record 2000. See the project's progress. 
ongoing: blocks to go to class record (unknown); all blocks up to 76,160 complete; all class records below 2,000 known 


Help the Distributed Search for Fermat Number Divisors project find unique Fermat Number factors.
This site is also available in Italian , Russian , and German . Version 4.1 of the client is available as of September 7, 2001. Version 2.0 of the project's GMP_Fermat client is available as of June 10, 2008. Version 3.2.3 of the project's PFGW client is available as of November 3, 2009. The project has found the following factors recently:

ongoing 


The
PCP@Home project looks for short cases of
Post's Correspondence
Problem with large
shortest solutions. This theoretical computer science problem has been in
existence since 1946. It demonstrates undecidability: "a problem that cannot
be solved for all cases by any algorithm whatsoever." Finding PCPs in this
project will help define "decidability criteria for bounded PCP classes."
To participate in the project, download a precompiled, statically linked executable for Linux ELF, FreeBSD ELF, Solaris 5.6, or Windows (you can also download and compile the source code), and also download a perl script called PcpSieve.pl which runs the executable, scans the output for record solutions, and emails the solutions to the project coordinator (you can also run the executable manually, search the output manually and email any record solutions you find). Note to Windows users: the Windows client was compiled by Michael Keppler of Rechenkraft.net. He says that it has a serious memory leak, and that you may need to kill it and restart it every day. If anyone knows how to debug Windows application memory leaks, please contact him. This site is also available in German. 
possibly ended; Note: the project website has not been updated since 2004; the project may have ended 


Find generalized Fermat prime numbers in the
Generalized Fermat Prime Search. This project uses the
Proth program or the
GFNSieve21 program to find these numbers. Unixusers and other users
can compile the
C source code of "GeneFer" for the project and you can directly check
a presieved range with
it (note that the project owner of the presieving project has blocked the
website from viewers in the US, the UK, Australia, Denmark, and other
countries which "support the US's war on Iraq"). Version 1.2 of this code is
available as of June 10, 2002.
On January 6, 2003, Daniel Heuer discovered the largest known Generalized Fermat prime 1483076^{65536}+1 (404,434 digits), with GFNSieve+Proth, beating his previous record from October 8, 2002. "This number is the new largest known prime which is not a Mersenne prime, and the 6th largest known prime." On February 16, 2003, Michael Angel discovered the first prime of the form b^{217} + 1: 62722^{131072} + 1 (628,808 digits). This number is the 5th largest known prime. On February 21, 2003, the project completed the whole range 22,200,000 for exponent 32768. It found 35 primes in this range. On March 26, 2003, Franz Hagel discovered the 20th Generalized Fermat prime of the form b^{65536} + 1: 357868^{65536} + 1 (363,969 digits). On July 12, 2003, Michael Angel discovered the second known prime of the form b^{217} + 1: 130816^{131072} + 1. On August 22, 2003, Daniel Heuer discovered the largest known Generalized Fermat prime: 1176694^{217} + 1. This 795,695 digit number is now the 5th largest known prime. On September 22, 2003, Daniel Heuer discovered the new largest known Generalized Fermat prime: 1372930^{217} + 1. This 804,474 digit number is now the 5th largest known prime. On January 8, 2004, Yves Gallot discovered the 5th Generalized Fermat prime of the form b^{131072} + 1: 572186^{217} + 1 (754,652 digits). On May 30, 2004, Daniel Heuer discovered the two largest known Generalized Fermat primes: 1372930^{131072} + 1 (804,474 digits) and 1176694^{131072} + 1 (795,695 digits). Join a discussion forum about prime numbers. 
possibly ended;Note: the project website has not been updated since January, 2004; the project may have ended 


Help search for the 33rd largest prime number
in PSearch. A
Proth
prime is a prime number of the form Participants in the project should have at least a 600 Mhz PC. To join the project, first download George Woltman's PRP software for Windows or Linux. Then send email to William Garnett with your CPU type and speed and your operating system, and he will send you instructions for participating. Join a discussion forum about the project. 
24,092 of 37,328 candidates tested; should find one prime number in every 18,629 candidates; Note: the project website has not been updated since February, 2006; the project may have ended 


Help find the smallest
Sierpinski number in
Seventeen or Bust, a distributed attack on
the Sierpinski problem. The project looks for
Proth
prime numbers in which, for a number k, if every possible choice
of n results in a composite (nonprime) Proth number N,
k is a Sierpinski number.
The project began its k=33661 project on November 21, 2002, and added fifteen additional projects on November 23, 2002. It has found the following primes:
The recent discovery of the 11th prime for the project helped prove a new mathematical theorem: the Mixed Sierpinski Problem. The results were published in a paper in the journal INTEGERS on December 23, 2008. To participate in the project, sign up for an account, download the client, add your account name to the client configuration, and run it. The client does Proth tests on individual numbers. Each number should take a few hours to test on an average machine. When the project server assigns you a number, it waits for up to 10 days for you to return your search results, and reassigns the number to someone else if it doesn't receive your results within that time. The client supports users behind firewalls and proxy servers. Version 2.5 of the client is available for Windows and Linux as of September 10, 2005. Version 2.5 of the client is available for FreeBSD as of 2006. Version 2.2 of the client is available for BeOS as of December 11, 2004. A new client based on the Prime95 client is available for Windows, Mac OSX and Linux as of March 18, 2009. This client has significant improvements in speed and efficiency. Seventeen or Bust also has a supporting project to sieve numbers for the main project: sieving finds n numbers with small factors and removes them from the pool of prime number candidates which need to be tested by Seventeen or Bust. Two clients are available for sieving: SoBSieve (for Windows) and NBeGone (for multiple platforms). To reserve a range of numbers to sieve, post a message to the sieve coordination thread. Then submit the results from the range to the "sieve numbers" page mentioned above. The latest sob.dat file, with 10 k, is available as of January 3, 2005. As of January 9, 2005, users with regular user accounts can also perform secondpass tests of numbers the project has already tested once. This feature will be included in a future client, but for now it requires a bit of hacking for the Windows client. See details in this thread and participate at your own risk. See the project's Wiki. Join a discussion forum about the project. 
6 primes remaining to be found; 794,896 Proth tests completed 


Find factorizations of cyclotomic numbers at
Factorizations
of Cyclotomic Numbers. This site doesn't appear to be
organized as an official distributed computing project and doesn't have
any precompiled client software or explicit instructions for participating,
so it is probably best suited for people who understand the Mathematical
principles behind the project and how to compile source code.
The Phi(92) series was completely factored by November 2, 2002: the last composite number was factored by Tetsuya Kobayashi on that date. Katsuyuki Okeya finished the Phi(61) and Phi(122) series on December 30, 2002. The Phi(69) series was completely factored by January 12, 2003: the last composite number was factored by Alexander Kruppa. The Phi(112) series is completely factored as of September 25, 2004. The Phi(144) series is completely factored as of October 12, 2004. The Phi(104) series is completely factored as of November 30, 2004. The Phi(168) series is completely factored as of December 24, 2004. The Phi(180) series is completely factored as of January 18, 2005. The Phi(65) series is completely factored as of February 9, 2005. The Phi(130) series is completely factored as of February 26, 2005. The Phi(156) series is completely factored as of March 6, 2005. The Phi(210) series is completely factored as of March 22, 2005. The Phi(53) series is completely factored as of July 1, 2006. The Phi(198) series is completely factored as of September 13, 2008. The Phi(118) series is completely factored as of September 22, 2008. To participate in the project, you can download and compile a GMP or UBASIC factorization program, view a page of reserved numbers, then select a range of numbers to factorize and send email to Hisanori Mishima with the range information. Read a paper about cyclotomic polynomials and prime numbers by Yves Gallot. 
ongoing 


Join the
Goldbach Conjecture
Verification to help verify the conjecture through 1e18 (it is currently
verified through 1e16). The Goldbach conjecture is "one of the oldest
unsolved problems in number theory. ...it states that every even number
larger than two can be expressed as the sum of two prime numbers."
The client software consists of a server application which must be run on a GNU/Linux system with a version 2.4 or later kernel, and a client application which may be run on the same GNU/Linux system or on other GNU/Linux or Windows NT/2000/XP systems which can communicate with the server application over an intranet. As of May, 2005, "it is now possible to run the client program in "batch mode" in Windows. No server on GNU/Linux required. It will be necessary to manage things manually. The windows client program acts as a service. In particular, it does not run on a DOS windows. It runs invisibly in the background (at a very low priority)." To participate in the project, send email to Tomás Oliveira e Silva, the project coordinator, with information about the machine(s) on which you will run the server and client applications, and he will send you more information about how to participate. 
ongoing 


Help
The Riesel Problem project prove that k=509203 is the smallest
Riesel
Number. See the project's results on the
search status page.
To participate download the proth.exe client, view reserved ranges on the checked out and progress page, then reserve a range (and submit your results) on the range reservation page. The latest public Beta version of LLRNet is available as of April 5, 2004. 
ongoing 


Help find primes of the form 3 * 2^{n}  1
in the 3*2^n1 Search.
This project builds on the work of the project
to find primes of the form k * 2^{n}  1 for k < 300. For
3 * 2^{n}  1, n is known up to 2,000,000. This project
is currently looking for new ns between 2,000,000 and 3,000,000. The
search to n=2,000,000 (about 600,000 digits) was completed on July
1, 2005. As of March 12, 2007, candidates have been sieved to 245 trillion,
6,958 total candidates are ready for LLR testing, and 119 work blocks are
available for LLR testing.
The project has found the following primes recently:
To participate, download one of the following software clients: LLR, PFGW, PRP (see download links in the discussion forum), then reserve a range from the 34M reservations page and download a zip file of all the input files from a link on that page. After you run the client, email the results to Paul Underwood. Version 3.7.1 of LLR (available here) is available as of May 4, 2006. The latest sieved files are available as of February 23, 2007. Join a discussion forum about the project. 
87.54% for n up to 1,000,000 digits 


NFSNET uses "the
Number Field Sieve to find the factors of increasingly large numbers."
You can participate in the project by following the instructions on the
join page. See the project's
latest news.
On November 10, 2002, NFSNET completed the factorization of W(668), a 204digit special number field sieve (SNFS). The client is commandline, with a GUI wrapper client available. It is better for users with permanent Internet connections. It supports users behind firewalls but not users behind proxy servers. Release Candidate 1 of the client is available as of May 12, 2003. The project's 10 most recent factorizations:
Join a discussion forum about the project. Subscribe to the project mailing list. 
ongoing 


Join the
Search
for Multifactorial Primes. This project continues work started by
Ray Ballinger to find multifactorial prime numbers, primes of the form
n!!+/1, n!!!+/1, n!!!!+/1, searching for all primes
up to 10,000 digits for each multifactorial type.
The project has recently proven the following numbers are prime:
On March 29, 2005, the project finished !19 to 200,000. On May 31, 2005, the project finished !17 + 1 to 170,000. On August 6, 2005, the project finished !17  1 to 170,000. On August 21, 2005, the project finished !25 to 200,000. On September 9, 2005, the project finished !15 to 130,000. On November 26, 2005, the project finished !15 to 150,000. On November 26, 2005, the project tested all types up to 20 to 10,000 * type +/ 1. On December 20, 2005, the project finished !3 + 1 to 75,000. On February 28, 2006, the project finished !24 + 1 to 240,000. On March 27, 2008, the project finished !25 + 1 to 250,000. Participation instructions are at the top of the project page. Basically, you email the project coordinator to reserve a type, then use the multisieve and pfgw Windows applications to sieve the range and find primes in it, then submit your results to the project coordinator. 
ongoing 


Help find primes of the form 15k *
2^{n}  1 in the
15k Prime Search. The project is looking for 15k which produce many primes
n: "in general when k has many small factors, n is more likely to
produce a prime because it can't have those same factors." As of May 7, 2005,
the project is the #1 top project by number of primes, with 397
primes discovered. Note: As of April 24, 2008, the
project website URL no longer goes to a project website or page, but the
project's discussion forum and wiki (see links below) are still available.
The project has found the following prime numbers recently:
See all of the primes the project has found. To participate, follow the instructions for how to join, then the instructions for how to participate (novice or expert). The project uses the LLR.exe, NewPGen.exe and RMA.NET software executables. Note that you will need to download the Microsoft .NET runtime library if you don't already have it installed. Version 0.82 of RMA.NET is available as of December 3, 2005. Join a discussion forum about the project. See the project's wiki. 
ongoing 


Find factors of the Mersenne number
M(3326400) = 2^{3326400}  1 in
ElevenSmooth. Note:
this project is active, but the project website is not updated unless a major
event occurs. The website was last updated on May 1, 2009. See the
project's completed factorizations.
On February 1, 2004 the project "found a 42 digit factor of M(5280) using GMPECM with B=3M. This is expected to qualify for 9th place in Paul Zimmerman's Top Ten This Year list." On April 4, 2004, the project found P35, the first known primitive factor of M(15840). On May 14, 2004, the project found P34, the second known factor of M(10395). On June 9, 2004, the project found P25, the second known factor of the primitive part of M(66528). On June 12, 2004, the project found a P49 factor for M(1485), the largest factor found by ElevenSmooth using ECM. On July 20, 2004, the project completed the factorization of M(3960). On September 18, 2004, the project found a P28 factor of M(95040): this is the first known factor of the primitive part of M(95040). On October 19, 2004, the project found a P36 factor of M(11880), "the second known factor for the primitive part of this number." On July 28, 2005, the project found a P35 factor of M(47520), the third factor the project has found for the primitive part of M(47520). In early December, 2005. the project found a 41digit factor of M(6336). In March, 2008, the project completed the factorization of M(1575). On May 7, 2008, the project completed the factorization of M(2376). On July 16, 2008, the project found a P34 factor of M(5400) (using ECM at the B1=1M level). This factor reduces the unfactored residual from C406 to C373. This is the second factor ElevenSmooth has found for this number. On November 15, 2008, the project found a P37 factor of M(100800). This factor reduces the unfactored residual from C6925 to C6889. On March 27, 2009, the project found a P51 factor of 2^{3360} + 1. This is the largest factor ElevenSmooth has found by ECM and is the fourteenth primitive for which ElevenSmooth has completed the factorization. See news of more recent factor discoveries on the project's main page. To participate in the project, download the ECMclient application and configure it according to the directions on the download page (if you already have the ECM or ECMclient application installed, you only need to reconfigure it to use server=wblipp.dynu.com and port=8194). Unix users can follow instructions to create an ECM client for Unix. Once ECMclient is configured, it contacts the ElevenSmooth project server to get work units and to return results. It processes a work unit for 30 minutes by default, but you can change the processing time by changing the maxfreq parameter. The project supports users behind firewalls and possibly proxy servers. It supports modem users with a little bit of work. See the help page for information about using firewalls, proxy servers, and modems. The project also has a Special Project subproject for users who have contributed at least one full week to the main ECM project. The Special Project "uses GIMPS' program Prime95 to work on all primitives of M(3326400) simultaneously. If any ECM work is going to be done on the largest composites, Prime95 is much faster. The subfactor composites are then tested 'for free.' However, even with Prime95, it takes a long time to run ECM curves on large numbers." Users who qualify for this project will be invited by email to join it. See the project's progress and completed factorizations. Join a discussion forum about the project. 
unknown 


Help the
Riesel Sieve's efforts to solve the
Riesel problem by
"removing prime candidates for the remaining k's from a huge .dat file....
The .dat file contains n values from a current low of about 1,700,000 to a high
of 20,000,000 per remaining k. Individual sieving efforts per single k can
take two weeks to a month to sieve to a sufficient level. This coordinated
sieving effort will allow us to sieve 100 times deeper and much quicker. No
more sieving to 3T and stopping in frustration as the hours per factor mount,
now we can go to 300T and beyond..." Before the project began, there were 101
candidate k's and over 11 million k/n pairs. See the
status of all remaining k
values. See an overview
of the tests remaining to be completed.
Note: the project website was unreachable between July, 2008 and October, 2008. The status of the project is unknown. Look for news updates in the News column of the PrimeGrid project main web page and in the Riesel Sieve "backup forums." As of February 18, 2005, the project has sieved all of its ks to 100T. As of June 18, 2005, the project has 5,488,686 k/n pairs left to test. As of March 22, 2006, the project has completed the 2^20 to 2^21 stage of its first run. As of February 27, 2007, the project has sieved all of its ks to 500T. On September 16, 2005, the project offered a US$100 prize to the person who found the next prime for the project. Project participant NeoLogic found the prizewinning prime, 357659 * 2^1779748  1, on September 24. On September 26, the project began a Prime Bounty Contest, which rewards both prime hunter and sieve participants in the project. On September 28, 2005, the project began a Riesel Sieve Prime and Sieve Bounty donation fund at fundable. This fund will be used for rewards for project participants who find primes and who sieve significant factors for the project, according to the contest rules. The project has found the following prime numbers recently:
The project offers the independent LLRNet client and a BOINCbased Sieve client. To participate in the project, follow the BOINC Sieve client instructions, or use the LLRNet client to automatically download ranges of numbers and to submit results (see instructions for using it), or view instructions on the download page to use the rieselsieve.exe client. Basically you download the rieselsieve.exe executable and the riesel.dat data file (about 6 MB compressed and 27 MB fully expanded). Then you reserve a range of numbers through the automated reservation page, process them with rieselsieve.exe, and submit your resulting factors. The riesel.dat file is updated regularly and gets smaller as prime candidates are removed. Version 0.42 of the Proth_sieve client is available for Windows and Linux as of February 12, 2004. This version is 510% faster than the previous version. A client should be available for FreeBSD soon. Version 3.5 of LLRNet is available as of May 2, 2005. Version 5.27 of the BOINC Sieve client is available for Windows as of August 27, 2006. The riesel.dat file was last updated on December 3, 2006. An updated Windows GUI client should be available soon. See the project's wiki. Join a discussion forum about the project. 
on hold? k remaining 


Help
The Prime Sierpinski Project
find the smallest prime
Sierpinski number. "The smallest known prime Sierpinski number is
k=271129. Finding a prime of type k * 2^{n} + 1 for all prime
k < 271129 will be sufficient to prove that 271129 is the smallest prime
Sierpinski number." As of January 2, 2005, 24 k have been eliminated and 7 k
remain to be tested. It is currently searching the following k: 79309,
79817, 90527, 152267, 156511, 168451, 222113, 225931, 237019, 258317.
The project's first anniversary was on November 8, 2004. By that date it eliminated 11 k's by finding 11 large primes, and also sieved to almost 40 trillion. In the next year it hopes to reach at least n=2.5 million for PRP, to find serveral new primes, and to sieve to 100 trillion. As of October 1, 2005, it has tested all n below n=1600000 at least once. With help from PrimeGrid, the project's sieve entered the 10P range by September 30, 2008. The project has found the following prime numbers recently:
To participate in the project, read the Getting Started discussion thread, then download and run the network LLR client. The client automatically reserves work units and submit results. Join a discussion forum about this project. 
7 k remaining; untested pairs up to n=50,000,000 


Help
P.I.E.S (Prime Internet
Eisenstein Search) find large prime
Generalised
Eisenstein Fermat numbers numbers. The project's main goal is to study
the properties of these numbers, and for that it needs to find some prime
numbers.
To participate in the project, send email to the project owner, user "thefatphil" at host "yahoo.co.uk", to let him know you're interested. Then download the client and follow the instructions on the download page for running it. Version 0.7 of the client is available for Windows. Version 0.8 is available for Linux, FreeBSD, AIX and Irix. 
ongoing; Note: the project website has not been updated since 2005 and may be inactive 


Help find
Factors of k*2^n±1 for k=3,5,7,9,11,13 and N < 1000.
See the 50 most recent factors. As of September 5, 2004, the project has reached n=500 for all k=11. The project now includes numbers for k=13, also factored up to n=500. "Numbers for k=13, n > 500 have had very little ecm done on them." The doecm client downloads composites and submits results automatically, but you can manually reserve numbers and submit factors through the website. Version 1.01 of the client is available for Windows and Linux. You can also download and compile the source code for the client. 
ongoing 


Help factor numbers of the form
x^{y} + y^{x} in the
XYYXF project.
The project completed the factorization of all numbers with y < 11 as of February 7, 2005. It completed the factorization of all numbers up to x = 90 as of March 16, 2005. It completed the factorization of all numbers with y < 16 as of April 27, 2005. The number of composites was reduced to 2500 as of September 10, 2005. It completed the factorization of all numbers with y <= 100 as of October 28. The number of composites was reduced to 2300 as of October 18, 2007. It completed the factorization of all numbers up to x = 100 as of October 28, 2007. The number of composites was reduced to 1800 as of November 25, 2009. The project added a Primes and PRPs of the form x^{y} + y^{x} page to its website on June 6, 2008. The project has factored the following numbers recently:
The project has also factored the following numbers recently:
You can reserve numbers manually through the project website and factor them with your favorite factoring client application (GMPECM is reocmmended), or you can use the ECMclient application and automatically reserve numbers and submit results (use the ecmserver childers.myip.org, port 34). Version 6.0 of GMPECM is available as of February 28, 2005. Version 2.5.6 of ECMclient is available as of March 16, 2005. Version 1.39 of MSieve, another client which can be used for the project, is available as of December 2, 2008. As of November 19, 2004, there are 3,242 XYYXF composites from C93 to C321. 761 of them are reserved; 2,481 (including 123 more wanted) are available. Due to a massive SNFS attack, only 38 new numbers were added to the "most wanted" list for 2005. Join a Yahoo! Group discussion forum about this project. 
ongoing 


Help the 12121
Search find large primes of the form 121 * 2^{n}  1,
a subsidiary of the search of k * 2^{n}  1 for
k < 300. This project plans to search for n up to 1,000,000 in the short
term, and for larger n in the long term.
The project has found the following prime numbers recently:
To participate in the project, download the LLR.exe client from a link on the project web page, then reserve a range on the project page. When the test is complete, submit the results on the project page. A new LLR.exe client was released on August 2, 2004: it appears to work faster than the old LLR.exe on SSE2 Systems (P4 and AMD64) and slower on nonSSE2 systems. Join a discussion forum about this project. 
ongoing 


Help the 2721 Search
find large primes of the form 27 * 2^{n}  1. This
is a sister project to the 12121 Search.
The project has found the following prime numbers recently:
To participate in the project, download the LLR.exe client from a link on the project web page, then reserve a range on the project page. When the test is complete, submit the results on the project page. A new LLR.exe client was released on August 2, 2004: it appears to work faster than the old LLR.exe on SSE2 Systems (P4 and AMD64) and slower on nonSSE2 systems. 
ongoing 


Help search for a billiondigit Mersenne prime in
Operation Billion Digits. The project website is also available
in Italian
. This project is
attempting a nearlyimpossible goal. Since today's technology and
algorithms can't find a prime as large 1 billion digits in less than 853
years, this project is doing trial factoring of potential numbers. This
factoring will help future searches and will help improve computer
science and number theory techniques. The project passed the 1,000 Pentium 90
CPU hours mark on February 12, 2005.
To participate in the project, download Luigi Morelli's factor3_2.exe client and some Cygwin files from the project web page, then reserve an unassigned exponent in the project's discussion forum. Version 2 of the client is currently available. It is 25% faster than the previous version. Join a discussion forum about this project. See the project's latest progress updates. 
ongoing; currently at level 12.00 (9 candidates trial factored to 74 bits) 


Help
SIGPS (The Small
Internet GFN Prime Search) search for primes of the form b^{8192} + 1
(b > 99999999), a Generalized Fermat prime number. The project uses
the AthGFNsv.exe client to sieve candidate primes. The project also has
several other subprojects:
The project has found the following prime numbers recently:
To participate in one of the project's subprojects, follow the directions on each subproject page for downloading and running the commandline client. The Fermat Euler Theorem for Fermat number F25 client is available for PS3 as of April 25, 2009. 
ongoing 
PS3 

Help
Primesearch find primes of the form k *
2^{n}  1. The project is currently searching k between 301399
with n at least 16001.
To participate in the project, sign up for an account on the website, then reserve ranges and submit results through the website. Use either the proth or primeform application: links to these applications are on Prime Links++ to process your reserved ranges. 
ongoing 


Lone
Mersenne Hunters looks for Mersenne prime numbers which
have not been tested by other projects or by GIMPS'
Primenet server.
To participate, read the instructions in the How to start? discussion thread. Note: this project only has a discussion forum and no website. 
ongoing 


Factoring
is a collection of factoring projects.
Factoring completed the factorization of 2^791+1 (to 45 digits) on May 2, 2005. It completed the factorization of 2,1342L on May 8, 2005. It achieved a new P  1 record, 2,2098M c281 = p58 * c224, on September 28, 2005. Factoring Projects:
To participate, read the instructions in the forum. Note: these projects only have a discussion forum and no websites. 
ongoing 


Help the
100 Million digits prefactor project
remove exponents which can be factored now from
GIMPS' search for the first known 100 million digit prime
number. This is a sister project to
Operation Billion
Digits. The project does "wide" prefactoring, in which it prefactors
"large ranges of exponents [at a depth of no less than 50 bits and no more
than 55 bits] to eliminate large numbers of exponents," and "deep"
prefactoring, in which it prefactors "individual exponents to higher bit
depths, usually into the mid 60's (possibly higher)." As of January 21, 2009,
the project has deep prefactored to bit depths as high as 77.
To participate in the project, download Luigi Morelli's factor3_2.exe client and some Cygwin files, or Mfactor for win32, or 32bit or 64bit Linux, from links on the project web page. (See more information in the guide.) Then look for an available range or exponent in the table on the project web page and follow the instructions on the project web page to reserve the range or exponent and to submit results. Version 2 of the factor3_2 client is currently available. It is 25% faster than the previous version. Join a discussion forum about this project. 
ongoing0 exponents factored> 


Help
Repdigit Prime Problems find prime numbers of the form n * k, where k is a single
digit which can be repeated any number of times (for example, for n = 47
and k = 3, a possible repdigit prime might be 473333).
To participate in the project, use the primeform application (follow the directions on the project page for using primeform), and send email to the project coordinator to reserve a range to check and to submit results. 
ongoing 


Help
Mersenneplustwo Factorization factor numbers of the form 2^p+1.
To participate in the project, use one of the software clients listed on the project website. The project website does not contain details about how to use the clients or about how to reserve numbers and submit results. More information may be available in the project's discussion forum. Also see the project's wiki. 
ongoing 


Help
Sierpinski/Riesel Base 5 for the smallest base 5 Sierpinski and Riesel numbers. The project
does not have a website, only a discussion forum.
The project has found the following primes recently:
To participate in the project, use NewPGen to sieve and PRP to test, and follow these instructions. As of October 15, 2006, a Linux version of the LLRNet client is available from http://base5.greenbank.org/. See instructions for using this client. Note that the reservation list reached the 10,000 character limit on October 15, 2005, so participants should follow the links to the sieve files on the reservations page. 
ongoing 


Help
SZTAKI Desktop Grid find all generalized binary number systems up to dimension 11. The project website is written in Hungarian, but some of the text is also available in English. A detailed project description is available in English. The project completed its 10 dimensional project and began its 11 dimension project on August 2, 2005. The project will provide detailed information about the 10 dimension project results soon.
The project passed 1 TeraFLOPS/second of computing power on February 27, 2006. On September 12, 2006, the project began a new test project called SZTAKI Desktop Grid Research Facility (szdgr). This project will "improve the testing process of applications, thus improving userexperience (get rid of the credit problems, etc.) of SZTAKI Desktop Grid." The project uses a BOINCbased client. See the BOINC platform information for the latest version of the BOINC client. Version 2.01 of the project's NumSys Search client is available for Windows as of October 16, 2006. Version 2.03 is available for Linux as of August 1, 2006. Version 2.00 is available for Mac OSX as of July 5, 2006. Join a discussion forum about the project. 
163,931,407 credits 


PrimeGrid is a test project for PerlBOINC, a Perllanguagebased port of the
BOINC platform. The project's first
subproject was a cryptography project which attempted to
factor the number in the RSA Factoring Challenge.
Currently the project is running a subproject, Primegen, to generate a public
sequential prime number database, and is supporting a number of other
mathematics distributed comptuing projects.
On February 28, 2007, the project reported its 100th prime to the prime pages. On November 26, 2006, the project began working with Twin Internet Prime Search, and is supporting a second subproject to help that project. It completed its search on August 6, 2009, with the discovery of twin primes. On October 3, 2008, the project achieved "'optimal' sieve depth [in the Cullen/Woodall project] ...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. For more information, please see this forum post." On December 27, 2008, the project began a new subproject, AP26 Search, "an Arithmetic 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." On August 8, 2008, the project announced a "Dog Days of Summer Challenge." The threeday challenge ran from August 2224 and supported PrimeGrid's 321 Prime Search LLR application. See more information in a forum thread about the challenge. On September 6, 2008, the project announced a "Back to the Future Challenge." The 14day challenge ran from September 1327 and supported the Woodall Prime Search for the next record Woodall prime. During the challenge, "over 8,000 Woodall [work units] were completed by 204 teams and 1108 individuals." See more information in the challenge's forum thread. On January 24, 2009, the project announced a "Year of the Ox Challenge." The 5day challenge supported the project's 321 Prime Search (LLR) subproject. See more information in the challenge's forum thread. The project began its Tour de Primes 2009 contest on February 1, 2009. On February 14, 2009, the project announced a partnership with 12121 Search. On April 20, 2009, the project's Cullen Prime Search found a World Record Cullen Mega Prime: 6328548 * 2^{6328548} + 1 (1,905,090 digits). At that time this prime was the largest Cullen prime found and the largest Mega Prime found using LLR. On August 6, 2009, the project's Cullen Prime Search found its next World Record Cullen Mega Prime: 6679881 * 2^{6679881} + 1 (2,010,852 digits). The project uses a BOINCbased client. See the BOINC platform information for the latest version of the BOINC client. Version 5.13 of the project's Prime Generator client is available as of May 16, 2006. Version 5.04 of the project's LLR Prime Search client is available as of November 25, 2006. Join a discussion forum about this project. 
1,558,626,413 credits 


Help find Riesel primes, primes of the form k * 2^{n}  1, with k > 1, in the
Riesel Prime Search.
This project has three subprojects:
See the latest primes found by the project here and here. To participate, look for (or ask for) instructions in the project forums. Note: this project only has a discussion forum and no website. 
ongoing 


Help
Rectilinear Crossing Number
determine "the least number of crossings for a straightedge drawing of the
complete graph on top of a set of n points in a plane." See
more information about
the project. The project is currently focusing on n=18. The project website
is also available in Russian
and German.
On May 21, 2008 the project began releasing W7 work units. The project uses a BOINCbased client. See the BOINC platform information for the latest version of the BOINC client. Version 5.45 of the project's CAPE Crossing Number client is available for Linux as of August 3, 2006. Version 5.41 is available for Windows as of July 4, 2006. Version 5.49 of the project's TCAPE Crossing Number client is available for Linux and Windows as of August 5, 2006. Join a discussion forum about the project. 
8,222,202 credits 


Help
ABC@home find abc triples for the
ABC Conjecture,
"one of the greatest open problems in mathematics." "abc triples are positive
integers a,b,c such that a+b = c, a < b < c, a,b,c have no common
divisors and c > rad(abc), the socalled radical of abc. The ABC conjecture
says that there are only finitely many a,b,c such that log(c) / log(rad(abc))
> h for any real h > 1. ... If i[the conjecture] is proven to be true,
a lot of other open problems can be answered directly from it." The project
completed its first major goal in Janaury, 2009, and will restart in February,
2009, with a new, better algorithm and new work units.
The project uses a BOINCbased client. See the BOINC platform information for the latest version of the BOINC client. Version 1.00 of the project's ABC finder client is available for Windows and Linux as of January 13, 2007. Join a discussion forum about the project. 
101,152 credits 


Help the
WEPM+2 Project find
factors of Mersenneplustwo numbers. "Mersenneplustwo numbers are those
integers that are two more than a Mersenne prime. Mersenne primes are of the
form 2^p1 (see Mersenne Prime Search).
This makes Mersenneplustwo numbers of the form 2^p+1."
The project uses a BOINCbased client. See the BOINC platform information for the latest version of the BOINC client. Version 1.06 of the project's "Randombase WEP Factorization" client is available for Linux/x86 as of January 4, 2007. Version 1.07 of the client is available for Linux/AMD64 as of January 21, 2007. Version 1.04 of the client is available for Mac OSX as of December 5, 2006. Join a discussion forum about the project. 
unknown credits 


yoyo@home OGR is
a BOINCbased wrapper for
distributed.net's
OGR25 project.
The project uses a BOINCbased client. See the BOINC platform information for the latest version of the BOINC client. Version 1.08 of the project's Cruncher application is available for Windows as of September 2, 2007. Version 1.07 is available for Linux/X86 as of August 30, 2007. Version 1.08 is available for Linux/X8664 as of October 2, 2007. Version 1.07 is available for Mac OSX as of August 31, 2007. Version 1.08 is available for Solaris and FreeBSD as of September 30, 2007. Version 1.09 is available for PS3 as of September 30, 2007. Join a discussion forum about yoyo@home. 
70,543,602 credits for all yoyo@home projects 


Help TSP find
the shortest route between the 48 capital cities of the contiguous United
States of America. The project is solving this problem to study the
Traveling Salesman Problem,
an NPHard problem for
which there is no efficient general solution. The project is first "using
the brute force method to find an optimal solution to a 48 city TSP. Once the
optimal path(s) is/are known evaluation of other algorithms can begin. Future
algorithms include genetic algorithms, repetitive nearest neighbor, simulated
annealing and ant colony optimization." TSP is the first distributed
computing project to be developed and hosted in American Samoa.
See the best path discovered by the project today. The project uses a BOINCbased client. See the BOINC platform information for the latest version of the BOINC client. Version 2.15 of the project's TravelingSalesmanProblem application is available for Windows, Linux, Mac OSX and FreeBSD as of November 28, 2007. Join a discussion forum about this project. 
credits 


Help Wieferich@Home
find Wieferich primes. Only two Wieferich primes are known: 1093 and 3511.
See more information
about the project.
To participate in the project, download and run the project's software client. Version 2.0 of the client is available for Windows as of February 4, 2008. This version "accelerates searching in complete and periodical test. Software makes use of totally new algorithms, which are very efficient for mathematical method: exponentiation and congruency. New units for complete test are 10x larger and in periodical test 1.5x larger." Join a discussion forum about this project. 
0 Wieferich primes found 


Help No Prime Left Behind
find Riesel primes of the form k *
2^{n}  1 with odd k and 300 < k <= 1001 and n > 260,000,
and not reserved by others with highly presieved ranges.
To participate in the project, follow instructions in the project's Software/instructions/questions discussion thread. The project uses the LLR, NewPGen, Sr1sieve, Sr2sieve, Srfile, and Srsieve applications. Join a discussion forum about this project. 
ongoing 


Help k6465
find primes of the form 6465 * 2^{n}  1.
To participate in the project, send email to the project owner to reserve a range, then download NewPGen version 2.82 for presieveing and LLR version 3.71c for finding primes (you can download these applications from http://gbarnes017.googlepages.com/primebehindprogs.zip or from links listed in other projects above), then search for prime numbers within that range, then email the results to the project owner. 
ongoing 


Help Ramsey@Home find Ramsey numbers. "Ramsey theory, named for Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear. Problems in Ramsey theory typically ask a question of the form: how many elements of some structure must there be to guarantee that a particular property will hold?" The project uses a BOINCbased client. See the BOINC platform information for the latest version of the BOINC client. See the project's Applications page for information about the client applications and versions the project is using. Join a discussion forum about this project. 
78,842,929 credits 


Help NFS@Home complete the lattice sieving step of number field sieve factorizations of large integers. The project is currently working on Cunningham composites. The project uses a BOINCbased client. See the BOINC platform information for the latest version of the BOINC client. See the project's Applications page for information about the client applications and versions the project is using. Join a discussion forum about this project. 
unknown credits 

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