PrimeGrid explained

Author:Rytis Slatkevičius
Released:[1]
Status:Active
Goal:Finding prime numbers of various types
Software:PRPNet, Genefer, LLR, PFGW
Funding:Corporate sponsorship, crowdfunding[2] [3]
Performance:3,398.914 TFLOPS[4]
Active Users:2,330 (August 2022)
Total Users:353,245
Active Hosts:11,504 (August 2022)
Total Hosts:21,985
Platform:BOINC
Screenshot Caption:PrimeGrid screensaver
Screenshot Size:250px

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.

History

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.

Projects

, PrimeGrid is working on or has worked on the following projects:

ProjectActive sieve project?Active LLR project?StartEndBest result
321 Prime Search (primes of the form 3 × 2n ± 1)30 June 2008Ongoingdata-sort-value="5477721" 3 × 218196595 − 1, largest prime found in the 321 Prime Search project[8]
AP26 Search (Arithmetic progression of 26 primes)27 December 200812 April 2010data-sort-value="17.2435" 43142746595714191 + 23681770 × 23# × n, n = 0, ..., 25 (AP26)[9]
AP27 Search (Arithmetic progression of 27 primes)20 September 2016Ongoingdata-sort-value="17.8427" 224584605939537911 + 81292139 × 23# × n, n = 0, ..., 26 (AP27)[10]
Generalized Fermat Prime Search[11] [12]
(active: n = 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304 inactive: n = 8192, 16384)
(manual sieving)January 2012Ongoingdata-sort-value="6598776" 19637361048576 + 1, largest known Generalized Fermat prime[13]
Cullen Prime SearchAugust 2007Ongoingdata-sort-value="2010851" 6679881 × 26679881 + 1, largest known Cullen prime[14]
Message712 June 2005August 2005PerlBOINC testing successful
Prime Sierpinski Problem10 July 2008Ongoingdata-sort-value="5832521" 168451 × 219375200 + 1[15]
Extended Sierpinski Problem7 June 2014Ongoingdata-sort-value="6418120" 202705 × 221320516 + 1, largest prime found in the Extended Sierpinski Problem[16]
PrimeGenMarch 2006February 2008
Proth Prime Search29 February 2008Ongoingdata-sort-value="1738748" 7 × 25775996 + 1[17]
Riesel ProblemMarch 2010Ongoingdata-sort-value="3429396" 9221 × 211392194 − 1, [18]
RSA-640August 2005November 2005
RSA-768November 2005March 2006
Seventeen or Bust31 January 2010Ongoingdata-sort-value="9383760" 10223 × 231172165 + 1
Sierpinski/Riesel Base 5 Problem14 June 2013Ongoingdata-sort-value="2892597" 213988×54138363 − 1, largest prime found in the Sierpinski/Riesel Base 5 Problem
Sophie Germain Prime Search16 August 2009Ongoingdata-sort-value="388341" 2618163402417 × 21290000 − 1 (2p − 1 = 2618163402417 × 21290001 − 1), the world record Sophie Germain prime;[19] and 2996863034895 × 21290000 ± 1, the world record twin primes[20]
Twin prime Search26 November 200625 July 2009data-sort-value="100354" 65516468355 × 2333333 ± 1[21]
Woodall Prime SearchJuly 2007Ongoingdata-sort-value="5122514" 17016602 × 217016602 − 1, largest known Woodall prime[22]
Generalized Cullen/Woodall Prime Search22 October 2016Ongoingdata-sort-value="4705887" 2525532 × 732525532 + 1, largest known generalized Cullen prime[23]
Wieferich Prime Search2020[24] 2022
Wall-Sun-Sun Prime Search20202022

321 Prime Search

321 Prime Search is a continuation of Paul Underwood's 321 Search 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:

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

Primes known for 3 · 2n − 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

PRPNet projects

ProjectActive?StartEndBest result
27 Prime SearchMarch 2022[25] 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[26]
121 Prime SearchApril 2021[27] 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[28]
Extended Sierpinski problem2014data-sort-value="2758092" 90527 × 29162167 + 1[29]
Factorial Prime SearchOngoingdata-sort-value="700176" 147855! − 1, 5th largest known factorial prime
Dual Sierpinski problem (Five or Bust)All were done (all PRPs were found)data-sort-value="2737082" 29092392 + 40291
Generalized Cullen/Woodall Prime Search2017[30] data-sort-value="877068" 427194 × 113427194 + 1, then largest known GCW prime[31]
Mega Prime Search2014data-sort-value="1052459" 87 × 23496188 + 1, largest known prime for k = 87
Primorial Prime Search2008[32] Ongoingdata-sort-value="476311" 3267113# − 1, largest known primorial prime[33]
Proth Prime Search20082012[34] data-sort-value="9383760" 10223 × 231172165 + 1, largest known Proth prime
Sierpinski Riesel Base 52009[35] 2013[36] data-sort-value="1572122" 180062 × 52249192 − 1
Wieferich Prime Search2012[37] 2017[38] data-sort-value="16" 82687771042557349, closest near-miss above 3 × 1015
Wall-Sun-Sun Prime Search20122017data-sort-value="15" 6336823451747417, closest near-miss above 9.7 × 1014

Accomplishments

AP26

One of PrimeGrid projects was AP26 Search which searched for a record 26 primes in arithmetic progression. The search was successful in April 2010 with the finding of the first known AP26:

is prime for .[39]

, or 23 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. The search was successful in September 2019 with the finding of the first known AP27:

is prime for .[40]

, or 23 primorial, is the product of all primes up to 23.

Cullen prime search

PrimeGrid is also running a search for 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 at over 2 million digits.[41]

Generalized Fermat prime search

On 24 September 2022, PrimeGrid discovered the largest known Generalized Fermat prime to date, . This prime is 6,598,776 digits long and is only the second Generalized Fermat prime found for . It ranks as the 13th largest known prime overall.[42]

Riesel Problem

, PrimeGrid has eliminated 18 values of k from the Riesel problem[43] 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 to search for a record-sized twin prime at approximately 58,700 digits. The new world's largest known twin prime 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 . Continued testing for twin primes in conjunction with the search for a Sophie Germain prime yielded a new record twin prime in September 2016 upon finding the number composed of 388,342 digits.

Woodall prime search

, the project has discovered the four largest Woodall primes known to date.[44] The largest of these is and was found in 21 March 2018. The search continues for an even bigger Woodall prime.PrimeGrid also found the largest known generalized Woodall prime,[45] .

Media coverage

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,relating mathematics and volunteering and featuring the history of the project.

External links

Notes and References

  1. Web site: PrimeGrid's Challenge Series - 2008 Final Standings . PrimeGrid . 2011-09-19 . 2011-09-26 . https://web.archive.org/web/20110926230014/http://www.primegrid.com/challenge/2008_challenge.php . live .
  2. Web site: PrimeGrid's new server (again) . PrimeGrid . 2016-10-09 . 2017-02-08 . https://web.archive.org/web/20170208020307/http://www.primegrid.com/forum_thread.php?id=5233&nowrap=true#68716 . live .
  3. Web site: Donations to PrimeGrid. 2018-07-27. 2018-07-27. https://web.archive.org/web/20180727085006/https://www.primegrid.com/donations.php. live.
  4. Web site: PrimeGrid - Detailed Stats. BOINCstats. 21 August 2022. 17 September 2017. https://web.archive.org/web/20170917213948/https://boincstats.com/en/stats/11/project/detail/overview. live.
  5. Web site: Prime Lists . PrimeGrid . 2011-09-19 . https://web.archive.org/web/20100530071550/http://primegrid.com/orig/torrent.php . 2010-05-30 . dead.
  6. Web site: PrimeGrid forum: PPS Sieve. John. PrimeGrid. 2011-09-19. 2011-09-26. https://web.archive.org/web/20110926225430/http://www.primegrid.com/forum_thread.php?id=973. live.
  7. Web site: PrimeGrid forum: Seventeen or Bust and the Sierpinski Problem. John. PrimeGrid. 2011-09-19. 2011-09-26. https://web.archive.org/web/20110926225718/http://www.primegrid.com/forum_thread.php?id=1647. live.
  8. Web site: PrimePage Primes: 3·2^18196595 - 1 . t5k.org . 12 March 2023 . 23 January 2022 . https://web.archive.org/web/20220123094556/https://primes.utm.edu/primes/page.php?id=133193 . live .
  9. Web site: PrimeGrid's AP26 Search. PrimeGrid. 2011-09-19. 2011-09-26. https://web.archive.org/web/20110926231931/http://www.primegrid.com/download/AP26.pdf. live.
  10. Web site: PrimeGrid's AP26 Search. PrimeGrid. 2019-10-23. 2019-10-05. https://web.archive.org/web/20191005202722/https://www.primegrid.com/download/AP27-81292139.pdf. live.
  11. Web site: Genefer statistics . PrimeGrid . 2015-11-04 . 2019-06-23 . https://web.archive.org/web/20190623190358/http://www.primegrid.com/stats_genefer.php . live .
  12. Web site: GFN Prime Search Status and History. PrimeGrid. 2017-03-04. 2017-03-05. https://web.archive.org/web/20170305035335/http://www.primegrid.com/gfn_history.php. live.
  13. Web site: PrimeGrid's Generalized Fermat Prime Search. PrimeGrid. 2019-07-28. 2021-01-15. https://web.archive.org/web/20210115172745/http://www.primegrid.com/download/GFN-1059094_1048576.pdf. live.
  14. Web site: PrimeGrid's Cullen Prime Search . PrimeGrid . 2011-09-19 . https://web.archive.org/web/20110926231457/http://www.primegrid.com/download/Cullen6679881.pdf . 2011-09-26 . dead.
  15. Web site: PrimeGrid's Prime Sierpinski Problem. PrimeGrid. 2019-07-28. 2019-07-16. https://web.archive.org/web/20190716113614/http://www.primegrid.com/download/PSP_168451.pdf. live.
  16. Web site: PrimeGrid's Extended Sierpinski Problem. PrimeGrid. 2022-01-27. 2022-01-27. https://web.archive.org/web/20220127205849/http://primegrid.com/download/ESP-202705.pdf. live.
  17. Web site: PrimeGrid's Proth Prime Search. PrimeGrid. 10 March 2016. 4 March 2016. https://web.archive.org/web/20160304201330/http://www.primegrid.com/download/PPS-5775996.pdf. live.
  18. Web site: PrimeGrid's The Riesel Problem. PrimeGrid. 2022-01-27. 2022-01-27. https://web.archive.org/web/20220127205820/http://primegrid.com/download/TRP-9221.pdf. live.
  19. Web site: World Record Sophie Germain prime. PrimeGrid. 2019-07-28. 2019-07-16. https://web.archive.org/web/20190716110354/http://www.primegrid.com/download/SGS_2618163402417_1290000.pdf. live.
  20. Web site: World Record Sophie Germain prime. PrimeGrid. 2019-07-28. 2016-10-19. https://web.archive.org/web/20161019105748/http://www.primegrid.com/download/twin-1290000.pdf. live.
  21. Web site: PrimeGrid's Twin Prime Search . PrimeGrid . 2011-09-19 . https://web.archive.org/web/20110926230509/http://www.primegrid.com/download/Twin333333.pdf . 2011-09-26 . dead.
  22. Web site: PrimeGrid's Woodall Prime Search . PrimeGrid . 2019-07-28 . 2021-01-21 . https://web.archive.org/web/20210121012221/https://www.primegrid.com/download/WOO-17016602.pdf . live .
  23. Web site: PrimeGrid's Generalized Cullen/Woodall Prime Search. PrimeGrid. 2022-01-27. 2022-01-27. https://web.archive.org/web/20220127211019/http://primegrid.com/download/GC73-2525532.pdf. live.
  24. Web site: Welcome to the Wieferich and Wall-Sun-Sun Prime Search. PrimeGrid. 2022-08-22. 2022-08-22. https://web.archive.org/web/20220822171847/https://www.primegrid.com/forum_thread.php?id=9436. live.
  25. Web site: Roman. Trunov. The 27 project is almost finished. PrimeGrid. 19 August 2022. 5 September 2022. https://web.archive.org/web/20220905052349/https://www.primegrid.com/forum_thread.php?id=9850. live.
  26. Web site: PrimeGrid Primes: 27 Prime Search . www.primegrid.com . 2022-01-27 . 2022-01-27 . 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= . live .
  27. Web site: Michael. Goetz. The 121 project is almost finished. PrimeGrid. 19 August 2022. 20 August 2022. https://web.archive.org/web/20220820034220/https://www.primegrid.com/forum_thread.php?id=9612. live.
  28. Web site: PrimeGrid Primes: 121 Prime Search . www.primegrid.com . 2022-01-27 . 2022-01-27 . 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= . live .
  29. Web site: The Prime Database: 211195*2^3224974+1. The Prime Pages. 2023-03-12. 2013-12-22. https://web.archive.org/web/20131222202140/http://primes.utm.edu/primes/page.php?id=111554. live.
  30. Web site: JimB. PRPNet GCW Port 12004 being closed soon. PrimeGrid. 10 November 2017. 5 September 2022. https://web.archive.org/web/20220905052349/https://www.primegrid.com/forum_thread.php?id=7401&nowrap=true#107080. live.
  31. Web site: PrimeGridʼs Generalized Cullen/Woodall Prime Search. PrimeGrid. 2014-03-09. 2013-11-26. https://web.archive.org/web/20131126234658/http://www.primegrid.com/download/gc113-427194.pdf. live.
  32. Web site: PrimeGrid news archive . PrimeGrid . 2014-04-23 . 2014-05-15 . https://web.archive.org/web/20140515214737/http://www.primegrid.com/old_news.php . live .
  33. Web site: PrimeGridʼs Primorial Prime Search. PrimeGrid. 2014-03-09. 2013-11-26. https://web.archive.org/web/20131126234358/http://www.primegrid.com/download/prs-1098133.pdf. live.
  34. Web site: PRPNet PPSELow on prpnet2.mine.nu will be closed.. PrimeGrid. 2013-07-13. 2015-09-24. https://web.archive.org/web/20150924112704/http://www.primegrid.com/forum_thread.php?id=4236&nowrap=true#55044. live.
  35. Web site: PRNet Discussion(Old). PrimeGrid. 2013-07-01. 2013-08-17. https://web.archive.org/web/20130817015530/http://www.primegrid.com/forum_thread.php?id=1212&nowrap=true#14864. live.
  36. Web site: SR5 Has moved to BOINC, PRPNet port to close soon.. PrimeGrid. 2013-07-01. 2013-10-09. https://web.archive.org/web/20131009002021/http://primegrid.com/forum_thread.php?id=5110. live.
  37. Web site: Welcome to a week of Wieferich and Wall-Sun-Sun. PrimeGrid. 2013-07-03. 2013-08-17. https://web.archive.org/web/20130817144351/http://www.primegrid.com/forum_thread.php?id=3890&nowrap=true#45950. live.
  38. Web site: Goetz. Michael. WSS and WFS are suspended. PrimeGrid Forum. PrimeGrid. 2020-09-06. 2020-10-01. https://web.archive.org/web/20201001234940/https://www.primegrid.com/forum_thread.php?id=7436. live.
  39. Web site: AP26 Found!!!. John. PrimeGrid. 2011-09-19. 2011-09-14. https://web.archive.org/web/20110914084116/http://www.primegrid.com/forum_thread.php?id=1246&nowrap=true#22466. live.
  40. Web site: AP27 Found!!!. Michael Goetz. PrimeGrid. 2020-07-09. 2020-07-09. https://web.archive.org/web/20200709181832/https://www.primegrid.com/forum_thread.php?id=7012&nowrap=true#133172. live.
  41. Web site: The Top Twenty: Cullen primes. The Prime Pages. 2023-03-12. 2011-10-06. https://web.archive.org/web/20111006022800/http://primes.utm.edu/top20/page.php?id=6. live.
  42. Web site: 1963736^1048576+1 is prime!. The Prime Pages. 2023-03-12. 2022-10-08. https://web.archive.org/web/20221008183939/https://primes.utm.edu/primes/page.php?id=134423. live.
  43. Web site: PrimeGridʼs The Riesel Problem. PrimeGrid. 2017-12-22. 2017-12-22. https://web.archive.org/web/20171222162930/http://www.primegrid.com/download/TRP-273809.pdf. live.
  44. Web site: The Top Twenty: Woodall Primes. The Prime Pages. 2023-03-12. 2023-01-20. https://web.archive.org/web/20230120060150/https://primes.utm.edu/top20/page.php?id=7. live.
  45. Web site: The Top Twenty: Generalized Woodall. The Prime Pages. 2023-03-12. 2011-10-06. https://web.archive.org/web/20111006023222/http://primes.utm.edu/top20/page.php?id=45. live.
  46. News: Spreading the load. The Economist. 2007-12-06. 2010-02-08. 2009-12-18. https://web.archive.org/web/20091218025540/http://www.economist.com/science/tq/displaystory.cfm?story_id=10202635. live.
  47. News: Viewpoint: The Age of Citizen Cyberscience . Francois Grey . Francois Grey . . 2009-04-29 . 2010-04-26 . 2010-03-23 . https://web.archive.org/web/20100323091456/http://cerncourier.com/cws/article/cern/38718 . live .
  48. Citizen Cyberscience . Francois Grey . 2009-03-26 . 2010-04-26 . 2011-03-09 . https://web.archive.org/web/20110309144809/http://www2.warwick.ac.uk/newsandevents/podcasts/media/more/tedx/?podcastItem=francois_grey.mp4 . live .