PrimeGrid is a volunteer computing project that searches for very large (up to world-record size) prime numbers whilst also aiming to solve long-standing mathematical conjectures. It uses the Berkeley Open Infrastructure for Network Computing (BOINC) platform. PrimeGrid offers a number of subprojects for prime-number sieving and discovery. Some of these are available through the BOINC client, others through the PRPNet client. Some of the work is manual, i.e. it requires manually starting work units and uploading results. Different subprojects may run on different operating systems, and may have executables for CPUs, GPUs, or both; while running the Lucas–Lehmer–Riesel test, CPUs with Advanced Vector Extensions and Fused Multiply-Add instruction sets will yield the fastest results for non-GPU accelerated workloads.

PrimeGrid awards badges to users in recognition of achieving certain defined levels of credit for work done. The badges have no intrinsic value but are valued by many as a sign of achievement. The issuing of badges should also benefit PrimeGrid by evening out the participation in the less popular sub projects. The easiest of the badges can often be obtained in less than a day by a single computer, whereas the most challenging badges will require far more time and computing power.

This section needs to be updated. (March 2023)

PrimeGrid started in June 2005^[1] under the name Message@home and tried to decipher text fragments hashed with MD5. Message@home was a test to port the BOINC scheduler to Perl to obtain greater portability. After a while the project attempted the RSA factoring challenge trying to factor RSA-640. After RSA-640 was factored by an outside team in November 2005, the project moved on to RSA-768. With the chance to succeed too small, it discarded the RSA challenges, was renamed to PrimeGrid, and started generating a list of the first prime numbers. At 210,000,000,000^[5] the primegen subproject was stopped.

In June 2006, dialog started with Riesel Sieve to bring their project to the BOINC community. PrimeGrid provided PerlBOINC support and Riesel Sieve was successful in implementing their sieve as well as a prime finding (LLR) application. With collaboration from Riesel Sieve, PrimeGrid was able to implement the LLR application in partnership with another prime finding project, Twin Prime Search (TPS). In November 2006, the TPS LLR application was officially released at PrimeGrid. Less than two months later, January 2007, the record twin was found by the original manual project. TPS has since been completed, while the search for Sophie Germain primes continues.

In the summer of 2007, the Cullen and Woodall prime searches were launched. In the Fall, more prime searches were added through partnerships with the Prime Sierpinski Problem and 3*2^n-1 Search projects. Additionally, two sieves were added: the Prime Sierpinski Problem combined sieve which includes supporting the Seventeen or Bust sieve and the combined Cullen/Woodall sieve. In the fall of the same year, PrimeGrid migrated its systems from PerlBOINC to standard BOINC software.

Since September 2008, PrimeGrid is also running a Proth prime sieving subproject.^[6]

In January 2010 the subproject Seventeen or Bust (for solving the Sierpinski problem) was added.^[7] The calculations for the Riesel problem followed in March 2010.

As of January 2023^[update], PrimeGrid is working on or has worked on the following projects:

PrimeGrid's author Rytis Slatkevičius has been featured as a young entrepreneur in The Economist.^[46]

PrimeGrid has also been featured in an article by Francois Grey in the CERN Courier and a talk about citizen cyberscience in TEDx Warwick conference.^[47][48]

In the first Citizen Cyberscience Summit, Rytis Slatkevičius gave a talk as a founder of PrimeGrid, named Finding primes: from digits to digital technology,^[49] relating mathematics and volunteering and featuring the history of the project.^[50]