PrimeGrid

PrimeGrid
PrimeGrid logo
PrimeGrid screensaver displaying the 321 Prime Search application
Project
Status	Active
Category	Mathematics, Number theory
Compute	CPU & GPU
Development
Developer	Rytis Slatkevičius and the PrimeGrid community
Author	Rytis Slatkevičius
Maintainer	PrimeGrid administrators and volunteers
Initial release	June 12, 2005  (21 years ago)
Repository	https://www.primegrid.com/
Software
Written in	C, C++, Perl
Operating system	Windows, Linux, macOS, FreeBSD, Android
Size	Varies by application
BOINC statistics
Stats as of	May 22, 2026  (0 years ago)
Performance	3.2 PFLOPS
Active users	3,146
Total users	357,586
Active hosts	13,355
Total hosts	889,268
Metadata
Website	https://www.primegrid.com/
License	Mixed; mostly proprietary scientific applications with open-source components

BOINC project PrimeGrid is a volunteer computing project dedicated to the discovery of large prime numbers and the advancement of computational number theory. Running on the BOINC platform, it invites volunteers worldwide to donate spare CPU and GPU processing power to mathematical research that would be impossible on a single computer. As of mid-2026, the project sustains over 3.2 PFLOPS of combined computing power contributed by more than 357,000 registered volunteers.

History

Basic patterns of prime numbers. PrimeGrid's subprojects probe far beyond this range, searching numbers with millions of digits.

PrimeGrid was launched on 12 June 2005 at approximately 14:00 UTC under the original name Message@Home. The project was operated from founder Rytis Slatkevičius' personal laptop and initially served as a test bed for PerlBOINC, an effort to implement the BOINC server software in the Perl programming language to make BOINC infrastructure accessible on Microsoft Windows servers.

With PerlBOINC development as the primary focus, the team needed a short work unit with a consistent result. The project's first application, Message7, attempted by brute-force to recover a message encoded with the MD5 hashing algorithm. In August 2005, the RSA-640 Factoring Challenge application replaced Message7, and in November 2005 the project was renamed PrimeGrid following a short public naming contest.

In March 2006, the RSA factoring applications were set aside in favour of primegen, an application to build a sequential prime number database, bringing PrimeGrid into prime-finding territory for the first time. In June 2006, collaboration began with the Riesel Sieve project, which led to the implementation of the LLR (Lucas-Lehmer-Riesel) primality-testing application. In partnership with the Twin Prime Search (TPS) project, PrimeGrid officially launched the TPS LLR application in November 2006, and within two months a record twin prime was found.

The summer of 2007 saw further rapid expansion: Cullen and Woodall prime searches were launched, partnerships were established with the Prime Sierpinski Problem and 321 Prime Search projects, and two new sieves were added. In autumn 2007, PrimeGrid migrated many of its core systems from PerlBOINC to standard BOINC software, though several services continued to run on PerlBOINC for some time.

Subproject additions continued through the following years. The Seventeen or Bust collaboration for the Sierpinski problem was added in September 2010, and the Riesel Problem search followed in March 2010. The AP26 Search launched in December 2008 and achieved a landmark result in April 2010 (see Prime discoveries below).

Goals

The prime-counting function $\pi (n)$, which gives the number of primes up to $n$. PrimeGrid pushes this frontier by orders of magnitude, searching ranges with billions of digits.

PrimeGrid's central mission is to advance mathematics by enabling everyday computer users to contribute processing power toward prime-number discovery. As stated on the project's own website and wiki:

• Discover prime numbers of world-record size and enter them into The Largest Known Primes Database.
• Solve or advance longstanding mathematical conjectures and open problems, such as the Sierpinski and Riesel problems.
• Provide educational materials about prime numbers and number theory to the public.
• Demonstrate how much computation is required to crack cryptographic algorithms, contributing to understanding of cryptographic security.

Prime numbers underpin public-key cryptographic systems such as RSA encryption. Large-prime research helps mathematicians and computer scientists better understand computational limits and the security of modern cryptographic infrastructure.

Volunteers participate by downloading the BOINC client, attaching to the PrimeGrid project URL (https://www.primegrid.com/), and selecting one or more subprojects through the preferences page.

Methods

PrimeGrid operates multiple independent mathematical subprojects, each targeting a different class of prime numbers or unsolved problem in number theory. Broadly, these searches evaluate candidate integers for primality using a combination of sieving (to quickly eliminate composite numbers) and deterministic or probabilistic primality tests, chiefly:

• LLR (Lucas-Lehmer-Riesel) - for numbers of the form $k\cdot 2^n\pm 1$
• PRP (Probable Prime test) - a fast probabilistic filter before full verification
• PFGW (Prime Form / GW) - for generalized forms not covered by LLR
• Genefer - specialized for Generalized Fermat numbers

CPUs with Advanced Vector Extensions (AVX) and Fused Multiply-Add (FMA) instruction sets yield the fastest results for non-GPU work.

Subprojects

PrimeGrid has operated more than twenty distinct BOINC subprojects since its founding. The following are current and notable historical subprojects:

321 Prime Search

A continuation of Paul Underwood's 321 Search, this project looks for primes of the form:

$3\cdot 2^n\pm 1$

PrimeGrid added the +1 form and searches to $n=25,000,000$. The search has yielded many large primes linked to OEIS sequences A002253 and A002254.

Cullen Prime Search

Searches for Cullen primes, numbers of the form:

$n\cdot 2^n+1$

first studied by Reverend James Cullen in 1905. PrimeGrid holds the record for the largest known Cullen prime: $6,679,881\times 2^{6,679,881}+1$.

Woodall Prime Search

Searches for Woodall primes, numbers of the form:

$n\cdot 2^n-1$

first studied by Allan Cunningham and H. J. Woodall in 1917. PrimeGrid has found four of the largest known Woodall primes, including $17,016,602\times 2^{17,016,602}-1$.

Generalized Cullen/Woodall Prime Search

Searches for generalized Cullen and Woodall primes of the form:

$n\cdot b^n+1\text{and}n\cdot b^n-1$

where $n+2>b$. This subproject moved from PRPNet to BOINC in September 2016. PrimeGrid holds the record for the largest known Generalized Cullen prime: $2,525,532\times 73^{2,525,532}+1$.

Generalized Fermat Prime Search

Searches for Generalized Fermat primes of the form:

$b^{2^n}+1$

Active levels include $n=65,536$, $131,072$, $262,144$, $524,288$, and $1,048,576$. The current record generalized Fermat prime found by PrimeGrid is $19637361^{1,048,576}+1$.

Prime Sierpinski Problem

Attempts to solve the Sierpinski problem by finding primes of the form $k\cdot 2^n+1$ for remaining candidate values of $k$. A notable discovery was $168,451\times 2^{19,375,200}+1$.

Seventeen or Bust

Joined by PrimeGrid in September 2010, this subproject targets the remaining unresolved values of $k$ from the original Seventeen or Bust project, aiming to prove no primes of the form $k\cdot 2^n+1$ exist for those values.

The Riesel Problem

Searches for values of $k$ such that $k\cdot 2^n-1$ is always composite for all positive integers $n$, aiming to resolve the Riesel conjecture. Work on this problem began at PrimeGrid in March 2010.

Extended Sierpinski Problem

A broader extension of the classical Sierpinski problem. A major discovery was $202,705\times 2^{21,320,516}+1$, the largest prime found within this subproject.

Proth Prime Search

Searches for Proth primes of the form:

$k\cdot 2^n+1$

for small odd $k$. A Proth prime sieving subproject has been running since September 2008.

AP26 and AP27 Searches

Searches for long arithmetic progressions of prime numbers, sequences of the form $p+d\cdot n$ yielding primes for 26 or 27 consecutive values of $n$.

Twin Prime Search

Searches for twin primes, pairs of the form $p$ and $p+2$. This was one of PrimeGrid's earliest active searches, launched in November 2006. The Twin Prime Search has since been completed.

Sophie Germain Prime Search

Searched for primes $p$ such that $2p+1$ is also prime. This subproject was suspended in 2024.

Wieferich and Wall-Sun-Sun Prime Search

Ran from 2020 to December 2022, searching for rare primes connected to Fermat's Last Theorem and Fibonacci sequences via modular arithmetic conditions.

Fermat Divisor Search

Searched for large prime divisors of Fermat numbers. Completed in April 2021.

Software and hardware support

PrimeGrid screensaver showing the 321 Prime Search application.

PrimeGrid supports both CPU and GPU computation across a wide range of operating systems:

• Microsoft Windows
• Linux
• macOS
• Android
• FreeBSD

GPU applications support NVIDIA CUDA, OpenCL, and Apple Silicon GPUs for selected subprojects. PrimeGrid also provides ARM-compatible applications for certain Windows-on-ARM systems as of 2025.

For LLR-based subprojects, CPUs equipped with Advanced Vector Extensions (AVX) and Fused Multiply-Add (FMA) instruction sets achieve the best performance on non-GPU workloads.

Prime discoveries

PrimeGrid participants have discovered thousands of large primes, including many megaprimes (primes with more than one million decimal digits). The project regularly reports discoveries to The Largest Known Primes Database (Top5000), operated by the Prime Pages.

As of mid-2026, PrimeGrid had reported more than 38,000 primes to the Top5000 database and discovered more than 3,600 megaprimes. PrimeGrid has also directly discovered six megaprimes, three Fermat Number divisors, and more than 4,000 titanic primes (primes with more than 1,000 decimal digits).

Arithmetic progression records

One of PrimeGrid's most celebrated areas of research is the search for long arithmetic progressions of primes. On 12 April 2010, participant Benoît Perichon using PrimeGrid's AP26 Search program (adapted from Jarosław Wróblewski's algorithm for BOINC) discovered the first ever known arithmetic progression of 26 primes (AP26):

$43,142,746,595,714,191+23,681,770\times 23\mathrm{\#}\times n(n=0,\dots ,25)$

where $23\mathrm{\#}=223,092,870$ is the 23rd primorial. This discovery was verified using PrimeForm/GW (PFGW) software.

On 23 September 2019, participant Rob Gahan discovered the first ever known arithmetic progression of 27 primes (AP27), using a GPU-accelerated task during a PrimeGrid challenge event:

$224,584,605,939,537,911+81,292,139\times 23\mathrm{\#}\times n(n=0,\dots ,26)$

This 18-digit-base sequence simultaneously qualifies as the largest known AP24, AP25, and AP26, and no longer arithmetic progression of primes has been discovered since.

Twin prime records

In August 2009, PrimeGrid and the Twin Prime Search project announced a world-record twin prime pair: $65,516,468,355\times 2^{333,333}\pm 1$, each containing 100,355 decimal digits.

On 25 December 2011, PrimeGrid participant Timothy D. Winslow discovered the then world's largest known twin prime pair: $3,756,801,695,685\times 2^{666,669}\pm 1$. As of early 2024, the record stands at $2,996,863,034,895\times 2^{1,290,000}\pm 1$, with 388,342 decimal digits, found on 14 September 2016.

Record Cullen and Woodall primes

PrimeGrid holds the record for the largest known Cullen prime ($6,679,881\times 2^{6,679,881}+1$), the largest known Woodall prime ($17,016,602\times 2^{17,016,602}-1$), the largest known Generalized Cullen prime, and the fourth-largest known Generalized Woodall prime.

Published result datasets

PrimeGrid makes raw sieving data from several searches available as torrents:

Twin Prime Search, n=195,000

Raw data from the Twin Prime Search project for $n=195,000$. Compressed size: 20.9 MiB.

Download torrent

Twin Prime Search, n=333,333

Raw data from the Twin Prime Search project for $n=333,333$. Compressed size: 607 MiB.

Download torrent

Infrastructure

PrimeGrid uses the BOINC infrastructure combined with several additional computational tools:

• LLR (Lucas-Lehmer-Riesel) - primality testing for Riesel and Proth numbers
• PRPNet - client for manual and semi-manual prime searches
• Genefer - specialized application for Generalized Fermat prime candidates
• PFGW (PrimeForm/GW) - verification of generalized prime forms

The project distributes work units to volunteer computers, validates returned computations through redundant checking, and maintains statistical rankings for individual users, teams, and hardware configurations.

According to the PrimeGrid server status page, the project operates at more than 3 PFLOPS of combined computing power, with hundreds of thousands of registered users contributing across nearly 900,000 registered hosts.

Community

PrimeGrid maintains an active international volunteer community. Participants communicate through the project's own forums, a Discord server, and external mathematical discussion boards such as the Mersenne Forum.

The project hosts a Challenge Series: periodic competitive events where participants race to generate the highest volume of computational credit within a defined time window. The Challenge Series was established in March 2008 and has run continuously since.

PrimeGrid awards badges to participants who reach defined credit thresholds. While the badges carry no monetary value, they are a popular motivational feature within the community.

PrimeGrid is frequently cited within the BOINC community as one of the most reliable projects due to its consistent availability of work units across multiple subprojects and its broad hardware support.

Scientific publications

1. 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.

1. 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.

1. Bethune, Iain and Michael Goetz. Extending the Generalized Fermat Prime Number Search Beyond One Million Digits Using GPUs. Parallel Processing and Applied Mathematics (2014). DOI: 10.1007/978-3-642-55224-3_11.

1. Anderson, David P. BOINC: A System for Public-Resource Computing and Storage. Proceedings of the Fifth IEEE/ACM International Workshop on Grid Computing (2004).

See also

• BOINC
• Volunteer computing
• Prime number
• Megaprime
• Sierpinski number
• Riesel number
• Twin prime
• Cullen number
• Woodall number
• Primes in arithmetic progression

External links

• Official website
• PrimeGrid forums
• Published results
• Challenge Series
• PrimeGrid Wiki
• The Largest Known Primes Database
• BOINC GitHub repository