# PrimeGrid

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{{Short description|BOINC based volunteer computing project researching prime numbers}}

{{Infobox distributed computing project
| logo = Logo_of_the_PrimeGrid_project,_2023.svg
| logo_size  = 250px
| author = [Rytis Slatkevičius](/source/Rytis_Slatkevi%C4%8Dius)
| released  = {{start date and age|2005|6|12}}<ref name=race08>{{cite web | url = https://www.primegrid.com/challenge/2008_challenge.php | title = PrimeGrid's Challenge Series - 2008 Final Standings | publisher = PrimeGrid | access-date = 2011-09-19 | archive-date = 2011-09-26 | archive-url = https://web.archive.org/web/20110926230014/http://www.primegrid.com/challenge/2008_challenge.php | url-status = live }}</ref>
| status = Active
| goal = Finding prime numbers of various types
| software   = PRPNet, Genefer, LLR, PFGW
| funding  = Corporate sponsorship, crowdfunding<ref>{{cite web | url = https://www.primegrid.com/forum_thread.php?id=5233&nowrap=true#68716 | title = PrimeGrid's new server (again) | publisher = PrimeGrid | access-date = 2016-10-09 | archive-date = 2017-02-08 | archive-url = https://web.archive.org/web/20170208020307/http://www.primegrid.com/forum_thread.php?id=5233&nowrap=true#68716 | url-status = live }}</ref><ref>{{Cite web|url=https://www.primegrid.com/donations.php|title=Donations to PrimeGrid|access-date=2018-07-27|archive-date=2018-07-27|archive-url=https://web.archive.org/web/20180727085006/https://www.primegrid.com/donations.php|url-status=live}}</ref>
| website = {{URL|1=https://www.primegrid.com/}}
| performance  = 3,398.914 [TFLOPS](/source/FLOPS)<ref name="boincstats">{{cite web| url = https://boincstats.com/en/stats/11/project/detail/overview| title = PrimeGrid - Detailed Stats| publisher = BOINCstats| access-date = 21 August 2022| archive-date = 17 September 2017| archive-url = https://web.archive.org/web/20170917213948/https://boincstats.com/en/stats/11/project/detail/overview| url-status = live}}</ref>
| active users = 2,330 (August 2022)<ref name="boincstats"/>
| total users = 353,245<ref name="boincstats"/>
| active hosts = 11,504 (August 2022)<ref name="boincstats"/>
| total hosts = 21,985<ref name="boincstats"/>
|screenshot=Primegrid.gif|platform=[BOINC](/source/BOINC)|screenshot caption=PrimeGrid screensaver|screenshot_size=250px}}
'''PrimeGrid''' is a [volunteer computing](/source/volunteer_computing) project that searches for very large (up to world-record size) [prime number](/source/prime_number)s whilst also aiming to solve long-standing [mathematical conjecture](/source/mathematical_conjecture)s. It uses the [Berkeley Open Infrastructure for Network Computing](/source/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](/source/BOINC_client%E2%80%93server_technology), 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](/source/Lucas%E2%80%93Lehmer%E2%80%93Riesel_test), CPUs with [Advanced Vector Extensions](/source/Advanced_Vector_Extensions) and [Fused Multiply-Add](/source/FMA_instruction_set) 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.

==History==
{{update|section|date=March 2023}}
PrimeGrid started in June 2005<ref name=race08/> under the name Message@home and tried to decipher text fragments hashed with [MD5](/source/MD5). Message@home was a test to port the BOINC scheduler to [Perl](/source/Perl) to obtain greater portability. After a while the project attempted the [RSA factoring challenge](/source/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<ref>{{cite web
 |url          = https://www.primegrid.com/orig/torrent.php
 |title        = Prime Lists
 |publisher    = PrimeGrid
 |access-date   = 2011-09-19
 |archive-url  = https://web.archive.org/web/20100530071550/http://primegrid.com/orig/torrent.php
 |archive-date = 2010-05-30
 |url-status     = dead
}}</ref>
the primegen subproject was stopped.

In June 2006, dialog started with [Riesel Sieve](/source/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](/source/Lucas%E2%80%93Lehmer%E2%80%93Riesel_test)) application. With collaboration from Riesel Sieve, PrimeGrid was able to implement the LLR application in partnership with another prime finding project, [Twin Prime Search](/source/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, and the search for [Sophie Germain prime](/source/Sophie_Germain_prime)s was suspended in 2024.

In the summer of 2007, the [Cullen](/source/Cullen_prime) and [Woodall](/source/Woodall_prime) prime searches were launched. In the Fall, more prime searches were added through partnerships with the [Prime Sierpinski Problem](/source/Sierpinski_number) and [https://www.mersenneforum.org/forumdisplay.php?f=14 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](/source/BOINC) software.

Since September 2008, PrimeGrid is also running a [Proth prime](/source/Proth_prime) sieving subproject.<ref>{{cite web
| url = https://www.primegrid.com/forum_thread.php?id=973
| title = PrimeGrid forum: PPS Sieve
| author = John
| publisher = PrimeGrid
| access-date = 2011-09-19
| archive-date = 2011-09-26
| archive-url = https://web.archive.org/web/20110926225430/http://www.primegrid.com/forum_thread.php?id=973
| url-status = live
}}</ref>

In January 2010 the subproject Seventeen or Bust (for solving the [Sierpinski problem](/source/Sierpinski_problem)) was added.<ref>{{cite web
| url = https://www.primegrid.com/forum_thread.php?id=1647
| title = PrimeGrid forum: Seventeen or Bust and the Sierpinski Problem
| author = John
| publisher = PrimeGrid
| access-date = 2011-09-19
| archive-date = 2011-09-26
| archive-url = https://web.archive.org/web/20110926225718/http://www.primegrid.com/forum_thread.php?id=1647
| url-status = live
}}</ref>
The calculations for the [Riesel problem](/source/Riesel_problem) followed in March 2010.

==Projects==
{{As of|2023|1}}, PrimeGrid is working on or has worked on the following projects:
{| class="wikitable sortable"
|-
! Project
! Active [sieve](/source/Generating_primes) project?
! Active [LLR](/source/Lucas%E2%80%93Lehmer%E2%80%93Riesel_test) project?
! Start
! End
! Best result<!-- sorted by decimal logarithm of the biggest number (if many), rounded down -->
|-
| [321 Prime](/source/321_prime) Search (primes of the form 3 × 2<sup>''n''</sup> ±&thinsp;1)
| {{No}}
| {{Yes}}
| 30 June 2008
| Ongoing
| data-sort-value="5477721" | 3 × 2<sup>18196595</sup> − 1, largest prime found in the 321 Prime Search project<ref>{{cite web |title=PrimePage Primes: 3·2^18196595 - 1 |url=https://t5k.org/primes/page.php?id=133193 |website=t5k.org |access-date=12 March 2023 |archive-date=23 January 2022 |archive-url=https://web.archive.org/web/20220123094556/https://primes.utm.edu/primes/page.php?id=133193 |url-status=live }}</ref>
|-
| AP26 Search ([Arithmetic progression](/source/Primes_in_arithmetic_progression) of 26 primes)
| {{N/A}}
| {{N/A}}
| 27 December 2008
| 12 April 2010
| data-sort-value="17.2435" | 43142746595714191 + 23681770 × 23# × ''n'', ''n'' = 0, ..., 25 (AP26)<ref>{{cite web
| url = https://www.primegrid.com/download/AP26.pdf
| title = PrimeGrid's AP26 Search
| publisher = PrimeGrid
| access-date = 2011-09-19
| archive-date = 2011-09-26
| archive-url = https://web.archive.org/web/20110926231931/http://www.primegrid.com/download/AP26.pdf
| url-status = live
}}</ref>
|-
| AP27 Search (Arithmetic progression of 27 primes)
| {{N/A}}
| {{N/A}}
| 20 September 2016
| Ongoing
| data-sort-value="17.8427" | 605185576317848261 + 155368778 × 23# × ''n'', ''n'' = 0, ..., 26 (AP27)<ref>{{cite web |date=10 Dec 2023 |title=PrimeGrid's AP26 Search |url=https://www.primegrid.com/forum_thread.php?id=7012&nowrap=true#167007 |url-status=live |archive-url=https://web.archive.org/web/20250101191319/https://www.pzktupel.de/JensKruseAndersen/AP27.php |archive-date=2025-01-01 |access-date=2025-01-01 |publisher=PrimeGrid}}</ref>
|-
| [Generalized Fermat Prime](/source/Fermat_prime) Search<ref>{{cite web | title = Genefer statistics | publisher = PrimeGrid | url = https://www.primegrid.com/stats_genefer.php | access-date = 2015-11-04 | archive-date = 2019-06-23 | archive-url = https://web.archive.org/web/20190623190358/http://www.primegrid.com/stats_genefer.php | url-status = live }}</ref><ref>{{cite web|title=GFN Prime Search Status and History|publisher=PrimeGrid|url=https://www.primegrid.com/gfn_history.php|access-date=2017-03-04|archive-date=2017-03-05|archive-url=https://web.archive.org/web/20170305035335/http://www.primegrid.com/gfn_history.php|url-status=live}}</ref><br>('''<span style="color:green;">active</span>''': ''n'' = 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304 '''<span style="color:red;">inactive</span>''': ''n'' = 8192, 16384, 32768)
| {{Yes}} (manual sieving)
| {{N/A}}
| January 2012
| Ongoing
| data-sort-value="6598776" | 1963736<sup>1048576</sup> + 1, largest known Generalized Fermat prime<ref>{{cite web
| url = https://www.primegrid.com/download/GFN-1059094_1048576.pdf
| title = PrimeGrid's Generalized Fermat Prime Search
| publisher = PrimeGrid
| access-date = 2019-07-28
| archive-date = 2021-01-15
| archive-url = https://web.archive.org/web/20210115172745/http://www.primegrid.com/download/GFN-1059094_1048576.pdf
| url-status = live
}}</ref>
|-
| [Cullen Prime](/source/Cullen_prime) Search
| {{No}}
| {{Yes}}
| August 2007
| Ongoing
| data-sort-value="2010851" | 6679881 × 2<sup>6679881</sup> + 1, largest known Cullen prime<ref>{{cite web
 |url          = https://www.primegrid.com/download/Cullen6679881.pdf
 |title        = PrimeGrid's Cullen Prime Search
 |publisher    = PrimeGrid
 |access-date   = 2011-09-19
 |archive-url  = https://web.archive.org/web/20110926231457/http://www.primegrid.com/download/Cullen6679881.pdf
 |archive-date = 2011-09-26
 |url-status     = dead
}}</ref>
|-
| Message7
| {{No}}
| {{N/A}}
| 12 June 2005
| August 2005
| PerlBOINC testing successful
|-
| [Prime Sierpinski Problem](/source/Sierpinski_number)
| {{No}}
| {{Yes}}
| 10 July 2008
| Ongoing
| data-sort-value="5832521" | 168451 × 2<sup>19375200</sup> + 1<ref>{{cite web
| url = https://www.primegrid.com/download/PSP_168451.pdf
| title = PrimeGrid's Prime Sierpinski Problem
| publisher = PrimeGrid
| access-date = 2019-07-28
| archive-date = 2019-07-16
| archive-url = https://web.archive.org/web/20190716113614/http://www.primegrid.com/download/PSP_168451.pdf
| url-status = live
}}</ref>
|-
| [Extended Sierpinski Problem](/source/Sierpinski_number)
| {{No}}
| {{Yes}}
| 7 June 2014
| Ongoing
| data-sort-value="6418120" | 202705 × 2<sup>21320516</sup> + 1, largest prime found in the Extended Sierpinski Problem<ref>{{cite web
| url = https://www.primegrid.com/download/ESP-202705.pdf
| title = PrimeGrid's Extended Sierpinski Problem
| publisher = PrimeGrid
| access-date = 2022-01-27
| archive-date = 2022-01-27
| archive-url = https://web.archive.org/web/20220127205849/http://primegrid.com/download/ESP-202705.pdf
| url-status = live
}}</ref>
|-
| PrimeGen
| {{No}}
| {{N/A}}
| March 2006
| February 2008
| {{N/A}}
|-
| [Proth Prime](/source/Proth_prime) Search
| {{No}}
| {{Yes}}
| 29 February 2008
| Ongoing
| data-sort-value="1738748" | 7 × 2<sup>5775996</sup> + 1<ref>{{cite web
| url = https://www.primegrid.com/download/PPS-5775996.pdf
| title = PrimeGrid's Proth Prime Search
| publisher = PrimeGrid
| access-date = 10 March 2016
| archive-date = 4 March 2016
| archive-url = https://web.archive.org/web/20160304201330/http://www.primegrid.com/download/PPS-5775996.pdf
| url-status = live
}}</ref>
|-
|[Riesel Problem](/source/Riesel_number)
| {{No}}
| {{Yes}}
| March 2010
| Ongoing
| data-sort-value="3429396" | 9221 × 2<sup>11392194</sup> − 1,<ref>{{cite web
| url = https://www.primegrid.com/download/TRP-9221.pdf
| title = PrimeGrid's The Riesel Problem
| publisher = PrimeGrid
| access-date = 2022-01-27
| archive-date = 2022-01-27
| archive-url = https://web.archive.org/web/20220127205820/http://primegrid.com/download/TRP-9221.pdf
| url-status = live
}}</ref>
|-
| [RSA-640](/source/RSA-640)
| {{No}}
| {{N/A}}
| August 2005
| November 2005
| {{N/A}}
|-
| [RSA-768](/source/RSA-768)
| {{No}}
| {{N/A}}
| November 2005
| March 2006
| {{N/A}}
|-
| [Seventeen or Bust](/source/Sierpinski_number)
| {{No}}
| {{Yes}}
| 31 January 2010
| Ongoing
| data-sort-value="9383760" | 10223 × 2<sup>31172165</sup> + 1
|-
| [Sierpinski](/source/Sierpinski_number)/[Riesel](/source/Riesel_number) Base 5 Problem
| {{Yes}}
| {{Yes}}
| 14 June 2013
| Ongoing
| data-sort-value="2892597" | 213988×5<sup>4138363</sup> − 1, largest prime found in the Sierpinski/Riesel Base 5 Problem
|-
| [Sophie Germain Prime](/source/Sophie_Germain_prime) Search
| {{No}}
| {{No}}
| 16 August 2009
| February 2024
| data-sort-value="388341" | 2618163402417 × 2<sup>1290000</sup> − 1 (2''p'' − 1 = 2618163402417 × 2<sup>1290001</sup> − 1), the world record Sophie Germain prime;<ref>{{cite web
| url = https://www.primegrid.com/download/SGS_2618163402417_1290000.pdf
| title = World Record Sophie Germain prime
| publisher = PrimeGrid
| access-date = 2019-07-28
| archive-date = 2019-07-16
| archive-url = https://web.archive.org/web/20190716110354/http://www.primegrid.com/download/SGS_2618163402417_1290000.pdf
| url-status = live
}}</ref> and 2996863034895 × 2<sup>1290000</sup> ±&thinsp;1, the world record twin primes<ref>{{cite web
| url = https://www.primegrid.com/download/twin-1290000.pdf
| title = World Record Sophie Germain prime
| publisher = PrimeGrid
| access-date = 2019-07-28
| archive-date = 2016-10-19
| archive-url = https://web.archive.org/web/20161019105748/http://www.primegrid.com/download/twin-1290000.pdf
| url-status = live
}}</ref>
|-
| [Twin prime](/source/Twin_Primes) Search
| {{No}}
| {{N/A}}
| 26 November 2006
| 25 July 2009
| data-sort-value="100354" | 65516468355 × 2<sup>333333</sup> ±&thinsp;1<ref>{{cite web
 |url          = https://www.primegrid.com/download/Twin333333.pdf
 |title        = PrimeGrid's Twin Prime Search
 |publisher    = PrimeGrid
 |access-date   = 2011-09-19
 |archive-url  = https://web.archive.org/web/20110926230509/http://www.primegrid.com/download/Twin333333.pdf
 |archive-date = 2011-09-26
 |url-status     = dead
}}</ref>
|-
| [Woodall Prime](/source/Woodall_prime) Search
| {{No}}
| {{Yes}}
| July 2007
| Ongoing
| data-sort-value="5122514" | 17016602 × 2<sup>17016602</sup> − 1, largest known Woodall prime<ref>{{cite web
 |url          = https://www.primegrid.com/download/WOO-17016602.pdf
 |title          = PrimeGrid's Woodall Prime Search
 |publisher          = PrimeGrid
 |access-date          = 2019-07-28
 |archive-date          = 2021-01-21
 |archive-url          = https://web.archive.org/web/20210121012221/https://www.primegrid.com/download/WOO-17016602.pdf
 |url-status          = live
 }}</ref>
|-
|Generalized Cullen/Woodall Prime Search
| {{No}}
| {{Yes}}
| 22 October 2016
| Ongoing
| data-sort-value="4705887" | 2525532 × 73<sup>2525532</sup> + 1, largest known generalized Cullen prime<ref>{{cite web
| url = https://www.primegrid.com/download/GC73-2525532.pdf
| title = PrimeGrid's Generalized Cullen/Woodall Prime Search
| publisher = PrimeGrid
| access-date = 2022-01-27
| archive-date = 2022-01-27
| archive-url = https://web.archive.org/web/20220127211019/http://primegrid.com/download/GC73-2525532.pdf
| url-status = live
}}</ref>
|-
| [Wieferich Prime](/source/Wieferich_prime) Search
| {{N/A}}
| {{N/A}}
| 2020<ref>{{cite web
| url = https://www.primegrid.com/forum_thread.php?id=9436
| title = Welcome to the Wieferich and Wall-Sun-Sun Prime Search
| publisher = PrimeGrid
| access-date = 2022-08-22
| archive-date = 2022-08-22
| archive-url = https://web.archive.org/web/20220822171847/https://www.primegrid.com/forum_thread.php?id=9436
| url-status = live
}}</ref>
| 2022
| {{N/A}}
|-
| [Wall-Sun-Sun Prime](/source/Wall%E2%80%93Sun%E2%80%93Sun_prime) Search
| {{N/A}}
| {{N/A}}
| 2020
| 2022
| {{N/A}}
|}

===321 Prime Search===

321 Prime Search is a continuation of Paul Underwood's [https://www.mersenneforum.org/forumdisplay.php?f=14 321 Search] which looked for primes of the form 3&nbsp;·&nbsp;2<sup>''n''</sup>&nbsp;−&nbsp;1. PrimeGrid added the +1 form and continues the search up to&nbsp;''n''&nbsp;=&nbsp;25''M''.

Primes known for 3&nbsp;·&nbsp;2<sup>''n''</sup>&nbsp;+&nbsp;1 occur at the following ''n'':
: 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 {{OEIS|A002253}}

Primes known for 3&nbsp;·&nbsp;2<sup>''n''</sup>&nbsp;−&nbsp;1 occur at the following ''n'':
: 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 {{OEIS|A002235}}

===PRPNet projects===
{| class="wikitable sortable"
|-
! Project
! Active?
! Start
! End
! Best result
|-
| 27 Prime Search
| {{No}}
| {{N/A}}
|  March 2022<ref>{{cite web|first1=Roman|last1=Trunov|title=The 27 project is almost finished|url=https://www.primegrid.com/forum_thread.php?id=9850|website=PrimeGrid|access-date=19 August 2022|archive-date=5 September 2022|archive-url=https://web.archive.org/web/20220905052349/https://www.primegrid.com/forum_thread.php?id=9850|url-status=live}}</ref>
| data-sort-value="1569461" | 27 × 2<sup>7046834</sup> + 1, largest known Sierpinski prime for ''b'' = 2 and ''k'' = 27<br>27×2<sup>8342438</sup> − 1, largest known Riesel prime for ''b'' = 2 and ''k'' = 27<ref>{{cite web |title=PrimeGrid Primes: 27 Prime Search |url=https://www.primegrid.com/primes/primes.php?project=27&factors=+&only=ALL&announcements=ALL&sortby=size&dc=no&search= |website=www.primegrid.com |access-date=2022-01-27 |archive-date=2022-01-27 |archive-url=https://web.archive.org/web/20220127084208/https://www.primegrid.com/primes/primes.php?project=27&factors=+&only=ALL&announcements=ALL&sortby=size&dc=no&search= |url-status=live }}</ref>
|-
| 121 Prime Search
| {{No}}
| {{N/A}}
| April 2021<ref>{{cite web|first1=Michael|last1=Goetz|title=The 121 project is almost finished|url=https://www.primegrid.com/forum_thread.php?id=9612|website=PrimeGrid|access-date=19 August 2022|archive-date=20 August 2022|archive-url=https://web.archive.org/web/20220820034220/https://www.primegrid.com/forum_thread.php?id=9612|url-status=live}}</ref>
| data-sort-value="1370862" | 121 × 2<sup>9584444</sup> − 1, largest known Sierpinski prime for ''b'' = 2 and ''k'' = 121<br>121 × 2<sup>4553899</sup> − 1, largest known Riesel prime for ''b'' = 2 and ''k'' = 121<ref>{{cite web |title=PrimeGrid Primes: 121 Prime Search |url=https://www.primegrid.com/primes/primes.php?project=121&factors=+&only=ALL&announcements=ALL&sortby=size&dc=no&search= |website=www.primegrid.com |access-date=2022-01-27 |archive-date=2022-01-27 |archive-url=https://web.archive.org/web/20220127084214/https://www.primegrid.com/primes/primes.php?project=121&factors=+&only=ALL&announcements=ALL&sortby=size&dc=no&search= |url-status=live }}</ref>
|-
| Extended [Sierpinski problem](/source/Sierpinski_problem)
| {{No}}
| {{N/A}}
| 2014
| data-sort-value="2758092" | 90527 × 2<sup>9162167</sup> + 1<ref>{{cite web
| url = https://t5k.org/primes/page.php?id=111554
| title = The Prime Database: 211195*2^3224974+1
| publisher = The Prime Pages
| access-date = 2023-03-12
| archive-date = 2013-12-22
| archive-url = https://web.archive.org/web/20131222202140/http://primes.utm.edu/primes/page.php?id=111554
| url-status = live
}}</ref>
|-
| [Factorial Prime](/source/Factorial_prime) Search
| {{Yes}}
| {{N/A}}
| Ongoing
| data-sort-value="700176" | 147855! − 1, 5th largest known factorial prime
|-
| Dual Sierpinski problem (Five or Bust)
| {{No}}
| {{N/A}}
| All were done (all PRPs were found)
| data-sort-value="2737082" | 2<sup>9092392</sup> + 40291
|-
| Generalized [Cullen](/source/Cullen_number)/[Woodall](/source/Woodall_number) Prime Search
| {{No}}
| {{N/A}}
| 2017<ref>{{cite web|last1=JimB|title=PRPNet GCW Port 12004 being closed soon|url=https://www.primegrid.com/forum_thread.php?id=7401&nowrap=true#107080|website=PrimeGrid|access-date=10 November 2017|archive-date=5 September 2022|archive-url=https://web.archive.org/web/20220905052349/https://www.primegrid.com/forum_thread.php?id=7401&nowrap=true#107080|url-status=live}}</ref>
| data-sort-value="877068" | 427194 × 113<sup>427194</sup> + 1, then largest known GCW prime<ref>{{cite web
| url = https://www.primegrid.com/download/gc113-427194.pdf
| title = PrimeGridʼs Generalized Cullen/Woodall Prime Search
| publisher = PrimeGrid
| access-date = 2014-03-09
| archive-date = 2013-11-26
| archive-url = https://web.archive.org/web/20131126234658/http://www.primegrid.com/download/gc113-427194.pdf
| url-status = live
}}</ref>
|-
| Mega Prime Search
| {{No}}
| {{N/A}}
| 2014
| data-sort-value="1052459" | 87 × 2<sup>3496188</sup> + 1, largest known prime for ''k'' = 87
|-
| [Primorial Prime](/source/Primorial_Prime) Search
| {{Yes}}
| 2008<ref>{{cite web | url = https://www.primegrid.com/old_news.php | title = PrimeGrid news archive | publisher = PrimeGrid | access-date = 2014-04-23 | archive-date = 2014-05-15 | archive-url = https://web.archive.org/web/20140515214737/http://www.primegrid.com/old_news.php | url-status = live }}</ref>
| Ongoing
| data-sort-value="476311" | 9562633# + 1 (4151498 digits), largest known primorial prime<ref>{{cite web
| url = https://t5k.org/top20/page.php?id=5#records
| title = PrimePage Primes: Primorial
| access-date = 2026-02-27
| url-status = live
}}</ref>
|-
| Proth Prime Search
| {{No}}
| 2008
| 2012<ref>{{cite web
| url = https://www.primegrid.com/forum_thread.php?id=4236&nowrap=true#55044
| title = PRPNet PPSELow on prpnet2.mine.nu will be closed.
| publisher = PrimeGrid
| access-date = 2013-07-13
| archive-date = 2015-09-24
| archive-url = https://web.archive.org/web/20150924112704/http://www.primegrid.com/forum_thread.php?id=4236&nowrap=true#55044
| url-status = live
}}</ref>
| data-sort-value="9383760" | 10223 × 2<sup>31172165</sup> + 1, largest known Proth prime
|-
| Sierpinski Riesel Base 5
| {{No}}
| 2009<ref>{{cite web
| url = https://www.primegrid.com/forum_thread.php?id=1212&nowrap=true#14864
| title = PRNet Discussion( Old )
| publisher = PrimeGrid
| access-date = 2013-07-01
| archive-date = 2013-08-17
| archive-url = https://web.archive.org/web/20130817015530/http://www.primegrid.com/forum_thread.php?id=1212&nowrap=true#14864
| url-status = live
}}</ref>
| 2013<ref>{{cite web
| url = https://www.primegrid.com/forum_thread.php?id=5110
| title = SR5 Has moved to BOINC, PRPNet port to close soon.
| publisher = PrimeGrid
| access-date = 2013-07-01
| archive-date = 2013-10-09
| archive-url = https://web.archive.org/web/20131009002021/http://primegrid.com/forum_thread.php?id=5110
| url-status = live
}}</ref>
| data-sort-value="1572122" | 180062 × 5<sup>2249192</sup> − 1
|-
| [Wieferich Prime](/source/Wieferich_prime) Search
| {{No}}
| 2012<ref name=Week>{{cite web
| url = https://www.primegrid.com/forum_thread.php?id=3890&nowrap=true#45950
| title = Welcome to a week of Wieferich and Wall-Sun-Sun
| publisher = PrimeGrid
| access-date = 2013-07-03
| archive-date = 2013-08-17
| archive-url = https://web.archive.org/web/20130817144351/http://www.primegrid.com/forum_thread.php?id=3890&nowrap=true#45950
| url-status = live
}}</ref>
| 2017<ref name="PRPNet no work">{{cite web|last=Goetz|first=Michael|title=WSS and WFS are suspended|url=https://www.primegrid.com/forum_thread.php?id=7436|website=PrimeGrid Forum|publisher=PrimeGrid|access-date=2020-09-06|archive-date=2020-10-01|archive-url=https://web.archive.org/web/20201001234940/https://www.primegrid.com/forum_thread.php?id=7436|url-status=live}}</ref>
| data-sort-value="16" | 82687771042557349, closest near-miss above 3 × 10<sup>15</sup>
|-
| [Wall-Sun-Sun Prime](/source/Wall%E2%80%93Sun%E2%80%93Sun_prime) Search
| {{No}}
| 2012<ref name=Week/>
| 2017<ref name="PRPNet no work"/>
| data-sort-value="15" | 6336823451747417, closest near-miss above 9.7 × 10<sup>14</sup>
|}

==Accomplishments==

===AP26===
One of PrimeGrid projects was AP26 Search which searched for a record 26 [primes in arithmetic progression](/source/primes_in_arithmetic_progression). The search was successful in April 2010 with the finding of the first known AP26:
: {{math|43142746595714191 + 23681770 · 23# · ''n''}} is prime for {{math|''n'' {{=}} 0, ..., 25}}.<ref>{{cite web
| url = https://www.primegrid.com/forum_thread.php?id=1246&nowrap=true#22466
| title = AP26 Found!!!
| author = John
| publisher = PrimeGrid
| access-date = 2011-09-19
| archive-date = 2011-09-14
| archive-url = https://web.archive.org/web/20110914084116/http://www.primegrid.com/forum_thread.php?id=1246&nowrap=true#22466
| url-status = live
}}</ref>
: {{Math|1=23# = 2·3·5·7·11·13·17·19·23 = 223092870}}, or 23 [primorial](/source/primorial), is the product of all primes up to 23.

===AP27===
Next target of the project was AP27 Search which searched for a record 27 [primes in arithmetic progression](/source/primes_in_arithmetic_progression). The search was successful in September 2019 with the finding of the first known AP27:
: {{math|224584605939537911 + 81292139 · 23# · ''n''}} is prime for {{math|''n'' {{=}} 0, ..., 26}}.<ref>{{cite web
| url = https://www.primegrid.com/forum_thread.php?id=7012&nowrap=true#133172
| title = AP27 Found!!!
| author = Michael Goetz
| publisher = PrimeGrid
| access-date = 2020-07-09
| archive-date = 2020-07-09
| archive-url = https://web.archive.org/web/20200709181832/https://www.primegrid.com/forum_thread.php?id=7012&nowrap=true#133172
| url-status = live
}}</ref>
: {{math|1=23# = 2·3·5·7·11·13·17·19·23 = 223092870}}, or 23 [primorial](/source/primorial), is the product of all primes up to 23.

===Cullen prime search===
PrimeGrid is also running a search for [Cullen prime](/source/Cullen_prime) 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 {{math|6679881 · 2<sup>6679881</sup> + 1}} at over 2 million digits.<ref>{{cite web
| url = https://t5k.org/top20/page.php?id=6
| title = The Top Twenty: Cullen primes
| publisher = The Prime Pages
| access-date = 2023-03-12
| archive-date = 2011-10-06
| archive-url = https://web.archive.org/web/20111006022800/http://primes.utm.edu/top20/page.php?id=6
| url-status = live
}}</ref>

===Generalized Fermat prime search===
On 24 September 2022, PrimeGrid discovered the largest known [Generalized Fermat prime](/source/Fermat_number) to date, {{math|1963736<sup>1048576</sup> + 1}}. This prime is 6,598,776 digits long and is only the second Generalized Fermat prime found for {{math|''n'' {{=}} 20}}. It ranks as the 13th largest known prime overall.<ref>{{cite web
| url = https://t5k.org/primes/page.php?id=134423
| title = 1963736^1048576+1 is prime!
| publisher = The Prime Pages
| access-date = 2023-03-12
| archive-date = 2022-10-08
| archive-url = https://web.archive.org/web/20221008183939/https://primes.utm.edu/primes/page.php?id=134423
| url-status = live
}}</ref>

===Riesel Problem===
{{as of|2022|12|13}}, PrimeGrid has eliminated 18 values of ''k'' from the [Riesel problem](/source/Riesel_number)<ref>{{cite web|url=http://www.primegrid.com/download/TRP-273809.pdf|title=PrimeGridʼs The Riesel Problem|publisher=PrimeGrid|access-date=2017-12-22|archive-date=2017-12-22|archive-url=https://web.archive.org/web/20171222162930/http://www.primegrid.com/download/TRP-273809.pdf|url-status=live}}</ref>
and is continuing the search to eliminate the 43 remaining numbers. 3 values of ''k'' are found by independent searchers.

===Twin prime search===
Primegrid worked with the [Twin Prime Search](/source/Twin_Prime_Search) to search for a record-sized [twin prime](/source/twin_prime) at approximately 58,700 digits. The new world's largest known twin prime {{math|2003663613 × 2<sup>195000</sup> ±&thinsp;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 {{math|65516468355 × 2<sup>333333</sup> ±&thinsp;1}}. Continued testing for twin primes in conjunction with the search for a [Sophie Germain prime](/source/Sophie_Germain_prime) yielded a new record twin prime in September 2016 upon finding the number {{math|2996863034895 × 2<sup>1290000</sup> ±&thinsp;1}} composed of 388,342 digits.

===Woodall prime search===
{{As of|2018|4|22}}, the project has discovered the four largest [Woodall primes](/source/Woodall_number) known to date.<ref>{{cite web
| url = https://t5k.org/top20/page.php?id=7
| title = The Top Twenty: Woodall Primes
| publisher = The Prime Pages
| access-date = 2023-03-12
| archive-date = 2023-01-20
| archive-url = https://web.archive.org/web/20230120060150/https://primes.utm.edu/top20/page.php?id=7
| url-status = live
}}</ref>
The largest of these is {{math|17016602 × 2<sup>17016602 </sup> − 1}} and was found on 21 March 2018.{{citation needed|date=February 2023}} The search continues for an even bigger Woodall prime.
PrimeGrid also found the largest known generalized Woodall prime,<ref>{{cite web
| url = https://t5k.org/top20/page.php?id=45
| title = The Top Twenty: Generalized Woodall
| publisher = The Prime Pages
| access-date = 2023-03-12
| archive-date = 2011-10-06
| archive-url = https://web.archive.org/web/20111006023222/http://primes.utm.edu/top20/page.php?id=45
| url-status = live
}}</ref>
{{math|563528 × 13<sup>563528</sup> − 1}}.

==Media coverage==
PrimeGrid's author Rytis Slatkevičius has been featured as a young entrepreneur in ''[The Economist](/source/The_Economist)''.<ref>{{cite news
| url = http://www.economist.com/science/tq/displaystory.cfm?story_id=10202635
| title = Spreading the load
| newspaper = [The Economist](/source/The_Economist)
| date = 2007-12-06
| access-date = 2010-02-08
| archive-date = 2009-12-18
| archive-url = https://web.archive.org/web/20091218025540/http://www.economist.com/science/tq/displaystory.cfm?story_id=10202635
| url-status = live
}}</ref>

PrimeGrid has also been featured in an article by [Francois Grey](/source/Francois_Grey) in the ''[CERN Courier](/source/CERN_Courier)'' and a talk about citizen cyberscience in [TEDx](/source/TEDx) Warwick conference.<ref>{{Cite news |title=Viewpoint: The Age of Citizen Cyberscience |url=http://cerncourier.com/cws/article/cern/38718 |author=Francois Grey |author-link=Francois Grey |work=[CERN Courier](/source/CERN_Courier) |date=2009-04-29 |access-date=2010-04-26 |archive-date=2010-03-23 |archive-url=https://web.archive.org/web/20100323091456/http://cerncourier.com/cws/article/cern/38718 |url-status=live }}</ref><ref>{{Cite podcast |title=Citizen Cyberscience |url=https://www2.warwick.ac.uk/newsandevents/podcasts/media/more/tedx?podcastItem=francois_grey.mp4 |author=Francois Grey |date=2009-03-26 |access-date=2010-04-26 |archive-date=2011-03-09 |archive-url=https://web.archive.org/web/20110309144809/http://www2.warwick.ac.uk/newsandevents/podcasts/media/more/tedx/?podcastItem=francois_grey.mp4 |url-status=live }}</ref>

In the first [Citizen Cyberscience Summit](/source/Citizen_Cyberscience_Summit), Rytis Slatkevičius gave a talk as a founder of PrimeGrid, named ''Finding primes: from digits to digital technology'',<ref>{{citation
 |url         = http://www.citizencyberscience.net/summit/CCC-programme.htm
 |url-status    = dead
 |title       = Finding primes: from digits to digital technology
 |author      = Rytis Slatkevičius
 |date        = 2010-09-02
 |access-date  = 2010-12-03
 |archive-url  = https://web.archive.org/web/20100915130639/http://www.citizencyberscience.net/summit/CCC-programme.htm
 |archive-date = 2010-09-15
}}</ref>
relating mathematics and volunteering and featuring the history of the project.<ref>{{citation
| url = https://citizencyberscience.blogspot.com/2010/08/giant-prime-numbers.html
| title = Giant Prime Numbers
| author = Rytis Slatkevičius
| date = 2010-08-13
| access-date = 2010-12-03
| archive-date = 2011-07-08
| archive-url = https://web.archive.org/web/20110708031228/http://citizencyberscience.blogspot.com/2010/08/giant-prime-numbers.html
| url-status = live
}}</ref>

==References==
{{Reflist|colwidth=30em}}

==External links==
* {{Official website}}
*[//www.discord.com/channels/357493752434130944/ PrimeGrid Discord chat server] (almost daily discovery announcements)
*[https://t5k.org/bios/page.php?id=950 PrimeGrid's results] at [The Prime Pages](/source/The_Prime_Pages)

{{Commons}}

{{BOINC topics}}

{{DEFAULTSORT:PrimeGrid}}
Category:Science in society
Category:Free science software
Category:Volunteer computing projects
Category:Distributed prime searches
Category:Cross-platform free software

---
Adapted from the Wikipedia article [PrimeGrid](https://en.wikipedia.org/wiki/PrimeGrid) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/PrimeGrid?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.