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 26 May 2023, 01:04:36 UTC, PrimeGrid's AP27 Search (Arithmetic Progression of 27 primes) found the progression of 27 primes
277699295941594831+170826477*23#*n for n=0..26
This is the second known AP27.
The discovery was made by Tom Greer ( tng) of the United States using an NVIDIA GeForce RTX 4080 on an AMD Ryzen 9 7950X CPU @ 4.50GHz running Microsoft Windows 10 Professional x64 Edition.
This GPU took about 4 minutes and 22 seconds to complete the task (each task tests 100 progression differences of 10 shifts each). Tom Greer is a member of the Antarctic Crunchers team.
The task was verified on 26 May 2023, 01:04:39 UTC, by Vasil Zakiev ( zvasi_000) of Russia using an NVIDIA GeForce RTX 4090 on an AMD Ryzen 9 7950X CPU @ 4.50GHz running Microsoft Windows 11 Professional x64 Edition.
This computer took about 1 minute and 27 seconds to complete the task. Vasil Zakiev is a member of the Crystal Dream team.
For more information, please see the Official Announcement.
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.
Other significant primes
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News 
AP27 Found!
On 26 May 2023, 01:04:36 UTC, PrimeGrid’s AP27 Search (Arithmetic Progression of 27 primes) found the progression of 27 primes:
277699295941594831+170826477*23#*n for n=0..26
This is the second known AP27.
The discovery was made by Tom Greer (tng) of the United States using a NVIDIA GeForce RTX 4080 on an AMD Ryzen 9 7950X CPU @ 4.50GHz running Microsoft Windows 10 Professional x64 Edition. This computer took about 4 minutes and 22 seconds to process the task (each task tests 100 progression differences of 10 shifts each). Tom Greer is a member of the Antarctic Crunchers team.
The AP27 task was double checked by Vasil Zakiev (zvasi_000) of Russia and was returned on 26 May 2023 01:04:39 UTC. This task was run on an NVIDIA GeForce RTX 4090 on an AMD Ryzen 9 7950X CPU @ 4.50GHz running Microsoft Windows 11 Professional x64 Edition. The double check took about 1 minute and 27 seconds to complete. Vasil Zakiev is a member of the Crystal Dream team.
For more details, please see the official announcement.
3 Jun 2023 | 15:55:26 UTC
· Comment
AP27 now supports Intel ARC GPUs
The AP27 project now supports Intel ARC GPUs on both Windows and Linux.
This version of the app is faster than the previous version and all GPUs under Linux and Windows should see faster run times.
For discussion and more information, please see this forum thread.
5 May 2023 | 22:50:37 UTC
· Comment
Restarting of Cullen/Woodall Sieve
Sometime later today (UTC) we expect to be resuming the Cullen/Woodall Prime Search Sieve.
For more information and discussion, please follow this link.
1 May 2023 | 23:17:45 UTC
· Comment
30 day warning for Primorial and Factorial shutting down on PRPNet
The last two PRPNet projects, Primorial and Factorial, will be ending soon. Discussion and information can be found on the forums.
15 Apr 2023 | 12:09:30 UTC
· Comment
Gotthold Eisenstein's Birthday Challenge starts April 16th
The third challenge of the 2023 Series will be a 7-day challenge celebrating the 200th birthday of German number theorist Ferdinand Gotthold Max Eisenstein. The challenge will be offered on the PSP-LLR application, beginning 16 April 16:00 UTC and ending 23 April 16:00 UTC.
To participate in the Challenge, please select only the Prime Sierpinski Problem (LLR) project in your PrimeGrid preferences section.
Comments? Concerns? Complaints? Critiques? Contemplations? Join the discussion at https://www.primegrid.com/forum_thread.php?id=10202
14 Apr 2023 | 16:08:27 UTC
· Comment
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Newly reported primes(Mega-primes are in bold.)
363514142^32768+1 (Ginga); 363285250^32768+1 (ikari); 9607*2^1747826+1 (composite); 8261372362785*2^1290000-1 (Nick); 363*2^4119017+1 (Scott Brown); 8263318188207*2^1290000-1 (Nick); 274171652^65536+1 (Michael Millerick); 8261204140425*2^1290000-1 (Adrian Schori); 8248324731117*2^1290000-1 (Nick); 8261241785247*2^1290000-1 (vaughan); 8260784018517*2^1290000-1 (Nick); 5105*2^1747067+1 (HAL9000); 7897*2^3471568+1 (w a h); 273498220^65536+1 (Derek); 8254144964637*2^1290000-1 (TimT); 8259901937115*2^1290000-1 (Nick); 8259870344847*2^1290000-1 (No_Name); 362730048^32768+1 (Johny); 2203*2^1747434+1 (Yegor001); 5925*2^1747386+1 (Yegor001) Top Crunchers:Top participants by RAC | Top teams by RAC |
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