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 6 September 2021, 07:16:28 UTC, PrimeGrid's 321 Search found the Mega Prime
3·217748034-1
The prime is 5,342,692 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 18 th overall.
The discovery was made by Marc Wiseler ( McDaWisel) of Ireland using an AMD Ryzen 9 5900X 12-Core Processor with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 2 hours and 41 minutes to complete the primality test using LLR2. Marc Wiseler is a member of the Storm team.
For more information, please see the Official Announcement.
On 28 August 2021, 09:10:17 UTC, PrimeGrid's Generalized Cullen/Woodall Prime Search found the largest known Generalized Cullen prime
2525532·732525532+1
The prime is 4,705,888 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 1 st for Generalized Cullen primes and 24 th overall.
The discovery was made by Tom Greer ( tng) of the United States using an Intel(R) Core(TM) i9-10920X CPU @ 3.50GHz with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 10 hours and 40 minutes to complete the primality test using LLR2. Tom Greer is a member of the Antarctic Crunchers team.
The prime was verified on 28 August 2021, 18:01 UTC, by an Intel(R) Core(TM) i7-9800X CPU @ 3.80GHz with 32GB of RAM, running CentOS. This computer took 3 hours and 39 minutes to complete the primality test using LLR2.
For more information, please see the Official Announcement.
On 1 March 2021, 02:47:51 UTC, PrimeGrid's Fermat Divisor Search found the Mega Prime
25·28788628+1
The prime is 2,645,643 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 75 th overall.
The discovery was made by Tom Greer ( tng) of the United States using an Authentic AMD Ryzen 9 5950X CPU @ 4.90GHz with 32GB RAM, running Microsoft Windows 10 Professional.
This computer took about 2 hours and 46 minutes to complete the primality test using LLR2. Tom Greer is a member of the Antarctic Crunchers team.
For more information, please see the Official Announcement.
Other significant primes
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News 
Euler's Number Challenge starts November 23rd
The eighth challenge of the 2021 Series will be a 3-day challenge in Thanksgiving™ of the anniversary of the introduction of e, or Euler's Number! The challenge will be offered on the AP27 Search subproject, beginning 23 November 05:00 UTC and ending 26 November 05:00 UTC.
To participate in the Challenge, please select only the AP 27 (AP27) project in your PrimeGrid preferences section.
For more info and discussion, check out the forum thread for this challenge: https://www.primegrid.com/forum_thread.php?id=9792&nowrap=true#152286
Best of luck!
20 Nov 2021 | 4:16:09 UTC
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GFN-17-Low is finishing
The GFN-17-LOW project has less than a million candidates to be tested, and thus will come to an end in the next few months.
Forum discussion thread: https://www.primegrid.com/forum_thread.php?id=9796
14 Nov 2021 | 17:27:34 UTC
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Martin Gardner's Birthday Challenge starts October 21
The seventh challenge of the 2021 Series will be a 7-day challenge in celebration of the 107th (prime number!) birthday of beloved American science communicator, Martin Gardner. The challenge will be offered on the GCW-LLR application, beginning 21 October 00:00 UTC and ending 28 October 00:00 UTC.
To participate in the Challenge, please select only the Generalized Cullen/Woodall Prime Search LLR (GCW) project in your PrimeGrid preferences section.
For more info and discussion, check out the forum thread for this challenge: https://www.primegrid.com/forum_thread.php?id=9767&nowrap=true#151803
Best of luck!
18 Oct 2021 | 21:43:24 UTC
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321 Mega Prime!
On 6 September 2021, 07:16:28 UTC, PrimeGrid's 321 Search found the Mega Prime:
3*2^17748034-1
The prime is 5,342,692 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 18th overall.
The discovery was made by Marc Wiseler (McDaWisel) of Ireland using an AMD Ryzen 9 5900X 12-Core Processor with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 2 hours, 45 minutes to complete the primality test using LLR2. Marc Wiseler is a member of the Storm team.
The prime was verified on 6 September 2021, 11:47 UTC, by an Intel(R) Core(TM) i7-9800X CPU @ 3.80GHz with 32GB of RAM, running CentOS. This computer took 2 hours and 41 minutes to complete the primality test using LLR2.
For more details, please see the official announcement.
23 Sep 2021 | 15:24:43 UTC
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World Record Generalized Cullen Prime!
On 28 August 2021, 09:10:17 UTC, PrimeGrid’s Generalized Cullen/Woodall Prime Search found the largest known Generalized Cullen prime:
2525532*732525532+1
Generalized Cullen numbers are of the form: n*bn+1. Generalized Cullen numbers that are prime are called Generalized Cullen primes. For more information, please see “Cullen prime” in The Prime Glossary.
The prime is 4,705,888 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Generalized Cullen primes and 24th overall.
Base 73 was one of 10 primeless Generalized Cullen bases for b ≤121 that PrimeGrid is searching. The remaining bases are 13, 29, 47, 49, 55, 69, 101, 109 & 121.
The discovery was made by Tom Greer (tng) of the United States using an Intel(R) Core(TM) i9-10920X CPU @ 3.50GHz with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 10 hours, 40 minutes to complete the primality test using LLR2. Tom is a member of the Antarctic Crunchers team.
The prime was verified on 28 August 2021, 18:01 UTC, by an Intel(R) Core(TM) i7-9800X CPU @ 3.80GHz with 32GB of RAM, running CentOS. This computer took 3 hours and 39 minutes to complete the primality test using LLR2.
For more details, please see the official announcement.
23 Sep 2021 | 15:16:52 UTC
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Newly reported primes(Mega-primes are in bold.)
6619101229167*2^1290000-1 (Johnny Rotten); 263754200^32768+1 (288larsson); 6614948733237*2^1290000-1 (Honza); 36416848^131072+1 (Jacques); 36422846^131072+1 (tng); 136787614^65536+1 (serge); 6614861556417*2^1290000-1 (mrzorronator); 6614018969745*2^1290000-1 (Honza); 263665534^32768+1 (288larsson); 6612301370265*2^1290000-1 (GhostOfElectricity); 6614565099777*2^1290000-1 (tng); 136637696^65536+1 (Merimac Strongbottom); 6601328496327*2^1290000-1 (Honza); 6612462956907*2^1290000-1 (Honza); 6612344420895*2^1290000-1 (YuW3-810); 263556556^32768+1 (Pooh Bear 27); 6612122541237*2^1290000-1 (Nita); 6610275013587*2^1290000-1 (spnorton); 6609726389607*2^1290000-1 (Shayol Ghul); 6609584862015*2^1290000-1 (haineons) Top Crunchers:Top participants by RAC | Top teams by RAC |
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