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 as
a Titan!
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.
- 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 Prime Sierpinski Project solve the Prime Sierpinski Problem.
- Proth Prime Search: searching for primes of the form k·2n+1.
- 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.
Recent Significant Primes
On 23 September 2019, 06:25:41 UTC, PrimeGrid's AP27 (Arithmetic Progression of 27 primes) Search found the first ever AP27:
224584605939537911+81292139*23#*n for n=0..26
In addition to being the first know AP27, it is also the largest known AP24, AP25 and AP26 (smaller start but larger end than old record).
The discovery was made by Rob Gahan ( Robish) of Ireland
using an NVIDIA GeForce GTX 1660 Ti GPU on an Intel(R) Core(TM) i5-9400 CPU @ 2.90GHz running Microsoft Windows 10 Professional x64 Edition.
This computer took about 22 minutes to process this task.
Rob is a member of the Storm team.
For more information, please see the Official Announcement.
On 18 September 2019, 11:52:32 UTC, PrimeGrid's Generalized Fermat Prime Search found the Generalized Fermat mega prime:
2985036524288+1
The prime is 3,394,739 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 3 rd for Generalized Fermat primes and 28 th overall.
The discovery was made by Peter Harvey ( eXaPower) of the United States
using an NVIDIA GeForce GTX 1070 in an Intel(R) Core(TM) i5-4440S CPU @ 2.80GHz CPU with 8GB RAM, running Windows 8.1.
This computer took about 1 hour and 49 minutes to probable prime (PRP) test with GeneferOCL3.
The PRP was confirmed prime by an Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz with 16GB RAM, running Windows 10 Professional. This computer took about 23 hours and 48 minutes to complete the primality test using multithreaded LLR.
For more information, please see the Official Announcement.
On 9 September 2019, 18:15:29 UTC, PrimeGrid's Generalized Fermat Prime Search found the Generalized Fermat mega prime:
8521794262144+1
The prime is 1,816,798 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 13 th for Generalized Fermat primes and 76 th overall.
The discovery was made by Ken Ito ( jpldcon4) of Japan
using an NVIDIA GeForce GTX 980 Ti in an Intel(R) Xeon(R) CPU E5-2687W v3 @ 3.10GHz with 64GB RAM, running Microsoft Windows Server 2016.
This computer took about 27 minutes to probable prime (PRP) test with GeneferOCL2.
Ken is a member of Team 2ch.
The PRP was confirmed prime by an Intel(R) Xeon(R) CPU E3-1240 v6 @ 3.70GHz with 32GB RAM, running DebianLinux. This computer took about 17 hours and30 minutes to complete the primality test using LLR.
For more information, please see the Official Announcement.
On 2 September 2019, 03:39:59 UTC, PrimeGrid's Generalized Cullen/Woodall Prime Search found the largest known Generalized Cullen prime:
2805222·252805222+1
The prime is 3,921,539 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 1 st for Generalized Cullen primes and 21 st overall.
The discovery was made by Tom Greer of the United States
using an Intel(R) Core(TM) i9-9900X CPU @ 3.50GHz with 32GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 3 hours and 23 minutes to complete the primality test using multithreaded LLR.
Tom is a member of the Sicituradastra team.
For more information, please see the Official Announcement.
Other significant primes
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News 
First Ever AP27 Discovered!
The search is over!
After a three year effort, the first ever AP27 (Arithmetic Progression of 27 primes) has been found:
224584605939537911+81292139*23#*n for n=0..26
The AP27 was found by Rob Gahan (Robish) of Ireland. The discovery was made on an NVIDIA GeForce GTX 1660 Ti GPU on an Intel(R) Core(TM) i5-9400 CPU @ 2.90GHz running Microsoft Windows 10 Professional x64 Edition. It took about 22 minutes and 34 seconds to process the task. Rob is a member of the Storm team.
Congratulations to everyone who participated in the AP27 search! It has been a very challenging and rewarding project.
For more information, please see the official announcement or our AP27 forums.
30 Sep 2019 | 20:41:09 UTC
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GFN-524288 Mega Prime!
On 18 September 2019, 11:52:32 UTC, PrimeGrid’s Generalized Fermat Prime Search found the Generalized Fermat mega prime:
2985036^524288+1
The prime is 3,394,739 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 3rd for Generalized Fermat primes and 28th overall.
The discovery was made by Peter Harvey (eXaPower) the United States using an NVIDIA GeForce GTX 1070 in an Intel(R) Core(TM) i5-4440S CPU @ 2.80GHz CPU with 8GB RAM, running Windows 8.1. This GPU took about 1 hour 49 minutes to probable prime (PRP) test with GeneferOCL3.
The PRP was verified on 19 September 2019, 22:56:55 UTC by Alexander Falk (Alexander Falk) using an NVIDIA GeForce GTX 970 in an Intel(R) Core(TM) i7-6700 CPU @ 3.40GHz with 16GB RAM, running Windows 10. This GPU took about 3 hours 17 minutes to probable prime (PRP) test with GeneferOCL5. Alexander is a member of The Knights Who Say Ni! Team.
The PRP was confirmed prime by an Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz with 16GB RAM, running Windows 10 Professional. This computer took about 23 hours 48 minutes to complete the primality test using multithreaded LLR.
For more details, please see the official announcement.
24 Sep 2019 | 18:08:54 UTC
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GFN-262144 Find!
On 9 September 2019, 18:15:29 UTC, PrimeGrid’s Generalized Fermat Prime Search found the Generalized Fermat mega prime:
8521794^262144+1
The prime is 1,816,798 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 13th for Generalized Fermat primes and 76th overall.
The discovery was made by Ken Ito (jpldcon4) of Japan using an NVIDIA GeForce GTX 980 Ti in an Intel(R) Xeon(R) CPU E5-2687W v3 @ 3.10GHz with 64GB RAM, running Microsoft Windows Server 2016. This GPU took about 27 minutes to probable prime (PRP) test with GeneferOCL2. Ken is a member of Team 2ch.
The prime was verified on 10 September 2019, 02:21:44 UTC by Brent Schneider (KWSN-SpongeBob SquarePants) of Nepal using an NVIDIA GeForce GTX 1080 in an Intel(R) Core(TM) i7-6700K CPU @ 4.00GHz with 16GB RAM, running Microsoft Windows 10 Enterprise. This GPU took about 28 minutes to probable prime (PRP) test with GeneferOCL2. Brent is a member of The Knights Who Say Ni! team.
The PRP was confirmed prime by an Intel(R) Xeon(R) E3-1240 v6 CPU @ 3.70GHz with 32 GB RAM, running Debian Linux. This computer took about 17 hours 30 minutes to complete the primality test using LLR.
For more details, please see the official announcement.
24 Sep 2019 | 17:30:17 UTC
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World Maths Day Challenge
Announcing a new Challenge slot! To celebrate World Maths Day, and our new PPS-DIV sub-project, we'll be running a 5 day Challenge from 10th October 18:00 UTC until 15th October 18:00 UTC. Other Challenge dates are unaffected.
The Fermat Divisor search is especially designed to have a better chance of finding a Fermat Divisor. It has a limited number of candidates to check, and once they're gone, the project is over. A new Fermat Prime Divisor earns the finder a rare  badge. The project has found 18 primes so far, but no divisor.
For more information and discussion, read this forum thread or join our Discord server.
12 Sep 2019 | 11:52:29 UTC
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World Record Generalized Cullen Prime
On 2 September 2019, 03:39:59 UTC, PrimeGrid’s Generalized Cullen/Woodall Prime Search found the largest known Generalized Cullen prime:
2805222*252805222+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 3,921,539 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Generalized Cullen primes and 21st overall.
Base 25 was one of 11 primeless Generalized Cullen bases for b ≤121 that PrimeGrid is searching. The remaining bases are 13, 29, 47, 49, 55, 69, 73, 101, 109 & 121.
The discovery was made by Tom Greer (tng*) of the United States using an Intel(R) Core(TM) i9-9900X CPU @ 3.50GHz with 32GB RAM, running Microsoft Windows 10 Professional x64 Edition. His computer took 3 hours and 23 minutes to complete the primality test using multithreaded LLR. Tom is a member of the Sicituradastra team.
The prime was verified on 3 September 2019 05:15:11 UTC by Tim Terry (TimT) of the United States using an Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 24 hours 11 minutes to complete the primality test using multithreaded LLR. Tim is a member of the Aggie The Pew team.
For more details, please see the official announcement.
11 Sep 2019 | 12:54:24 UTC
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Newly reported primes(Mega-primes are in bold.)
67641884^65536+1 (wwei25); 7075*2^1547656+1 (Vipek); 1071*2^2814469+1 (Randall J. Scalise); 29*2^4532463+1 (Jack Hiker); 67607058^65536+1 (Darryl); 143834570^32768+1 (Homefarm); 25*2^4481024+1 (bill1024); 143776348^32768+1 (=Lupus=); 143760606^32768+1 (Johny); 4671594093705*2^1290000-1 (Jeff17); 23*2^4300741+1 (Miklos M.); 143722214^32768+1 (obsproth); 4670994329757*2^1290000-1 (Charles Jackson); 16329572^131072+1 (Scott Brown); 4667875251135*2^1290000-1 (Nita); 4670066644785*2^1290000-1 (Cicu); 4669445208717*2^1290000-1 (Krzysiak_PL_GDA); 4667528501685*2^1290000-1 (Gibson Praise); 4668156921657*2^1290000-1 (CGB); 143605556^32768+1 (Johny) Top Crunchers:Top participants by RAC | Top teams by RAC |
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