PrimeGrid: Difference between revisions
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=== Riesel Problem === |
=== Riesel Problem === |
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{{as of| |
{{as of|2013|10|10}} PrimeGrid has eliminated 10 ''k'' from the [[Riesel number|Riesel problem]]<ref>{{cite web |
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| url = http://www.primegrid.com/download/TRP-398023.pdf |
| url = http://www.primegrid.com/download/TRP-398023.pdf |
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| title = PrimeGridʼs The Riesel Problem |
| title = PrimeGridʼs The Riesel Problem |
Revision as of 09:20, 11 October 2013
File:Primegrid logo.png | |
Original author(s) | Rytis Slatkevičius |
---|---|
Initial release | June 12, 2005[1] |
Development status | Active |
Project goal(s) | Finding prime numbers of various types |
Funding | Donations[2] |
Website | primegrid.com |
PrimeGrid is a distributed computing project for searching for prime numbers of world-record size. It makes use of the Berkeley Open Infrastructure for Network Computing (BOINC) platform. As of September 2011[update], there are about 7,500 active participants (on about 16,000 host computers) from 114 countries with a total BOINC credit of more than 112.16 billion, reporting about 1.663 petaflops (1.663 quadrillion operations per second) of processing power.[3]
History
PrimeGrid started in June 2005[1] under the name Message@home and tried to decipher text fragments encrypted 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[4] 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. 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. PrimeGrid and TPS then advanced their search for even larger twin primes.
The summer of 2007 was very active as 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 2007, PrimeGrid migrated its systems from PerlBOINC to standard BOINC software.
Since September 2008, PrimeGrid is also running a Proth prime sieving subproject.[5]
In January 2010 the subproject Seventeen or Bust was added.[6] The calculations for the Riesel problem followed in March 2010.
In addition, PrimeGrid is helping test for a record Sophie Germain prime and sieving for The Sierpinski Problem.
On 1 August 2013, Primegrid suffered an unrecoverable database crash which corrupted the BOINC database. The BOINC server became on line at about 2120 UTC. All data between 0800 UTC and 2120 UTC was lost including some potential prime discoveries.[7]
Projects
As of January 2012[update], PrimeGrid is working on or has worked on the following projects:
Project | Active sieve project? | Active LLR project? | Start | End | Best result |
---|---|---|---|---|---|
321 Prime Search (primes of the form 3×2n±1) | No | Yes | 30 June 2008 | Ongoing | 3×27033641+1[8] |
AP26 Search (Arithmetic progression of 26 primes) | — | — | 27 December 2008 | 12 April 2010 | 43142746595714191 + 23681770×23#×n, n = 0…25 (AP26)[9] |
Generalized Fermat Prime Search[10] (active: n = 1048576, 4194304 inactive: n = 8192, 16384, 32768, 65536, 131072, 262144, 524288, (n = 32768, 65536, 262144, 524288 are being run in PRPNet)) |
No | Yes (PRP) | January 2012 | Ongoing | 475856524288+1, largest known Generalized Fermat prime[11] |
Cullen Prime Search | No | Yes | August 2007 | Ongoing | 6679881×26679881+1, largest known Cullen prime[12] |
Message7 | No | — | 12 June 2005 | August 2005 | PerlBOINC testing successful |
Prime Sierpinski Problem | No | Yes | 10 July 2008 | Ongoing | — |
PrimeGen | No | — | March 2006 | February 2008 | — |
Proth Prime Search | Yes | Yes | 29 February 2008 | Ongoing | 659×2617815+1, divides F617813[13] |
Riesel Problem | Yes | Yes | March 2010 | Ongoing | 252191×25497878-1 |
RSA640 | No | — | August 2005 | November 2005 | N/A |
RSA768 | No | — | November 2005 | March 2006 | — |
Seventeen or Bust | No | Yes | 31 January 2010 | Ongoing | — |
Sierpinski/Riesel Base 5 Problem | No | Yes | 14 June 2013 | Ongoing | — |
Sophie Germain Prime Search | No | Yes | 16 August 2009 | Ongoing | 18543637900515×2666667-1(2p-1:18543637900515*2666668-1), the largest Sophie Germain prime[14] |
Twin Prime Search | No | — | 26 November 2006 | 25 July 2009 | 65516468355×2333333±1, largest known twin primes[15] |
Woodall Prime Search | No | Yes | July 2007 | Ongoing | 3752948×23752948−1, largest known Woodall prime[16] |
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 (sequence A002253 in the OEIS)
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 (sequence A002235 in the OEIS)
PRPNet projects
Project | Active? | Start | End | Best result |
---|---|---|---|---|
27 Prime Search | Yes | — | Ongoing | 27×23855094−1, largest known prime for k = 27[17] |
121 Prime Search | Yes | — | Ongoing | 121×24553899−1, largest known prime for k = 121[18] |
Extended Sierpinski problem | Yes | — | Ongoing | 211195×23224974+1 |
Factorial Prime Search | Yes | — | Ongoing | 110059!+1, largest known factorial prime |
Dual Sierpinski problem (Five or Bust) | No | — | — | — |
Generalized Cullen/Woodall Prime Search | Yes | — | Ongoing | 427194×113427194 + 1, largest known GCW prime |
Mega Prime Search | Yes | — | Ongoing | 81×23352924 + 1, largest known prime for k = 81 |
Primorial Prime Search | Yes | — | Ongoing | 1098133#−1, largest known primorial prime |
Proth Prime Search | No | 2008 | 2012[19] | — |
Sierpinski Riesel Base 5 | No | 2009[20] | 2013[21] | — |
Wieferich Prime Search | Yes | 2012[22] | Ongoing | 82687771042557349, closest near-miss above 3×1015 |
Wall-Sun-Sun Prime Search | Yes | 2012[22] | Ongoing | 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:
- 43142746595714191 + 23681770 · 23# · n is prime for n = 0, ..., 25.[23]
- 23# = 2·3·5·7·11·13·17·19·23 = 223092870, 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 is PrimeGrid's largest prime found 6679881 · 26679881+1 at over 2 million digits.[24]
Riesel Problem
As of 10 October 2013[update] PrimeGrid has eliminated 10 k from the Riesel problem[25] and is continuing the search to eliminate the remaining numbers.
Twin prime search
Primegrid then worked with the Twin Prime Search to search for a record-sized twin prime at approximately 58700 digits. The new worlds 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 100000 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 Sophie Germain prime yielded a new record twin prime on December 25, 2011 upon finding the number 3756801695685× 2666669 ± 1 composed of 200,700 digits.
Woodall prime search
As of 22 April 2010[update], the project has discovered the three largest Woodall primes known to date.[26] The largest of these, 3752948 × 23752948 − 1, is the first mega prime discovered by the project and is 1129757 digits long. It was discovered on December 21, 2007 by Matthew J Thompson using the LLR program.[27] The search continues for an even bigger Woodall prime. PrimeGrid also found the largest known generalized Woodall prime,[28] 563528 × 13563528 − 1.
Media coverage
PrimeGrid's author Rytis Slatkevičius has been featured as a young entrepreneur in The Economist.[29]
PrimeGrid has also been featured in an article by Francois Grey in the CERN Courier[30] and a talk about citizen cyberscience in TEDx Warwick conference.[31]
In the first Citizen Cyberscience Summit, Rytis Slatkevičius gave a talk as a founder of PrimeGrid, named Finding primes: from digits to digital technology,[32] relating mathematics and volunteering and featuring the history of the project.[33]
References
- ^ a b "PrimeGrid's Challenge Series - 2008 Final Standings". PrimeGrid. Retrieved 2011-09-19.
- ^ "Donations to PrimeGrid". PrimeGrid. Retrieved 2013-06-17.
- ^ "Prime Grid Credit Overview". BOINC. (updated automatically). Retrieved 2011-09-19.
{{cite web}}
: Check date values in:|date=
(help) - ^ "Prime Lists". PrimeGrid. Retrieved 2011-09-19.
- ^ John. "PrimeGrid forum: PPS Sieve". PrimeGrid. Retrieved 2011-09-19.
- ^ John. "PrimeGrid forum: Seventeen or Bust and the Sierpinski Problem". PrimeGrid. Retrieved 2011-09-19.
- ^ Michael Goetz. "PrimeGrid Database Crash". PrimeGrid. Retrieved 2013-08-02.
- ^ "PrimeGrid's 321 Prime Search" (PDF). PrimeGrid. Retrieved 2011-11-21.
- ^ "PrimeGrid's AP26 Search" (PDF). PrimeGrid. Retrieved 2011-09-19.
- ^ "Genefer statistics". PrimeGrid. Retrieved 2013-06-17.
- ^ "PrimeGrid's Generalized Fermat Prime Search" (PDF). PrimeGrid. Retrieved 2012-08-08.
- ^ "PrimeGrid's Cullen Prime Search" (PDF). PrimeGrid. Retrieved 2011-09-19.
- ^ "PrimeGrid's Proth Prime Search" (PDF). PrimeGrid. Retrieved 2011-09-19.
- ^ "World Record Sophie Germain prime" (PDF). PrimeGrid.
- ^ "PrimeGrid's Twin Prime Search" (PDF). PrimeGrid. Retrieved 2011-09-19.
- ^ "PrimeGrid's Woodall Prime Search" (PDF). PrimeGrid. Retrieved 2011-09-19.
- ^ "PrimeGrid's 27121 Prime Search" (PDF). PrimeGrid. Retrieved 2013-06-30.
- ^ "PrimeGrid's 27121 Prime Search" (PDF). Retrieved 2013-06-30.
- ^ "PRPNet PPSELow on prpnet2.mine.nu will be closed". PrimeGrid. Retrieved 2013-07-13.
- ^ "PRNet Discussion( Old )". PrimeGrid. Retrieved 2013-07-01.
- ^ "SR5 Has moved to BOINC, PRPNet port to close soon". PrimeGrid. Retrieved 2013-07-01.
- ^ a b "Welcome to a week of Wieferich and Wall-Sun-Sun". PrimeGrid. Retrieved 2013-07-03.
- ^ John. "AP26 Found!!!". PrimeGrid. Retrieved 2011-09-19.
- ^ "The Top Twenty: Cullen primes". University of Tennessee Martin. Retrieved 2011-09-19.
- ^ "PrimeGridʼs The Riesel Problem" (PDF). PrimeGrid. Retrieved 2013-10-10.
- ^ "The Top Twenty: Woodall Primes". University of Tennessee Martin. Retrieved 2011-09-19.
- ^ kp1139 (2007-12-28). "Cullen/Woodall prime search: First Woodall Mega Prime". PrimeGrid. Retrieved 2011-09-19.
{{cite web}}
: CS1 maint: numeric names: authors list (link) - ^ "The Top Twenty: Generalized Woodall". University of Tennessee Martin. Retrieved 2011-09-19.
- ^ "Spreading the load". The Economist. 2007-12-06. Retrieved 2010-02-08.
- ^ Francois Grey (2009-04-29). "Viewpoint: The age of citizen cyberscience". CERN Courier. Retrieved 26 April 2010.
- ^ Francois Grey (2009-03-26), Citizen Cyberscience, retrieved 2010-04-26
- ^ Rytis Slatkevičius (2010-09-02), Finding primes: from digits to digital technology, retrieved 2010-12-03
- ^ Rytis Slatkevičius (2010-08-13), Giant Prime Numbers, retrieved 2010-12-03