PrimeGrid

History

PrimeGrid started in June 2005 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 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.

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

In addition, PrimeGrid is helping test for a record Sophie Germain prime.

Projects

As of March 2016, PrimeGrid is working on or has worked on the following projects:

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 (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, 11484018 (sequence A002235 in the OEIS)

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# = 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 was PrimeGrid's largest prime found 6679881 · 2^6679881+1 at over 2 million digits.

Riesel Problem

As of 9 March 2014 PrimeGrid has eliminated 14 values of k from the Riesel problem and is continuing the search to eliminate the 50 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 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 Sophie Germain prime yielded a new record twin prime on September 2016 upon finding the number 2996863034895 × 2^1290000 ± 1 composed of 388,342 digits.

Woodall prime search

As of 22 April 2010, the project has discovered the three largest Woodall primes known to date. The largest of these, 3752948 × 2^3752948 − 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. The search continues for an even bigger Woodall prime. PrimeGrid also found the largest known generalized Woodall prime, 563528 × 13⁵⁶³⁵²⁸ − 1.

Media coverage

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

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.

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.