PrimeGrid
[[File:{{#setmainimage:Primegrid.jpg}}|alt=PrimeGrid logo|center|frameless]]
BOINC project PrimeGrid is a volunteer computing project focused on the discovery of large prime numbers and the advancement of computational number theory. The project operates on the BOINC platform and allows volunteers worldwide to donate unused CPU and GPU processing power to mathematical research.[1][2]
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.[3]
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.[4]
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.[1]
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.[5]
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.[1]
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.[6]
Methods
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>
or
<math>b^{2^n} + 1</math>
where integer values are tested for primality using probabilistic and deterministic algorithms including LLR, PRP, and sieving methods.
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 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.[7]
- 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.[8]
Software and hardware support
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.[9]
PrimeGrid also provides ARM-compatible applications for certain Windows-on-ARM systems.[10]
Scientific results
PrimeGrid has discovered thousands of large prime numbers, including many megaprimes containing more than one million decimal digits.[11]
The project maintains public databases of discoveries and published results.[12]
Twin Prime Search, n=195000
Contains raw data from the Twin Prime Search project for <math>n = 195000</math>. Compressed size: 20.9 MiB.
Twin Prime Search, n=333333
Contains raw data from the Twin Prime Search project for <math>n = 333333</math>. Compressed size: 607 MiB.
Prime discoveries
PrimeGrid participants have discovered many record-setting primes and megaprimes. The project regularly reports discoveries to The Largest Known Primes Database (Top5000).[13]
As of 2026, PrimeGrid had reported more than 38,000 primes to the Top5000 database and discovered more than 3,600 megaprimes.[2]
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.[1]
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.[2]
Community
PrimeGrid maintains an active international volunteer community through forums, Discord, and external mathematical discussion boards.[14]
The project also hosts periodic computational challenges where participants compete to generate the highest amount of computational credit during specific time windows.[15]
PrimeGrid is frequently recommended within the BOINC community due to its consistent availability of work units and broad hardware support.[16]
Scientific publications
- 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.[17]
- 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.[18]
- Bethune, Iain and Michael Goetz. Extending the Generalized Fermat Prime Number Search Beyond One Million Digits Using GPUs. Parallel Processing and Applied Mathematics (2014).[19]
- Anderson, David P. BOINC: A System for Public-Resource Computing and Storage. Proceedings of the Fifth IEEE/ACM International Workshop on Grid Computing (2004).[20]
See also
External links
References
- ↑ 1.0 1.1 1.2 1.3 PrimeGrid. Wikipedia.
- ↑ 2.0 2.1 2.2 PrimeGrid Server Status. PrimeGrid.
- ↑ History of PrimeGrid. PrimeGrid Wiki.
- ↑ History of PrimeGrid. PrimeGrid Wiki.
- ↑ PrimeGrid. PrimeGrid.
- ↑ PrimeGrid. PrimeGrid.
- ↑ Primes in arithmetic progression. Wikipedia.
- ↑ PrimeGrid project preferences. PrimeGrid.
- ↑ PrimeGrid Applications. PrimeGrid.
- ↑ Official PrimeGrid News - Windows/ARM support for GFN apps. Reddit.
- ↑ PrimeGrid. PrimeGrid.
- ↑ PrimeGrid Published Results. PrimeGrid.
- ↑ The Largest Known Primes Database. Prime Pages.
- ↑ PrimeGrid Forums. PrimeGrid.
- ↑ PrimeGrid Challenge Series. PrimeGrid.
- ↑ Rosetta, DENIS, GPUGRID, RNA World no tasks?. Reddit.
- ↑ PrimeGrid: a Volunteer Computing Platform for Number Theory.
- ↑ Genefer: Programs for Finding Large Probable Generalized Fermat Primes.
- ↑ Extending the Generalized Fermat Prime Number Search Beyond One Million Digits Using GPUs.
- ↑ BOINC publications. BOINC.