About
PrimeGrid's primary goal is to advance mathematics by enabling everyday computer users to contribute their system's processing power towards prime finding. By simply
downloading and installing BOINC and attaching to the PrimeGrid project,
participants can choose from a variety of prime forms to search. With a little patience, you may find a large or even record
breaking prime and enter into Chris Caldwell's The Largest Known Primes Database with a multi-million digit prime!
PrimeGrid's secondary goal is to provide relevant educational materials about primes. Additionally, we wish to contribute to the
field of mathematics.
Lastly, primes play a central role in the cryptographic systems which are used for computer security. Through the study of prime
numbers it can be shown how much processing is required to crack an encryption code and thus to determine whether current
security schemes are sufficiently secure. PrimeGrid is currently running several sub-projects:
- 321 Prime Search: searching for
mega primes of the form 3·2n±1.
- Cullen-Woodall Search: searching for
mega primes of forms n·2n+1 and
n·2n−1.
- Generalized Cullen-Woodall Search: searching for mega primes of forms n·bn+1 and
n·bn−1 where n + 2 > b.
- Extended Sierpinski Problem: helping solve the Extended Sierpinski Problem.
- Generalized Fermat Prime Search: searching for
megaprimes of the form b2n+1.
- Prime Sierpinski Project: helping the Prime Sierpinski Project solve the Prime Sierpinski Problem.
- Proth Prime Search: searching for primes of the form k·2n+1.
- Fermat Divisor Search: a subset of the Proth Prime Search specificically searching for divisors of
Fermat numbers.
- Seventeen or Bust: helping to solve the Sierpinski Problem.
- Sierpinski/Riesel Base 5: helping to solve the Sierpinski/Riesel Base 5 Problem.
- Sophie Germain Prime Search: searching for primes p and 2p+1.
- The Riesel problem: helping to solve the Riesel Problem.
- AP27 Search: searching for record length arithmetic progressions of primes.
Recent Significant Primes
On 9 August 2022, 11:56:02 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime
19517341048576+1
The prime is 6,595,985 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 1 st for Generalized Fermat primes and 13 th overall. This is the second-largest prime found by PrimeGrid, and the second-largest non-Mersenne prime.
The discovery was made by Kazuya Tanaka ( apophise@jisaku) of Japan using an NVIDIA GeForce RTX 3080 Ti in an Intel(R) Core(TM) i7-9700K CPU @ 3.60GHz with 64GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 1 hour, 2 minutes to complete the probable prime (PRP) test using GeneferOCL5. Kazuya Tanaka is a member of Team 2ch.
The prime was verified on 10 August 2022, 17:39:14 UTC by Jens Katzur ( Landjunge) of Germany using an NVIDIA GeForce RTX 3070 in an Intel(R) Xeon(R) CPU X5675 @ 3.07GHz with 40GB RAM, running Linux Ubuntu.
This computer took about 1 hour, 36 minutes to complete the probable prime (PRP) test using GeneferOCL5. Jens Katzur is a member of Planet 3DNow!.
The PRP was confirmed prime on 11 August 2022 by an AMD Ryzen 9 5950X @3.4GHz, running Linux Mint. This computer took about 51 hours, 52 minutes to complete the primality test using LLR2.
For more information, please see the Official Announcement.
On 19 June 2022, 04:26:15 UTC, PrimeGrid's Sierpinski/Riesel Base 5 Prime Search found the Mega Prime
63838·53887851-1
The prime is 2,717,497 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 99 th overall. 58 k's now remain in the Riesel Base 5 Problem.
The discovery was made by Scott Lee ( freestman) of China using an AMD Ryzen 5 2600X Six-Core Processor with 32GB RAM, running Microsoft Windows 11 Professional x64 Edition.
This computer took about 4 hours, 34 minutes to complete the PRP test using LLR2. Scott is a member of the Chinese Dream team.
The prime was verified on 19 June 2022, 22:29 UTC, by an Intel(R) Core(TM) i3-9100F CPU @ 3.60GHz with 16GB RAM, running Linux. This computer took about 11 hours and 57 minutes to complete the primality test using LLR2.
For more information, please see the Official Announcement.
On 15 May 2022, 17:29:48 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime
4896418524288+1
The prime is 3,507,424 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 3 rd for Generalized Fermat primes and 97 th overall.
The discovery was made by Tom Greer ( tng) of the United States using an GeForce RTX 3060 in an Intel(R) Core(TM) i7-6700 CPU @ 3.40GHz with 24GB RAM, running Microsoft Windows 10 Core x64 Edition.
This GPU took about 1 hour, 1 minute to complete the probable prime (PRP) test using GeneferOCL2. Tom Greer is a member of Antarctic Crunchers.
The prime was verified on 16 May 2022, 19:12:23 UTC, by Albert Pastuszka ( User B@P) of Poland using a GeForce GTX 750 in an AMD Athlon(tm) II X3 445 Processor with 6GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 6 hours, 46 minutes to complete the probable prime (PRP) test using GeneferOCL2. Albert Pastuszka is a member of BOINC@Poland.
The PRP was confirmed prime by an AMD Ryzen 5 3600 6-Core Processor with 4GB RAM, running Linux Ubuntu. This computer took about 22 hours, 17 minutes to complete the primality test using LLR.
For more information, please see the Official Announcement.
Other significant primes
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News 
GFN 20 Found!
On 9 August 2022, 11:56:02 UTC, PrimeGrid’s Generalized Fermat Prime Search found the Generalized Fermat mega prime:
1951734^1048576+1
The prime is 6,595,985 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Generalized Fermat primes and 13th overall. This is the second-largest prime found by PrimeGrid, and the second-largest non-Mersenne prime.
The discovery was made by Kazuya Tanaka (apophise@jisaku) of Japan using an NVIDIA GeForce RTX 3080 Ti in an Intel(R) Core(TM) i7-9700K CPU @ 3.60GHz with 64GB RAM, running Microsoft Windows 10 Professional x64 Edition. This GPU took about 1 hour, 2 minutes to complete the probable prime (PRP) test using GeneferOCL5. Kazuya Tanaka is a member of Team 2ch.
The prime was verified on 10 August 2022, 17:39:14 UTC by Jens Katzur (Landjunge) of Germany using an NVIDIA GeForce RTX 3070 in an Intel(R) Xeon(R) CPU X5675 @ 3.07GHz with 40GB RAM, running Linux Ubuntu. This computer took about 1 hour, 36 minutes to complete the probable prime (PRP) test using GeneferOCL5. Jens Katzur is a member of Planet 3DNow!.
The PRP was confirmed prime on 11 August 2022 by an AMD Ryzen 9 5950X @3.4GHz, running Linux Mint. This computer took about 51 hours, 52 minutes to complete the primality test using LLR2.
For more details, please see the official announcement.
17 Sep 2022 | 1:24:25 UTC
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Riemann's Birthday Challenge starts September 17th
The sixth challenge of the 2022 Series will be a 3-day challenge celebrating the 196th birthday of the German mathematician Bernhard Riemann. The challenge will be offered on the WW application, beginning 17 September 20:00 UTC and ending 20 September 20:00 UTC.
To participate in the Challenge, please select only the Wieferich and Wall-Sun-Sun Prime Search (WW) project in your PrimeGrid preferences section.
Issues? Inquiries? Interjections? Join the discussion at https://www.primegrid.com/forum_thread.php?id=9993&nowrap=true#156946
14 Sep 2022 | 18:05:24 UTC
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SR5 Mega Prime Find!
On 19 June 2022, 04:26:15 UTC, PrimeGrid’s Sierpinski/Riesel Base 5 Problem project eliminated k=63838 by finding the mega prime:
63838*5^3887851-1
The prime is 2,717,497 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 99th overall. 58 k’s now remain in the Riesel Base 5 problem.
The discovery was made by Scott Lee (freestman) of China using an AMD Ryzen 5 2600X Six-Core Processor with 32GB RAM, running Microsoft Windows 11 Professional x64 Edition. This computer took about 4 hours, 34 minutes to complete the prp test using LLR2. Scott is a member of the team, Chinese Dream.
The prime was verified on 19 June 2022, 22:29 UTC, by an Intel(R) Core(TM) i3-9100F CPU @ 3.60GHz with 16GB RAM, running Linux. This computer took about 11 hours and 57 minutes to complete the primality test using LLR2.
For more details, please see the official announcement.
18 Jul 2022 | 19:26:44 UTC
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Pi Approximation Day Challenge starts July 22
The fifth challenge of the 2022 Series will be a 3-day challenge celebrating the day that our arbitrary measurement units for the Earth's rotation align to numerically resemble the fraction 22/7, which approximates the value of the infamous circle constant 'pi' with an error of 400ppm! Honestly, I'm not sure why March 14th gets all the love -- 3.14 is a much worse approximation for pi!
The challenge will be offered on the PPS-LLR application, beginning 22 July 22:00 UTC and ending 25 July 22:00 UTC. To participate in the Challenge, please select only the Proth Prime Search LLR (PPS) project in your PrimeGrid preferences section.
For more info, questions, and lively debate about the best approximation for pi (it's 3 😁), check out the forum thread for this challenge: https://www.primegrid.com/forum_thread.php?id=9959&nowrap=true#156359
Happy 22/7!
17 Jul 2022 | 16:03:10 UTC
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M.C. Escher's Birthday Challenge starts June 17th
The fourth challenge of the 2022 Series will be a 5-day challenge marking the 124th birthday of Maurits Cornelis Escher, one of the world’s most famous graphic artists. His art is admired by millions of people worldwide, as can be seen by the many websites on the internet. The challenge will be offered on the SR5-LLR application, beginning 17 June 13:00 UTC and ending 22 June 13:00 UTC.
To participate in the Challenge, please select only the Sierpinski/Riesel Base 5 Prime Search LLR (SR5) project in your PrimeGrid preferences section.
Comments? Concerns? Conundrums? Check out the forum thread for this challenge: http://www.primegrid.com/forum_thread.php?id=9941&nowrap=true#155914
Happy crunching!
14 Jun 2022 | 2:39:31 UTC
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Newly reported primes(Mega-primes are in bold.)
310651816^32768+1 (Penguin); 7336040366475*2^1290000-1 (Torsten); 310587828^32768+1 (BlisteringSheep); 7351297202175*2^1290000-1 ([AF>Libristes]cguillem); 310583542^32768+1 (750); 7349967534327*2^1290000-1 (Jarekcz); 7349791551165*2^1290000-1 (Penguin); 7349172085335*2^1290000-1 (JH30895); 310432722^32768+1 (Penguin); 310434698^32768+1 (Penguin); 310416630^32768+1 (Penguin); 7335156077265*2^1290000-1 (DaveSun); 310370792^32768+1 (Penguin); 8845*2^1710902+1 (GDB); 310263662^32768+1 (Penguin); 170856176^65536+1 (jmswn89); 170826210^65536+1 (vaughan); 310175184^32768+1 (Penguin); 310148462^32768+1 (Vato); 7333511937705*2^1290000-1 (Nick) Top Crunchers:Top participants by RAC | Top teams by RAC |
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