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[[File:{{#setmainimage:Primegrid.jpg}}|alt=example image|center|frameless]]
{{Infobox software
| name                = PrimeGrid
| logo                = Primegrid.jpg
| logo caption        = PrimeGrid logo
| screenshot          = Primegrid.gif
| caption              = PrimeGrid screensaver displaying the 321 Prime Search application


BOINC project [https://www.primegrid.com/ '''''PrimeGrid'''''] is a '''''[[wikipedia:Volunteer computing|volunteer computing]]''''' project that needs your help to advance mathematics.[[File:Primegrid.gif|alt=PrimeGrid Screensaver - 321 Prime Search v5.09 - 2008 |thumb|<small>PrimeGrid Screensaver - 321 Prime Search v5.09 - 2008</small>]]
| status              = Active
== Why PrimeGrid? ==
| category            = Mathematics, Number theory
On 12 June 2005, at approximately 14:00 UTC, Message@Home (now PrimeGrid) opened account creation to 50 users. It was being run on Rytis’ home laptop and was developed as a test project for PerlBOINC, an effort to implement the BOINC server system in the Perl programming language in order to bring BOINC server software to Windows.
| compute              = CPU & GPU
| dependencies        =  


The first project was Message7, and it attempted by “brute-force” to recover a message encoded with the md5 algorithm. In August, the RSA 640 Factoring Challenge application replaced the Message7 application and in November the project was renamed PrimeGrid after a short public contest.[https://primegrid.fandom.com/wiki/History_of_PrimeGrid]
| developer            = Rytis Slatkevičius and the PrimeGrid community
| author              = Rytis Slatkevičius
| maintainer          = PrimeGrid administrators and volunteers
| released            = {{Start date and age|2005|06|12}}
| repository          = https://www.primegrid.com/


== Goal ==
| programming language = C, C++, Perl
PrimeGrid's primary goal is to advance mathematics by enabling everyday computer users to contribute their system's processing power towards prime finding. By simply downloading and installing BOINC and attaching to the PrimeGrid project, participants can choose from a variety of prime forms to search. With a little patience, you may find a large or even record breaking prime and enter into Chris Caldwell's The Largest Known Primes Database with a multi-million digit prime!
| operating system     = Windows, Linux, macOS, FreeBSD, Android
| size                = Varies by application


PrimeGrid's secondary goal is to provide relevant educational materials about primes. Additionally, we wish to contribute to the field of mathematics.
| stats as of         = {{Start date and age|2026|05|22}}
| average performance  = 3.2 PFLOPS
| active users        = 3146
| total users          = 357586
| active hosts        = 13355
| total hosts          = 889268


Lastly, primes play a central role in the cryptographic systems which are used for computer security. Through the study of prime numbers it can be shown how much processing is required to crack an encryption code and thus to determine whether current security schemes are sufficiently secure.
| website              = {{URL|https://www.primegrid.com/}}
| license              = Mixed; mostly proprietary scientific applications with open-source components
}}
 
[[File:{{#setmainimage:Primegrid.jpg}}|alt=PrimeGrid logo|center|frameless]]
 
BOINC project [https://www.primegrid.com/ '''''PrimeGrid'''''] is a '''[[wikipedia:Volunteer computing|volunteer computing]]''' project focused on the discovery of large [[wikipedia:Prime number|prime numbers]] and the advancement of computational [[wikipedia:Number theory|number theory]]. The project operates on the [[wikipedia:Berkeley Open Infrastructure for Network Computing|BOINC]] platform and allows volunteers worldwide to donate unused CPU and GPU processing power to mathematical research.<ref name="wiki">{{cite web |url=https://en.wikipedia.org/wiki/PrimeGrid |title=PrimeGrid |website=Wikipedia}}</ref><ref name="status">{{cite web |url=https://www.primegrid.com/server_status.php |title=PrimeGrid Server Status |website=PrimeGrid}}</ref>
 
== History ==
PrimeGrid began on 12 June 2005 under the name '''Message@Home'''. The original project was operated from founder Rytis Slatkevičius' personal laptop and initially served as a test platform for '''PerlBOINC''', an effort to implement BOINC server software in the Perl programming language to improve compatibility with Microsoft Windows systems.<ref>{{cite web |url=https://primegrid.fandom.com/wiki/History_of_PrimeGrid |title=History of PrimeGrid |website=PrimeGrid Wiki}}</ref>
 
The project's first application, '''Message7''', attempted to recover a message encoded with the MD5 hashing algorithm through brute-force search methods. In August 2005 the RSA-640 factoring challenge replaced the Message7 project, and later that year the community voted to rename the project to '''PrimeGrid'''.<ref>{{cite web |url=https://primegrid.fandom.com/wiki/History_of_PrimeGrid |title=History of PrimeGrid |website=PrimeGrid Wiki}}</ref>
 
PrimeGrid subsequently evolved into one of the largest distributed computing projects dedicated exclusively to prime number research. The project has discovered thousands of large prime numbers, including numerous world-record and megaprime discoveries.<ref name="wiki" />
 
== Goals ==
PrimeGrid's primary objective is to advance mathematical research through large-scale distributed searches for prime numbers of special forms. Volunteers install the BOINC client and select one or more PrimeGrid subprojects to process mathematical workloads on their computers.<ref>{{cite web |url=https://www.primegrid.com/ |title=PrimeGrid |website=PrimeGrid}}</ref>
 
The project also seeks to:
 
* Solve longstanding mathematical conjectures and open problems.
* Discover record-setting and megaprime numbers.
* Provide educational information about prime numbers and number theory.
* Demonstrate the computational complexity involved in modern cryptographic systems.<ref name="wiki" />
 
Prime numbers play an important role in public-key cryptography systems such as RSA encryption. Research into large primes helps mathematicians and computer scientists better understand computational limits and cryptographic security.<ref>{{cite web |url=https://www.primegrid.com/ |title=PrimeGrid |website=PrimeGrid}}</ref>


== Methods ==
== Methods ==
PrimeGrid is currently running several sub-projects:
PrimeGrid operates multiple independent mathematical subprojects, each targeting a different class of prime numbers or unsolved problem in number theory.
 
Many PrimeGrid searches involve evaluating expressions such as:
 
<math>k \cdot 2^n + 1</math>


* 321 Prime Search: searching for [http://en.wikipedia.org/wiki/Mega_prime '''''megaprimes'''''] of the form 3·2<sup>n</sup>±1.
or
* Cullen-Woodall Search: searching for megaprimes of forms n·2<sup>n</sup>+1 and n·2<sup>n</sup>−1.
* Generalized Cullen-Woodall Search: searching for megaprimes of forms n·b<sup>n</sup>+1 and n·b<sup>n</sup>−1 where n + 2 > b.
* Extended Sierpinski Problem: helping solve the '''''[https://www.primegrid.com/forum_thread.php?id=5758 Extended Sierpinski Problem]'''''.
* Generalized Fermat Prime Search: searching for megaprimes of the form <math>b^{2^{n}}</math>+1.
* Prime Sierpinski Project: helping the Prime Sierpinski Project solve the '''''[https://www.primegrid.com/forum_thread.php?id=972 Prime Sierpinski Problem]'''''.
* Proth Prime Search: searching for primes of the form k·2<sup>n</sup>+1.
* Seventeen or Bust: helping to solve the '''''[https://www.primegrid.com/forum_thread.php?id=1647&nowrap=true#20691 Sierpinski Problem]'''''.
* Sierpinski/Riesel Base 5: helping to solve the '''''[https://www.primegrid.com/forum_thread.php?id=5087 Sierpinski/Riesel Base 5 Problem]'''''.
* The Riesel problem: helping to solve the '''''[https://www.primegrid.com/forum_thread.php?id=1731&nowrap=true#21625 Riesel Problem]'''''.
* AP27 Search: searching for record length '''''[http://en.wikipedia.org/wiki/Primes_in_arithmetic_progression arithmetic progressions of primes]'''''.


You can choose the projects you would like to run by going to the [https://www.primegrid.com/prefs.php?subset=project '''''project preferences'''''] page.
<math>b^{2^n} + 1</math>


== Project team / Sponsors ==
where integer values are tested for primality using probabilistic and deterministic algorithms including LLR, PRP, and sieving methods.
Rytis Slatkevičius and the [https://www.primegrid.com/contact.php '''''PrimeGrid community'''''].
 
=== Current and historical subprojects ===
 
* '''321 Prime Search''' — Searches for primes of the form:
:<math>3 \cdot 2^n \pm 1</math>
 
* '''Cullen Prime Search''' — Searches for Cullen primes:
:<math>n \cdot 2^n + 1</math>
 
* '''Woodall Prime Search''' — Searches for Woodall primes:
:<math>n \cdot 2^n - 1</math>
 
* '''Generalized Cullen/Woodall Prime Search''' — Searches for generalized forms:
:<math>n \cdot b^n \pm 1</math>
 
* '''Generalized Fermat Prime Search''' — Searches for generalized Fermat primes:
:<math>b^{2^n} + 1</math>
 
* '''Prime Sierpinski Project''' — Attempts to solve the [[wikipedia:Sierpiński problem|Sierpiński problem]].
 
* '''Seventeen or Bust''' — Searches for a proof related to the Sierpiński problem by eliminating remaining candidate values of <math>k</math>.
 
* '''The Riesel Problem''' — Searches for values proving numbers of the form:
:<math>k \cdot 2^n - 1</math>
are always composite.
 
* '''Extended Sierpinski Problem''' — A broader extension of the classical Sierpiński problem.
 
* '''Proth Prime Search''' — Searches for Proth primes:
:<math>k \cdot 2^n + 1</math>
 
* '''AP27 Search''' — Searches for long arithmetic progressions of prime numbers.<ref>{{cite web |url=https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression |title=Primes in arithmetic progression |website=Wikipedia}}</ref>
 
* '''Twin Prime Search''' — Searches for twin primes of the form:
:<math>p</math> and <math>p+2</math>
 
* '''Wieferich and Wall-Sun-Sun Search''' — Searches for rare special classes of primes connected to modular arithmetic and Fibonacci sequences.
 
Users may select preferred subprojects through the PrimeGrid preferences page.<ref>{{cite web |url=https://www.primegrid.com/prefs.php?subset=project |title=PrimeGrid project preferences |website=PrimeGrid}}</ref>
 
== Software and hardware support ==
[[File:Primegrid.gif|alt=PrimeGrid Screensaver - 321 Prime Search v5.09 - 2008|thumb|PrimeGrid screensaver showing the 321 Prime Search application.]]PrimeGrid supports both CPU and GPU computation. Applications are available for:
 
* Microsoft Windows
* Linux
* macOS
* Android
* FreeBSD
 
GPU applications support NVIDIA CUDA, OpenCL, and Apple Silicon GPUs for selected subprojects.<ref>{{cite web |url=https://www.primegrid.com/apps.php |title=PrimeGrid Applications |website=PrimeGrid}}</ref>
 
PrimeGrid also provides ARM-compatible applications for certain Windows-on-ARM systems.<ref>{{cite web |url=https://www.reddit.com/r/BOINC/comments/1t0nk3m/official_primegrid_news_windowsarm_suppport_for/ |title=Official PrimeGrid News - Windows/ARM support for GFN apps |website=Reddit}}</ref>


== Scientific results ==
== Scientific results ==
* [https://www.primegrid.com/pubresults.php '''''Published results''''']
PrimeGrid has discovered thousands of large prime numbers, including many megaprimes containing more than one million decimal digits.<ref>{{cite web |url=https://www.primegrid.com/ |title=PrimeGrid |website=PrimeGrid}}</ref>
 
The project maintains public databases of discoveries and published results.<ref>{{cite web |url=https://www.primegrid.com/pubresults.php |title=PrimeGrid Published Results |website=PrimeGrid}}</ref>
 
=== Twin Prime Search, n=195000 ===
Contains raw data from the Twin Prime Search project for <math>n = 195000</math>. Compressed size: 20.9 MiB.
 
* [https://www.primegrid.com/download/torrent/TPS_195000.torrent Download torrent]
 
=== Twin Prime Search, n=333333 ===
Contains raw data from the Twin Prime Search project for <math>n = 333333</math>. Compressed size: 607 MiB.
 
* [https://www.primegrid.com/download/torrent/TPS_333333.torrent Download torrent]
 
== Prime discoveries ==
PrimeGrid participants have discovered many record-setting primes and megaprimes. The project regularly reports discoveries to [[wikipedia:The Largest Known Primes Database|The Largest Known Primes Database]] (Top5000).<ref>{{cite web |url=https://t5k.org/ |title=The Largest Known Primes Database |website=Prime Pages}}</ref>
 
As of 2026, PrimeGrid had reported more than 38,000 primes to the Top5000 database and discovered more than 3,600 megaprimes.<ref name="status" />
 
== Infrastructure ==
PrimeGrid uses the BOINC infrastructure combined with additional custom applications including:
 
* LLR (Lucas-Lehmer-Riesel)
* PRPNet
* Genefer
* PFGW
 
The project distributes work units to volunteer computers, validates returned computations, and maintains statistical rankings for users, teams, and hardware.<ref name="wiki" />
 
According to the PrimeGrid server status page, the project operates at more than 3 PFLOPS of computing power with hundreds of thousands of registered users and hosts.<ref name="status" />


==== Twin Prime Search, n=195000 ====
== Community ==
Contains raw data from Twin Prime Search, n=195000 project. Compressed size - 20.9MiB. '''''[https://www.primegrid.com/download/torrent/TPS_195000.torrent Download .torrent file]'''''
PrimeGrid maintains an active international volunteer community through forums, Discord, and external mathematical discussion boards.<ref>{{cite web |url=https://www.primegrid.com/forum_index.php |title=PrimeGrid Forums |website=PrimeGrid}}</ref>


==== Twin Prime Search, n=333333 ====
The project also hosts periodic computational challenges where participants compete to generate the highest amount of computational credit during specific time windows.<ref>{{cite web |url=https://www.primegrid.com/challenge/ |title=PrimeGrid Challenge Series |website=PrimeGrid}}</ref>
Contains raw data from Twin Prime Search, n=333333 project. Compressed size - 607MiB. '''''[https://www.primegrid.com/download/torrent/TPS_333333.torrent Download .torrent file]'''''
 
PrimeGrid is frequently recommended within the BOINC community due to its consistent availability of work units and broad hardware support.<ref>{{cite web |url=https://www.reddit.com/r/BOINC/comments/1qkoq90/rosetta_denis_gpugrid_rna_world_no_tasks/ |title=Rosetta, DENIS, GPUGRID, RNA World no tasks? |website=Reddit}}</ref>


== Scientific publications ==
== Scientific publications ==


# Bethune, Iain. [https://www.dropbox.com/s/6lmn8c7ujnj1cng/CMCGS_2015_Proceedings_Paper_20.pdf?dl=0 PrimeGrid: a Volunteer Computing Platform for Number Theory]. Annual International Conference on Computational Mathematics, Computational Geometry & Statistics (2015). DOI: 10.5176/2251-1911_CMCGS15.43.
# Bethune, Iain. ''PrimeGrid: a Volunteer Computing Platform for Number Theory''. Annual International Conference on Computational Mathematics, Computational Geometry & Statistics (2015). DOI: 10.5176/2251-1911_CMCGS15.43.<ref>{{cite web |url=https://www.dropbox.com/s/6lmn8c7ujnj1cng/CMCGS_2015_Proceedings_Paper_20.pdf?dl=0 |title=PrimeGrid: a Volunteer Computing Platform for Number Theory}}</ref>
# Bethune, Iain Arthur and Yves Gallot. Genefer: [https://openresearchsoftware.metajnl.com/article/10.5334/jors.ca/ Programs for Finding Large Probable Generalized Fermat Primes]. Journal of Open Research Software (2015). DOI: 10.5334/jors.ca.
 
# Bethune, Iain and Michael Goetz. [http://link.springer.com/10.1007/978-3-642-55224-3_11 Extending the Generalized Fermat Prime Number Search Beyond One Million Digits Using GPUs]. Parallel Processing and Applied Mathematics (2014).
# Bethune, Iain Arthur and Yves Gallot. ''Genefer: Programs for Finding Large Probable Generalized Fermat Primes''. Journal of Open Research Software (2015). DOI: 10.5334/jors.ca.<ref>{{cite web |url=https://openresearchsoftware.metajnl.com/article/10.5334/jors.ca/ |title=Genefer: Programs for Finding Large Probable Generalized Fermat Primes}}</ref>
 
# Bethune, Iain and Michael Goetz. ''Extending the Generalized Fermat Prime Number Search Beyond One Million Digits Using GPUs''. Parallel Processing and Applied Mathematics (2014).<ref>{{cite web |url=http://link.springer.com/10.1007/978-3-642-55224-3_11 |title=Extending the Generalized Fermat Prime Number Search Beyond One Million Digits Using GPUs}}</ref>
 
# Anderson, David P. ''BOINC: A System for Public-Resource Computing and Storage''. Proceedings of the Fifth IEEE/ACM International Workshop on Grid Computing (2004).<ref>{{cite web |url=https://boinc.berkeley.edu/pubs.php |title=BOINC publications |website=BOINC}}</ref>
 
== See also ==
* [[wikipedia:BOINC|BOINC]]
* [[wikipedia:Distributed computing|Distributed computing]]
* [[wikipedia:Prime number|Prime number]]
* [[wikipedia:Megaprime|Megaprime]]
* [[wikipedia:Sierpiński number|Sierpiński number]]
* [[wikipedia:Riesel number|Riesel number]]
 
== External links ==
* [https://www.primegrid.com/ Official website]
* [https://www.primegrid.com/forum_index.php PrimeGrid forums]
* [https://www.primegrid.com/pubresults.php Published results]
* [https://primegrid.fandom.com/wiki/PrimeGrid_Wiki PrimeGrid Wiki]
* [https://github.com/BOINC/boinc BOINC GitHub repository]
 
== References ==
{{Reflist}}
 
[[Category:BOINC]]
[[Category:Distributed computing projects]]
[[Category:Number theory]]
[[Category:Prime numbers]]
[[Category:Volunteer computing projects]]
[[Category:2005 software]]
Retrieved from "https://boincsynergy.ca/wiki/PrimeGrid"