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<title>PrimeGrid</title>

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PrimeGrid

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</style><table class="infobox vevent"><caption class="infobox-title summary">PrimeGrid</caption><tbody><tr><td colspan="2" class="infobox-image"></td></tr><tr><td colspan="2" class="infobox-image"><div class="infobox-caption">PrimeGrid screensaver</div></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap"><a href="Software_design" title="Software design">Original author(s)</a></th><td class="infobox-data">Rytis Slatkevičius</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Initial release</th><td class="infobox-data">June 12, 2005 (2005-06-12)<a href="#cite_note-race08-1">[1]</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Development status</th><td class="infobox-data">Active</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Project goal(s)</th><td class="infobox-data">Finding prime numbers of various types</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Software used</th><td class="infobox-data">PRPNet, Genefer, LLR, PFGW</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Funding</th><td class="infobox-data">Corporate sponsorship, crowdfunding<a href="#cite_note-2">[2]</a><a href="#cite_note-3">[3]</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap"><a href="Computing_platform" title="Computing platform">Platform</a></th><td class="infobox-data"><a href="BOINC" class="mw-redirect" title="BOINC">BOINC</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Average performance</th><td class="infobox-data">3,398.914 <a href="FLOPS" class="mw-redirect" title="FLOPS">TFLOPS</a><a href="#cite_note-boincstats-4">[4]</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Active users</th><td class="infobox-data">2,330 (August 2022)<a href="#cite_note-boincstats-4">[4]</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Total users</th><td class="infobox-data">353,245 <a href="#cite_note-boincstats-4">[4]</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Active hosts</th><td class="infobox-data">11,504 (August 2022)<a href="#cite_note-boincstats-4">[4]</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Total hosts</th><td class="infobox-data">21,985 <a href="#cite_note-boincstats-4">[4]</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap">Website</th><td class="infobox-data"><a rel="nofollow" class="external text" href="https://www.primegrid.com/">www.primegrid.com</a></td></tr></tbody></table>

PrimeGrid is a <a href="Volunteer_computing" title="Volunteer computing">volunteer computing</a> project that searches for very large (up to world-record size) <a href="Prime_number" title="Prime number">prime numbers</a> whilst also aiming to solve long-standing <a href="Mathematical_conjecture" class="mw-redirect" title="Mathematical conjecture">mathematical conjectures</a>. It uses the <a href="Berkeley_Open_Infrastructure_for_Network_Computing" title="Berkeley Open Infrastructure for Network Computing">Berkeley Open Infrastructure for Network Computing</a> (BOINC) platform. PrimeGrid offers a number of subprojects for prime-number sieving and discovery. Some of these are available through the <a href="BOINC_client%E2%80%93server_technology" title="BOINC client–server technology">BOINC client</a>, 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 <a href="Lucas%E2%80%93Lehmer%E2%80%93Riesel_test#LLR_software" title="Lucas–Lehmer–Riesel test">Lucas–Lehmer–Riesel test</a>, CPUs with <a href="Advanced_Vector_Extensions" title="Advanced Vector Extensions">Advanced Vector Extensions</a> and <a href="FMA_instruction_set" title="FMA instruction set">Fused Multiply-Add</a> 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.

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

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PrimeGrid started in June 2005<a href="#cite_note-race08-1">[1]</a> under the name Message@home and tried to decipher text fragments hashed with <a href="MD5" title="MD5">MD5</a>. Message@home was a test to port the BOINC scheduler to <a href="Perl" title="Perl">Perl</a> to obtain greater portability. After a while the project attempted the <a href="RSA_factoring_challenge" class="mw-redirect" title="RSA factoring challenge">RSA factoring challenge</a> 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<a href="#cite_note-5">[5]</a>

the primegen subproject was stopped.

In June 2006, dialog started with <a href="Riesel_Sieve" class="mw-redirect" title="Riesel Sieve">Riesel Sieve</a> 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 (<a href="Lucas%E2%80%93Lehmer%E2%80%93Riesel_test" title="Lucas–Lehmer–Riesel test">LLR</a>) application. With collaboration from Riesel Sieve, PrimeGrid was able to implement the LLR application in partnership with another prime finding project, <a href="Twin_Prime_Search" title="Twin Prime Search">Twin Prime Search</a> (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, and the search for <a href="Sophie_Germain_prime" class="mw-redirect" title="Sophie Germain prime">Sophie Germain primes</a> was suspended in 2024.

In the summer of 2007, the <a href="Cullen_prime" class="mw-redirect" title="Cullen prime">Cullen</a> and <a href="Woodall_prime" class="mw-redirect" title="Woodall prime">Woodall</a> prime searches were launched. In the Fall, more prime searches were added through partnerships with the <a href="Sierpinski_number" class="mw-redirect" title="Sierpinski number">Prime Sierpinski Problem</a> and <a rel="nofollow" class="external text" href="http://www.mersenneforum.org/forumdisplay.php?f=14">3*2^n-1 Search</a> 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 <a href="BOINC" class="mw-redirect" title="BOINC">BOINC</a> software.

Since September 2008, PrimeGrid is also running a <a href="Proth_prime" title="Proth prime">Proth prime</a> sieving subproject.<a href="#cite_note-6">[6]</a>

In January 2010 the subproject Seventeen or Bust (for solving the <a href="Sierpinski_problem" class="mw-redirect" title="Sierpinski problem">Sierpinski problem</a>) was added.<a href="#cite_note-7">[7]</a>

The calculations for the <a href="Riesel_problem" class="mw-redirect" title="Riesel problem">Riesel problem</a> followed in March 2010.

<div class="mw-heading mw-heading2"><h2 id="Projects">Projects</h2></div>

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

<th>Project

</th>

<th>Active <a href="Generating_primes" class="mw-redirect" title="Generating primes">sieve</a> project?

</th>

<th>Active <a href="Lucas%E2%80%93Lehmer%E2%80%93Riesel_test" title="Lucas–Lehmer–Riesel test">LLR</a> project?

</th>

<th>Start

</th>

<th>End

</th>

<th>Best result

</th></tr>

<tr>

<td><a href="321_prime" class="mw-redirect" title="321 prime">321 Prime</a> Search (primes of the form 3 × 2n ± 1)

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td>30 June 2008

</td>

<td>Ongoing

</td>

<td data-sort-value="5477721">3 × 218196595 − 1, largest prime found in the 321 Prime Search project<a href="#cite_note-8">[8]</a>

</td></tr>

<tr>

<td>AP26 Search (<a href="Primes_in_arithmetic_progression" title="Primes in arithmetic progression">Arithmetic progression</a> of 26 primes)

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>27 December 2008

</td>

<td>12 April 2010

</td>

</td></tr>

<tr>

<td>AP27 Search (Arithmetic progression of 27 primes)

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>20 September 2016

</td>

<td>Ongoing

</td>

</td></tr>

<tr>

<td><a href="Fermat_prime" class="mw-redirect" title="Fermat prime">Generalized Fermat Prime</a> Search<a href="#cite_note-11">[11]</a><a href="#cite_note-12">[12]</a> (active: n = 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304 inactive: n = 8192, 16384, 32768)

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes (manual sieving)

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>January 2012

</td>

<td>Ongoing

</td>

<td data-sort-value="6598776">19637361048576 + 1, largest known Generalized Fermat prime<a href="#cite_note-13">[13]</a>

</td></tr>

<tr>

<td><a href="Cullen_prime" class="mw-redirect" title="Cullen prime">Cullen Prime</a> Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td>August 2007

</td>

<td>Ongoing

</td>

<td data-sort-value="2010851">6679881 × 26679881 + 1, largest known Cullen prime<a href="#cite_note-14">[14]</a>

</td></tr>

<tr>

<td>Message7

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>12 June 2005

</td>

<td>August 2005

</td>

<td>PerlBOINC testing successful

</td></tr>

<tr>

<td><a href="Sierpinski_number" class="mw-redirect" title="Sierpinski number">Prime Sierpinski Problem</a>

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td>10 July 2008

</td>

<td>Ongoing

</td>

</td></tr>

<tr>

<td><a href="Sierpinski_number" class="mw-redirect" title="Sierpinski number">Extended Sierpinski Problem</a>

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td>7 June 2014

</td>

<td>Ongoing

</td>

<td data-sort-value="6418120">202705 × 221320516 + 1, largest prime found in the Extended Sierpinski Problem<a href="#cite_note-16">[16]</a>

</td></tr>

<tr>

<td>PrimeGen

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>March 2006

</td>

<td>February 2008

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td></tr>

<tr>

<td><a href="Proth_prime" title="Proth prime">Proth Prime</a> Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td>29 February 2008

</td>

<td>Ongoing

</td>

</td></tr>

<tr>

<td><a href="Riesel_number" title="Riesel number">Riesel Problem</a>

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td>March 2010

</td>

<td>Ongoing

</td>

</td></tr>

<tr>

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>August 2005

</td>

<td>November 2005

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td></tr>

<tr>

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>November 2005

</td>

<td>March 2006

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td></tr>

<tr>

<td>Seventeen or Bust

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td>31 January 2010

</td>

<td>Ongoing

</td>

<td data-sort-value="9383760">10223 × 231172165 + 1

</td></tr>

<tr>

<td><a href="Sierpinski_number" class="mw-redirect" title="Sierpinski number">Sierpinski</a>/<a href="Riesel_number#Riesel_number_base_b" title="Riesel number">Riesel</a> Base 5 Problem

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td>14 June 2013

</td>

<td>Ongoing

</td>

<td data-sort-value="2892597">213988×54138363 − 1, largest prime found in the Sierpinski/Riesel Base 5 Problem

</td></tr>

<tr>

<td><a href="Sophie_Germain_prime" class="mw-redirect" title="Sophie Germain prime">Sophie Germain Prime</a> Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td>16 August 2009

</td>

<td>February 2024

</td>

<td data-sort-value="388341">2618163402417 × 21290000 − 1 (2p − 1 = 2618163402417 × 21290001 − 1), the world record Sophie Germain prime;<a href="#cite_note-19">[19]</a> and 2996863034895 × 21290000 ± 1, the world record twin primes<a href="#cite_note-20">[20]</a>

</td></tr>

<tr>

<td><a href="Twin_Primes" class="mw-redirect" title="Twin Primes">Twin prime</a> Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>26 November 2006

</td>

<td>25 July 2009

</td>

</td></tr>

<tr>

<td><a href="Woodall_prime" class="mw-redirect" title="Woodall prime">Woodall Prime</a> Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td>July 2007

</td>

<td>Ongoing

</td>

<td data-sort-value="5122514">17016602 × 217016602 − 1, largest known Woodall prime<a href="#cite_note-22">[22]</a>

</td></tr>

<tr>

<td>Generalized Cullen/Woodall Prime Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td>22 October 2016

</td>

<td>Ongoing

</td>

<td data-sort-value="4705887">2525532 × 732525532 + 1, largest known generalized Cullen prime<a href="#cite_note-23">[23]</a>

</td></tr>

<tr>

<td><a href="Wieferich_prime" title="Wieferich prime">Wieferich Prime</a> Search

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

</td>

<td>2022

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td></tr>

<tr>

<td><a href="Wall%E2%80%93Sun%E2%80%93Sun_prime" title="Wall–Sun–Sun prime">Wall-Sun-Sun Prime</a> Search

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>2020

</td>

<td>2022

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td></tr></tbody></table>

<div class="mw-heading mw-heading3"><h3 id="321_Prime_Search">321 Prime Search</h3></div>

321 Prime Search is a continuation of Paul Underwood's <a rel="nofollow" class="external text" href="http://www.mersenneforum.org/forumdisplay.php?f=14">321 Search</a> which looked for primes of the form 3 · 2n − 1. PrimeGrid added the +1 form and continues the search up to n = 25M.

Primes known for 3 · 2n + 1 occur at the following n:

<dl><dd>1, 2, 5, 6, 8, 12, 18, 30, 36, 41, 66, 189, 201, 209, 276, 353, 408, 438, 534, 2208, 2816, 3168, 3189, 3912, 20909, 34350, 42294, 42665, 44685, 48150, 54792, 55182, 59973, 80190, 157169, 213321, 303093, 362765, 382449, 709968, 801978, 916773, 1832496, 2145353, 2291610, 2478785, 5082306, 7033641, 10829346, 16408818 (sequence <a href="https://oeis.org/A002253" class="extiw external" title="oeis:A002253">A002253</a> in the <a href="On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>)</dd></dl>

Primes known for 3 · 2n − 1 occur at the following n:

<dl><dd>0, 1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, 827, 1274, 3276, 4204, 5134, 7559, 12676, 14898, 18123, 18819, 25690, 26459, 41628, 51387, 71783, 80330, 85687, 88171, 97063, 123630, 155930, 164987, 234760, 414840, 584995, 702038, 727699, 992700, 1201046, 1232255, 2312734, 3136255, 4235414, 6090515, 11484018, 11731850, 11895718, 16819291, 17748034, 18196595 (sequence <a href="https://oeis.org/A002235" class="extiw external" title="oeis:A002235">A002235</a> in the <a href="On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>)</dd></dl>

<div class="mw-heading mw-heading3"><h3 id="PRPNet_projects">PRPNet projects</h3></div>

<th>Project

</th>

<th>Active?

</th>

<th>Start

</th>

<th>End

</th>

<th>Best result

</th></tr>

<tr>

<td>27 Prime Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>March 2022<a href="#cite_note-25">[25]</a>

</td>

<td data-sort-value="1569461">27 × 27046834 + 1, largest known Sierpinski prime for b = 2 and k = 27 27×28342438 − 1, largest known Riesel prime for b = 2 and k = 27<a href="#cite_note-26">[26]</a>

</td></tr>

<tr>

<td>121 Prime Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>April 2021<a href="#cite_note-27">[27]</a>

</td>

<td data-sort-value="1370862">121 × 29584444 − 1, largest known Sierpinski prime for b = 2 and k = 121 121 × 24553899 − 1, largest known Riesel prime for b = 2 and k = 121<a href="#cite_note-28">[28]</a>

</td></tr>

<tr>

<td>Extended <a href="Sierpinski_problem" class="mw-redirect" title="Sierpinski problem">Sierpinski problem</a>

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>2014

</td>

</td></tr>

<tr>

<td><a href="Factorial_prime" title="Factorial prime">Factorial Prime</a> Search

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>Ongoing

</td>

<td data-sort-value="700176">147855! − 1, 5th largest known factorial prime

</td></tr>

<tr>

<td>Dual Sierpinski problem (Five or Bust)

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>All were done (all PRPs were found)

</td>

<td data-sort-value="2737082">29092392 + 40291

</td></tr>

<tr>

<td>Generalized <a href="Cullen_number" title="Cullen number">Cullen</a>/<a href="Woodall_number" title="Woodall number">Woodall</a> Prime Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

</td>

<td data-sort-value="877068">427194 × 113427194 + 1, then largest known GCW prime<a href="#cite_note-31">[31]</a>

</td></tr>

<tr>

<td>Mega Prime Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—

</td>

<td>2014

</td>

<td data-sort-value="1052459">87 × 23496188 + 1, largest known prime for k = 87

</td></tr>

<tr>

<td><a href="Primorial_Prime" class="mw-redirect" title="Primorial Prime">Primorial Prime</a> Search

</td>

<td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Yes

</td>

</td>

<td>Ongoing

</td>

<td data-sort-value="476311">3267113# − 1, largest known primorial prime<a href="#cite_note-33">[33]</a>

</td></tr>

<tr>

<td>Proth Prime Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

<td>2008

</td>

</td>

<td data-sort-value="9383760">10223 × 231172165 + 1, largest known Proth prime

</td></tr>

<tr>

<td>Sierpinski Riesel Base 5

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

</td>

</td>

<td data-sort-value="1572122">180062 × 52249192 − 1

</td></tr>

<tr>

<td><a href="Wieferich_prime" title="Wieferich prime">Wieferich Prime</a> Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

</td>

</td>

<td data-sort-value="16">82687771042557349, closest near-miss above 3 × 1015

</td></tr>

<tr>

<td><a href="Wall%E2%80%93Sun%E2%80%93Sun_prime" title="Wall–Sun–Sun prime">Wall-Sun-Sun Prime</a> Search

</td>

<td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">No

</td>

</td>

</td>

<td data-sort-value="15">6336823451747417, closest near-miss above 9.7 × 1014

</td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Accomplishments">Accomplishments</h2></div>

One of PrimeGrid projects was AP26 Search which searched for a record 26 <a href="Primes_in_arithmetic_progression" title="Primes in arithmetic progression">primes in arithmetic progression</a>. The search was successful in April 2010 with the finding of the first known AP26:

<dl><dd>43142746595714191 + 23681770 · 23# · n is prime for n = 0, ..., 25.<a href="#cite_note-39">[39]</a></dd>

<dd>23# = 2·3·5·7·11·13·17·19·23 = 223092870, or 23 <a href="Primorial" title="Primorial">primorial</a>, is the product of all primes up to 23.</dd></dl>

Next target of the project was AP27 Search which searched for a record 27 <a href="Primes_in_arithmetic_progression" title="Primes in arithmetic progression">primes in arithmetic progression</a>. The search was successful in September 2019 with the finding of the first known AP27:

<dl><dd>224584605939537911 + 81292139 · 23# · n is prime for n = 0, ..., 26.<a href="#cite_note-40">[40]</a></dd>

<dd>23# = 2·3·5·7·11·13·17·19·23 = 223092870, or 23 <a href="Primorial" title="Primorial">primorial</a>, is the product of all primes up to 23.</dd></dl>

<div class="mw-heading mw-heading3"><h3 id="Cullen_prime_search">Cullen prime search</h3></div>

PrimeGrid is also running a search for <a href="Cullen_prime" class="mw-redirect" title="Cullen prime">Cullen prime</a> numbers, yielding the two largest known Cullen primes. The first one being the 14th largest known prime at the time of discovery, and the second one was PrimeGrid's largest prime found 6679881 · 26679881 + 1 at over 2 million digits.<a href="#cite_note-41">[41]</a>

<div class="mw-heading mw-heading3"><h3 id="Generalized_Fermat_prime_search">Generalized Fermat prime search</h3></div>

On 24 September 2022, PrimeGrid discovered the largest known <a href="Fermat_number#Generalized_Fermat_numbers" title="Fermat number">Generalized Fermat prime</a> to date, 19637361048576 + 1. This prime is 6,598,776 digits long and is only the second Generalized Fermat prime found for n = 20. It ranks as the 13th largest known prime overall.<a href="#cite_note-42">[42]</a>

<div class="mw-heading mw-heading3"><h3 id="Riesel_Problem">Riesel Problem</h3></div>

As of 13 December 2022, PrimeGrid has eliminated 18 values of k from the <a href="Riesel_number" title="Riesel number">Riesel problem</a><a href="#cite_note-43">[43]</a>

and is continuing the search to eliminate the 43 remaining numbers. 3 values of k are found by independent searchers.

<div class="mw-heading mw-heading3"><h3 id="Twin_prime_search">Twin prime search</h3></div>

Primegrid worked with the <a href="Twin_Prime_Search" title="Twin Prime Search">Twin Prime Search</a> to search for a record-sized <a href="Twin_prime" title="Twin prime">twin prime</a> at approximately 58,700 digits. The new world's largest known twin prime 2003663613 × 2195000 ± 1 was eventually discovered on January 15, 2007 (sieved by Twin Prime Search and tested by PrimeGrid). The search continued for another record twin prime at just above 100,000 digits. It was completed in August 2009 when Primegrid found 65516468355 × 2333333 ± 1. Continued testing for twin primes in conjunction with the search for a <a href="Sophie_Germain_prime" class="mw-redirect" title="Sophie Germain prime">Sophie Germain prime</a> yielded a new record twin prime in September 2016 upon finding the number 2996863034895 × 21290000 ± 1 composed of 388,342 digits.

<div class="mw-heading mw-heading3"><h3 id="Woodall_prime_search">Woodall prime search</h3></div>

As of 22 April 2018, the project has discovered the four largest <a href="Woodall_number" title="Woodall number">Woodall primes</a> known to date.<a href="#cite_note-44">[44]</a>

The largest of these is 17016602 × 217016602 − 1 and was found on 21 March 2018. The search continues for an even bigger Woodall prime.

PrimeGrid also found the largest known generalized Woodall prime,<a href="#cite_note-45">[45]</a>

563528 × 13563528 − 1.

<div class="mw-heading mw-heading2"><h2 id="Media_coverage">Media coverage</h2></div>

PrimeGrid's author Rytis Slatkevičius has been featured as a young entrepreneur in <a href="The_Economist" title="The Economist">The Economist</a>.<a href="#cite_note-46">[46]</a>

PrimeGrid has also been featured in an article by Francois Grey in the <a href="CERN_Courier" title="CERN Courier">CERN Courier</a> and a talk about citizen cyberscience in <a href="TEDx" class="mw-redirect" title="TEDx">TEDx</a> Warwick conference.<a href="#cite_note-47">[47]</a><a href="#cite_note-48">[48]</a>

In the first Citizen Cyberscience Summit, Rytis Slatkevičius gave a talk as a founder of PrimeGrid, named Finding primes: from digits to digital technology,<a href="#cite_note-49">[49]</a>

relating mathematics and volunteering and featuring the history of the project.<a href="#cite_note-50">[50]</a>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-21"><a href="#cite_ref-21">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110926230509/http://www.primegrid.com/download/Twin333333.pdf">"PrimeGrid's Twin Prime Search"</a> (PDF). PrimeGrid. Archived from <a rel="nofollow" class="external text" href="https://www.primegrid.com/download/Twin333333.pdf">the original</a> (PDF) on 2011-09-26. Retrieved 2011-09-19.</cite>

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<li id="cite_note-22"><a href="#cite_ref-22">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.primegrid.com/download/WOO-17016602.pdf">"PrimeGrid's Woodall Prime Search"</a> (PDF). PrimeGrid. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210121012221/https://www.primegrid.com/download/WOO-17016602.pdf">Archived</a> (PDF) from the original on 2021-01-21. Retrieved 2019-07-28.</cite>

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<li id="cite_note-23"><a href="#cite_ref-23">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.primegrid.com/download/GC73-2525532.pdf">"PrimeGrid's Generalized Cullen/Woodall Prime Search"</a> (PDF). PrimeGrid. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220127211019/http://primegrid.com/download/GC73-2525532.pdf">Archived</a> (PDF) from the original on 2022-01-27. Retrieved 2022-01-27.</cite>

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</ol></div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://primegrid.com/">Official website</a> </li>

<li><a rel="nofollow" class="external text" href="https://www.discord.com/channels/357493752434130944/">PrimeGrid Discord chat server</a> (almost daily discovery announcements)</li>

<li><a rel="nofollow" class="external text" href="https://t5k.org/bios/page.php?id=950">PrimeGrid's results</a> at <a href="The_Prime_Pages" class="mw-redirect" title="The Prime Pages">The Prime Pages</a></li></ul>

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</style><div id="Berkeley_Open_Infrastructure_for_Network_Computing_(BOINC)_projects186" style="font-size:114%;margin:0 4em"><a href="Berkeley_Open_Infrastructure_for_Network_Computing" title="Berkeley Open Infrastructure for Network Computing">Berkeley Open Infrastructure for Network Computing (BOINC)</a> projects</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Active</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Amicable_Numbers_project" class="mw-redirect" title="Amicable Numbers project">Amicable Numbers</a></li>

<li><a href="Asteroids%40home" class="mw-redirect" title="Asteroids@home">Asteroids@home</a></li>

<li><a href="Climateprediction.net" title="Climateprediction.net">climateprediction.net</a></li>

<li><a href="Collatz_Conjecture_project" class="mw-redirect" title="Collatz Conjecture project">Collatz Conjecture</a></li>

<li><a href="Einstein%40Home" title="Einstein@Home">Einstein@Home</a></li>

<li><a href="Gerasim%40Home" class="mw-redirect" title="Gerasim@Home">Gerasim@home</a></li>

<li><a href="GPUGRID.net" title="GPUGRID.net">GPUGRID.net</a></li>

<li>iThena</li>

<li><a href="MilkyWay%40home" title="MilkyWay@home">MilkyWay@home</a></li>

<li>Minecraft@home</li>

<li><a href="MindModeling%40Home" title="MindModeling@Home">MindModeling@Home</a></li>

<li><a href="Moo!_Wrapper" class="mw-redirect" title="Moo! Wrapper">Moo! Wrapper</a></li>

<li><a href="NumberFields%40home" class="mw-redirect" title="NumberFields@home">NumberFields@home</a></li>

<li>QuChemPedIA@home</li>

<li>RakeSearch</li>

<li>Ramanujan Machine</li>

<li><a href="Rosetta%40home" title="Rosetta@home">Rosetta@home</a></li>

<li><a href="SIDock%40home" class="mw-redirect" title="SIDock@home">SIDock@home</a></li>

<li><a href="SRBase" class="mw-redirect" title="SRBase">SRBase</a></li>

<li>Universe@Home</li>

<li><a href="World_Community_Grid" title="World Community Grid">World Community Grid</a> (subprojects <a href="Clean_Energy_Project" title="Clean Energy Project">Clean Energy Project</a>, <a href="Discovering_Dengue_Drugs_%E2%80%93_Together" title="Discovering Dengue Drugs – Together">Discovering Dengue Drugs – Together</a>, <a href="FightAIDS%40Home" title="FightAIDS@Home">FightAIDS@Home</a>, <a href="Fiocruz_Genome_Comparison_Project" title="Fiocruz Genome Comparison Project">Fiocruz Genome Comparison Project</a>, <a href="Help_Defeat_Cancer" title="Help Defeat Cancer">Help Defeat Cancer</a>, <a href="Help_Conquer_Cancer" title="Help Conquer Cancer">Help Conquer Cancer</a>, <a href="Help_Cure_Muscular_Dystrophy" title="Help Cure Muscular Dystrophy">Help Cure Muscular Dystrophy</a>, <a href="Human_Proteome_Folding_Project" title="Human Proteome Folding Project">Human Proteome Folding Project</a>, <a href="Help_Fight_Childhood_Cancer" class="mw-redirect" title="Help Fight Childhood Cancer">Help Fight Childhood Cancer</a>, <a href="Smash_Childhood_Cancer" class="mw-redirect" title="Smash Childhood Cancer">Smash Childhood Cancer</a>)</li>

<li>WUProp@Home</li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Beta</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>RNA World (beta)</li>

<li>WEP-M+2 Project</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Alpha</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>nanoHUB@home</li>

<li>RADIOACTIVE@HOME</li>

<li><a href="RALPH%40Home" class="mw-redirect" title="RALPH@Home">RALPH@home</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Technology, tools</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="BOINC_client%E2%80%93server_technology" title="BOINC client–server technology">BOINC client–server technology</a></li>

<li><a href="BOINC_Credit_System" title="BOINC Credit System">BOINC Credit System</a></li>

<li><a href="Gridcoin" title="Gridcoin">Gridcoin</a></li>

<li><a href="Charity_Engine" title="Charity Engine">Charity Engine</a></li>

<li><a href="GridRepublic" title="GridRepublic">GridRepublic</a></li>

<li><a href="Science_United" class="mw-redirect" title="Science United">Science United</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Terminated or inactive</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Artificial_Intelligence_System" title="Artificial Intelligence System">Artificial Intelligence System</a></li>

<li><a href="Climateprediction.net#BBC_Climate_Change_Experiment" title="Climateprediction.net">BBC Climate Change Experiment</a></li>

<li><a href="Big_and_Ugly_Rendering_Project" title="Big and Ugly Rendering Project">Big and Ugly Rendering Project</a></li>

<li>Cell Computing</li>

<li>Citizen Science Grid</li>

<li>Correlizer</li>

<li><a href="Cosmology%40Home" title="Cosmology@Home">Cosmology@Home</a></li>

<li>DistrRTgen</li>

<li><a href="Docking%40Home" title="Docking@Home">Docking@Home</a></li>

<li><a href="EDGeS%40Home" class="mw-redirect" title="EDGeS@Home">EDGeS@Home</a></li>

<li>Enigma@Home</li>

<li><a href="Evolution%40Home" title="Evolution@Home">Evolution@Home</a> (yoyo@home subproject)</li>

<li><a href="FreeHAL" title="FreeHAL">FreeHAL</a></li>

<li><a href="HashClash" title="HashClash">HashClash</a></li>

<li><a href="Ibercivis" title="Ibercivis">Ibercivis</a></li>

<li>Kryptos@Home</li>

<li><a href="The_Lattice_Project" title="The Lattice Project">The Lattice Project</a></li>

<li><a href="Leiden_Classical" title="Leiden Classical">Leiden Classical</a></li>

<li><a href="UFluids%40Home" title="UFluids@Home">uFluids@Home</a></li>

<li><a href="Malaria_Control_Project" title="Malaria Control Project">Malaria Control Project</a></li>

<li><a href="OProject%40Home" title="OProject@Home">OProject@Home</a></li>

<li><a href="Orbit%40home" title="Orbit@home">orbit@home</a></li>

<li><a href="Pirates%40home" class="mw-redirect" title="Pirates@home">Pirates@Home</a></li>

<li><a href="Predictor%40home" title="Predictor@home">Predictor@home</a></li>

<li><a href="Proteins%40home" title="Proteins@home">proteins@home</a></li>

<li><a href="Riesel_Sieve" class="mw-redirect" title="Riesel Sieve">Riesel Sieve</a> (merged with PrimeGrid)</li>

<li><a href="Seasonal_Attribution_Project" title="Seasonal Attribution Project">Seasonal Attribution Project</a></li>

<li><a href="SETI%40home" title="SETI@home">SETI@home</a> (subproject <a href="Astropulse" title="Astropulse">Astropulse</a>)</li>

<li><a href="Similarity_Matrix_of_Proteins" title="Similarity Matrix of Proteins">SIMAP</a></li>

<li><a href="SLinCA%40Home" title="SLinCA@Home">SLinCA@Home</a></li>

<li><a href="Spinhenge%40Home" title="Spinhenge@Home">Spinhenge@home</a></li>

<li>SZTAKI Desktop Grid</li>

<li><a href="TANPAKU" class="mw-redirect" title="TANPAKU">TANPAKU</a></li>

<li><a href="TheSkyNet" title="TheSkyNet">theSkyNet</a></li>

<li>XtremLab</li></ul>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-04-01" href="https://en.wikipedia.org/wiki/?title=PrimeGrid&oldid=1283403143">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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