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 29 May 2020, 07:52:25 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime:
3638450524288+1
The prime is 3,439,810 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 3 rd for Generalized Fermat primes and 35 th overall.
The discovery was made by Wolfgang Schwieger ( DeleteNull) of Germany using a GeForce RTX 2070 in an AMD Ryzen 7 3700X 8-Core Processor with 16GB RAM, running Linux openSUSE.
This GPU took about 31 minutes to complete the probable prime (PRP) test using GeneferOCL5. Wolfgang Schwieger is a member of the SETI.Germany team.
The PRP was verified on 29 May 2020, 08:23:51 UTC by Greg Miller ( Olgar) of the United States using an AMD Ryzen Threadripper 2990WX 32-Core Processor with 128GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 1 hour, 3 minutes to complete the probable prime (PRP) test using GeneferOCL5. Greg Miller is a member of the USA team.
The PRP was confirmed prime by an Intel(R) Xeon(R) CPU E3-1240 v6 @ 3.70GHz with 4GB RAM, running Linux Debian. This computer took about 1 day, 19 hours, 22 minutes to complete the primality test using LLR.
For more information, please see the Official Announcement.
On 1 May 2020, 04:01:08 UTC, PrimeGrid's Sierpinski/Riesel Base 5 Problem project eliminated k=118568 by finding the mega prime:
118568·53112069+1
The prime is 2,175,248 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 70 th overall and is the largest known base 5 prime. 30 k's now remain in the Sierpinski Base 5 problem.
The discovery was made by Honza Cholt ( Honza) of the Czech Republic using an Intel(R) Core(TM) i7-9700K CPU @ 3.60GHz with 32GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 49 minutes to complete the primality test using LLR. Honza Cholt is a member of Czech National Team.
The prime was verified on 2 May 2020, 09:00:41 UTC by Tom Murphy VII ( brighterorange) of the United States using a gfx1010 in an AMD FX-8370 Eight-Core Processor with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 1 day, 1 hour, 55 minutes to complete the primality test using LLR.
For more information, please see the Official Announcement.
On 16 March 2020, 08:21:46 UTC, PrimeGrid's Sierpinski/Riesel Base 5 Problem project eliminated k=207494 by finding the mega prime:
207494·53017502-1
The prime is 2,109,149 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 75 th overall and is the largest known base 5 prime. 63 k's now remain in the Riesel Base 5 problem.
The discovery was made by Todd Pickering ( EXT64) of the United States using an AMD EPYC 7601 32-Core Processor with 126GB RAM, running Linux Ubuntu.
This computer took about 1 day, 17 hours, 59 minutes to complete the primality test using LLR. Todd Pickering is a member of [H]ard|OCP.
The prime was verified internally using an Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz with 32GB RAM, running Linux Debian.
For more information, please see the Official Announcement.
Other significant primes
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News 
Katherine Johnson Memorial Challenge starts July 24th
In honor of the life of Katherine Johnson, PrimeGrid will be running a 7-day TRP-LLR challenge from 24 July 20:00 UTC to 31 July 20:00 UTC. Will we end this subproject's 3-year prime drought?
Also make sure to read Hidden Figures, a book about Katherine Johnson and some of her contemporaries, for the book club meeting!
Doubts? Disputes? Dubieties? Discuss in the forum thread for the challenge: https://www.primegrid.com/forum_thread.php?id=9217
21 Jul 2020 | 3:27:07 UTC
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Alan Turing's Birthday Challenge starts June 23rd
In honor of the 108th birthday of Alan Turing, English mathematician, computer scientist, logician, and more, PrimeGrid will be running a 3-day PPS-Sieve challenge from 23 June 22:00 UTC to 26 June 22:00 UTC!
The challenge subproject is available for both CPU and GPU.
Discuss in the forum post for the challenge: https://www.primegrid.com/forum_thread.php?id=9178
21 Jun 2020 | 22:17:10 UTC
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GFN-524288 Find!
On 29 May 2020, 07:52:25 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime:
3638450^524288+1
The prime is 3,439,810 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 3rd for Generalized Fermat primes and 35th overall.
The discovery was made by Wolfgang Schwieger (DeleteNull)of Germany using a GeForce RTX 2070 in an AMD Ryzen 7 3700X 8-Core Processor with 16GB RAM, running Linux openSUSE . This GPU took about 31 minutes to complete the probable prime (PRP) test using GeneferOCL5. Wolfgang Schwieger is a member of the SETI.Germany Team.
The PRP was verified on 29 May 2020, 08:23:51 UTC by Greg Miller (Olgar) of the United States using a gfx1010 in an AMD FX-8370 Eight-Core Processor with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 1 hour, 3 minutes to complete the probable prime (PRP) test using GeneferOCL5. Greg Miller is a member of the USA Team.
The PRP was confirmed prime by an Intel(R) Xeon(R) CPU E3-1240 v6 @ 3.70GHz with 4GB RAM, running Linux Debian . This computer took about 1 day, 19 hours, 22 minutes to complete the primality test using LLR.
For more details, please see the official announcement.
21 Jun 2020 | 16:12:45 UTC
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SR5 Mega Prime!
On 1 May 2020, 04:01:08 UTC, PrimeGrid’s Sierpinski/Riesel Base 5 Problem project eliminated k=118568 by finding the mega prime:
118568*5^3112069+1
The prime is 2,175,248 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 70th overall and is the largest known base 5 prime. 30 k’s now remain in the Sierpinski Base 5 problem.
The discovery was made by Honza Cholt (Honza) of the Czech Republic using an Intel(R) Core(TM) i7-9700K CPU @ 3.60GHz with 32GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 49 minutes to complete the primality test using LLR. Honza Cholt is a member of Czech National Team.
The prime was verified on 2 May 2020, 09:00:41 UTC by Tom Murphy VII (brighterorange) of the United States using an AMD Ryzen Threadripper 2990WX 32-Core Processor with 128GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 1 day, 1 hour, 55 minutes to complete the primality test using LLR.
For more details, please see the official announcement.
10 May 2020 | 20:10:18 UTC
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And Another SR5 Mega Prime!
On 16 March 2020, 08:21:46, PrimeGrid’s Sierpinski/Riesel Base 5 Problem project eliminated k=207494 by finding the mega prime:
207494*5^3017502-1
The prime is 2,109,149 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 75th overall and is the largest known base 5 prime. 63 k’s now remain in the Riesel Base 5 problem.
The discovery was made by Todd Pickering (EXT64) of the United States using an AMD EPYC 7601 32-Core Processor with 126GB RAM, running Linux Ubuntu. This computer took about 1 day, 17 hours, 59 minutes to complete the primality test using LLR. Todd Pickering is a member of the [H]ard|OCP team.
The prime was verified internally using an Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz with 32GB RAM, running Linux Debian.
For more details, please see the official announcement.
31 Mar 2020 | 14:55:09 UTC
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Newly reported primes(Mega-primes are in bold.)
188625786^32768+1 (robish); 188607700^32768+1 (Azmodes); 188602178^32768+1 (tng); 95306976^65536+1 (Azmodes); 8879*2^1583519+1 (vaughan); 188428752^32768+1 (Penguin); 188374856^32768+1 (Penguin); 188292328^32768+1 (Kellen); 188074644^32768+1 (tng); 187993282^32768+1 (tng); 187922612^32768+1 (tng); 8397*2^3336654+1 (Nita); 187905136^32768+1 (Penguin); 5512309897395*2^1290000-1 (jshriver); 5512230577485*2^1290000-1 (tng); 187539432^32768+1 (Penguin); 187464822^32768+1 (Penguin); 187332718^32768+1 (Penguin); 5509927172115*2^1290000-1 (vaclav_m); 5507274263487*2^1290000-1 (vaughan) Top Crunchers:Top participants by RAC | Top teams by RAC |
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