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 22 January 2020, 15:00:58 UTC, PrimeGrid's Fermat Divisor Search found the mega rime:
13·25523860+1
The prime is 1,662,849 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 115 th overall.
13·2 5523860+1 divides the Fermat number F 5523858, also written as 2 25523858+1, and is a new
world record for prime Fermat divisors. It is also ranked 4 th for "weighted" prime Fermat divisors.
The discovery was made by Scott Brown of the United States
using an Intel(R) Core(TM) i7-4790 CPU @ 3.60GHz with 16GB RAM, running Microsoft Windows 10 Core x64 Edition.
This computer took about 39 minutes to complete the primality test using multithreaded LLR.
Scott is a member of the Aggie the Pew team.
For more information, please see the Official Announcement.
On 21 January 2020, 00:49:54 UTC, PrimeGrid's Generalized Fermat Prime Search found the Generalized Fermat mega prime:
9450844262144+1
The prime is 1,828,578 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 15 th for Generalized Fermat primes and 85 th overall.
The discovery was made by Jacob Eikelenboom ( Eikelenboom) of The Netherlands
using an NVIDIA GeForce RTX 2060 in an Intel(R) Core(TM) i7-9700F CPU @ 3.00GHz with 16GB RAM, running Microsoft Windows 10 Core x64 Edition.
This computer took about 18 minutes to complete the probable prime (PRP) test with Genefer OCL2.
The PRP was confirmed prime by an Intel(R) Xeon(R) CPU E3-1240 v6 @ 3.70GHz with 4 GB RAM, running Linux Debian.
This computer took about 17 hours, 52 minutes to complete the primality test using multithreaded LLR.
For more information, please see the Official Announcement.
On 24 December 2019, 08:20:15 UTC, PrimeGrid's Generalized Fermat Prime Search found the Generalized Fermat mega prime:
3214654524288+1
The prime is 3,411,613 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 3 rd for Generalized Fermat primes and 30 th overall.
The discovery was made by Alen Kecic ( Freezing) of Germany
using an NVIDIA GeForce GTX 1660 Ti in an Intel(R) Core(TM) i7-7820X CPU @ 3.60GHz with 32GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 51 minutes to probable prime (PRP) test with GeneferOCL3.
Alen is a member of the SETI.Germany team.
The PRP was confirmed prime by an Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz with 32GB RAM, running Windows 10 Professional x64 Edition.
This computer took about 1 day, 1 hour and 45 minutes to complete the primality test using multithreaded LLR.
For more information, please see the Official Announcement.
On 24 December 2019, 01:28:13 UTC, PrimeGrid's Extended Sierpinski Problem found the Mega prime:
99739·214019102+1
The prime is 4,220,176 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 20 th overall.
This find eliminates k=99739; 9 k's remain in the Extended Sierpinski Problem.
The discovery was made by Brian D. Niegocki ( Penguin) of the United States
using an Intel(R) Xeon(R) Gold 6140 CPU @ 2.30GHz with 1GB RAM, running Linux Ubuntu.
This computer took about 14 hours and 14 minutes to complete the primality test using multithreaded LLR.
Brian is a member of the Antarctic Crunchers team.
For more information, please see the Official Announcement.
On 5 December 2019, 08:39:29 UTC, PrimeGrid's Generalized Fermat Prime Search found the Generalized Fermat mega prime:
9125820262144+1
The prime is 1,824,594 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 14 th for Generalized Fermat primes and 82 nd overall.
The discovery was made by Yoshimitsu Kato ( yoshi) of Japan
using an NVIDIA GeForce GTX 1660 Ti in an Intel(R) Core(TM) i7-6700 CPU @ 3.40GHz with 16GB RAM, running Microsoft Windows 10.
This computer took about 22 minutes to probable prime (PRP) test with Genefer OCL2.
Yoshimitsu Kato is a member of Team JPN.
The PRP was confirmed prime by an Intel(R) Core(TM) i7-6700 CPU @ 3.40GHz with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 16 hours, 30 minutes to complete the primality test using multithreaded LLR.
For more information, please see the Official Announcement.
Other significant primes
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News 
GFN-16 CPU tasks no longer available
We have exceeded the 'b' limit of the CPU version of the Genefer software on the GFN-16 project. No more GFN-16 CPU tasks will be sent.
GFN-16 GPU tasks will continue to be available.
Genefer CPU tasks continue to be available for GFN-17-Low, GFN-18, GFN-19, GFN-20, GFN-21, and GFN-22.
1 Feb 2020 | 22:03:59 UTC
· Comment
World Record Fermat Divisor Found!
On 22 January 2020, 15:00:58 UTC, PrimeGrid's Fermat Divisor Search found the Mega Prime:
13*2^5523860+1 Divides F(5523858)
The prime is 1,662,849 digits long and will enter Chris Caldwell's The Largest Known Primes Database ranked 115th overall. This is a world record for prime Fermat divisors, and it is also ranked 4th for “weighted” prime Fermat divisors.
The discovery was made by Scott Brown (Scott Brown) of the United States using an Intel(R) Core(TM) i7-4790 CPU @ 3.60GHz with 16GB RAM, running Microsoft Windows 10 Core x64 Edition. This computer took about 39 minutes to complete the primality test using multithreaded LLR. Scott is a member of the Aggie The Pew team.
The prime was verified on 22 January 2020, 15:11:39 UTC by Stefan Larsson (288larsson) of Sweden using an Intel(R) Core(TM) i9-9900K CPU @ 3.60GHz with 8GB RAM, running Microsoft Windows 10 Core x64 Edition. This computer took about 46 minutes to complete the primality test using multithreaded LLR. Stefan is a member of the Sicituradastra. team.
For more details, please see the official announcement.
25 Jan 2020 | 16:38:28 UTC
· Comment
Another GFN-262144 Find!!
On 21 January 2020, 00:49:54 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime:
9450844^262144+1
The prime is 1,828,578 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 15th for Generalized Fermat primes and 85th overall.
The discovery was made by Jacob Eikelenboom (Eikelenboom) of The Netherlands using an NVIDIA GeForce RTX 2060 in an Intel(R) Core(TM) i7-9700F CPU @ 3.00GHz with 16GB RAM, running Microsoft Windows 10 Core x64 Edition. This GPU took about 18 minutes to complete the probable prime (PRP) test using GeneferOCL2.
The prime was verified on 21 January 2020, 02:35:41 UTC by Igor Keller (IKI) of France using an NVIDIA GeForce GTX 1080 in an Intel(R) Core(TM) i5-4460 CPU @ 3.20GHz with 16GB RAM, running Microsoft Windows 8.1 Professional with Media Center x64 Edition. This computer took about 26 minutes to complete the probable prime (PRP) test using GeneferOCL2. Igor Keller is a member of the Gridcoin 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 17 hours, 52 minutes to complete the primality test using LLR.
For more details, please see the official announcement.
22 Jan 2020 | 21:12:59 UTC
· Comment
GFN-524288 Mega Prime!
On 24 December 2019, 08:20:15 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime:
3214654^524288+1
The prime is 3,411,613 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 3rd for Generalized Fermat primes and 30th overall.
The discovery was made by Alen Kecic (Freezing)of Germany using a GeForce GTX 1660 Ti in an Intel(R) Core(TM) i7-7820X CPU @ 3.60GHz with 32GB RAM, running Microsoft Windows 10 Professional x64 Edition. This GPU took about 51 minutes to complete the probable prime (PRP) test using GeneferOCL5. Alen is a member of the SETI.Germany Team.
The PRP was verified on 24 December 2019, 10:12:18 UTC by John Holmes (John J. Holmes) of the United States using a GeForce GTX 970 in an Intel(R) Core(TM) i7-4790 CPU @ 3.60GHz with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 2 hours, 4 minutes to complete the probable prime (PRP) test using GeneferOCL3.
The PRP was confirmed prime by an Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz with 32GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 1 day, 1 hour, 45 minutes to complete the primality test using multithreaded LLR.
For more details, please see the official announcement.
13 Jan 2020 | 16:29:44 UTC
· Comment
ESP Mega Prime!
On 24 December 2019, 01:28:13 UTC, PrimeGrid's Extended Sierpinski Problem found the Mega Prime:
99739*2^14019102+1
The prime is 4,220,176 digits long and will enter Chris Caldwell's The Largest Known Primes Database ranked 20th overall. This find eliminates k=99739; 9 k's remain in the Extended Sierpinski Problem.
The discovery was made by Brian D. Niegocki (Penguin) of the United States using an Intel(R) Xeon(R) Gold 6140 CPU @ 2.30GHz with 1GB RAM, running Linux Ubuntu. This computer took about 14 hours, 14 minutes to complete the primality test using LLR. Brian is a member of the Antarctic Crunchers team.
The prime was verified on 24 December 2019, 04:37:31 UTC by Pavel Atnashev (Pavel Atnashev) of Russia using an Intel(R) Xeon(R) E5-2680 v2 @ 2.80GHz with 8GB RAM, running Linux. This computer took about 4 hours, 6 minutes to complete the primality test using LLR. Pavel is a member of the Ural Federal University team.
For more details, please see the official announcement.
13 Jan 2020 | 12:50:37 UTC
· Comment
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Newly reported primes(Mega-primes are in bold.)
70893680^131072+1 (pew); 86037836^65536+1 (Rick Reynolds); 85908438^65536+1 (darkclown); 5143*2^1571040+1 (mattozan); 9275*2^1571019+1 (TimT); 4655*2^1570941+1 (RussEfarmer); 8391*2^1570896+1 (bcavnaugh); 85770052^65536+1 (Rick Reynolds); 6333*2^1570798+1 (JayPi); 4663*2^1570696+1 (Frank); 85636536^65536+1 (Bandwidtheater); 85598554^65536+1 (bcavnaugh); 3891*2^1570357+1 (4bc3); 70658696^131072+1 (zombie67 [MM]); 85516188^65536+1 (Mektacular); 85316028^65536+1 ([SG]KidDoesCrunch); 1191*2^2849315+1 (Sean); 3803*2^1570401+1 (Penguin); 85209154^65536+1 (RFGuy_KCCO); 7641*2^1570180+1 (TimT) Top Crunchers:Top participants by RAC | Top teams by RAC |
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