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 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 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 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.
On 12 March 2020, 19:16:51 UTC, PrimeGrid's Sierpinski/Riesel Base 5 Problem project eliminated k=238694 by finding the mega prime:
238694·52979422-1
The prime is 2,082,532 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 76 th overall and is the largest known base 5 prime. 64 k's now remain in the Riesel Base 5 problem.
The discovery was made by Chris Howell ( Khali) of the United States using an Intel(R) Core(TM) i9-9900K CPU @ 3.60GHz with 32GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 5 hours, 56 minutes to complete the primality test using LLR. Chris Howell is a member of Crunching@EVGA.
The prime was verified on 13 March 2020, 21:25:52 UTC by Yuki Yoshigoe ( SAKAGE@AMD@jisaku) of Japan using an AMD Ryzen Threadripper 3970X 32-Core Processor with 128GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 1 day, 5 hours, 24 minutes to complete the primality test using LLR. Yuki Yoshigoe is a member of Team 2ch.
For more information, please see the Official Announcement.
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News 
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
· Comment
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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Another SR5 Mega Prime!
On 12 March 2020, 19:16:51 UTC, PrimeGrid’s Sierpinski/Riesel Base 5 Problem project eliminated k=238694 by finding the mega prime:
238694*5^2979422-1
The prime is 2,082,532 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 76th overall and is the largest known base 5 prime. 64 k’s now remain in the Riesel Base 5 problem.
The discovery was made by Chris Howell (Khali) of the United States using an Intel(R) Core(TM) i9-9900K CPU @ 3.60GHz with 32GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 5 hours, 56 minutes to complete the primality test using LLR. Chris Howell is a member of the Crunching@EVGA team.
The prime was verified on 13 March 2020, 21:25:52 UTC by Yuki Yoshigoe (SAKAGE@AMD@jisaku) of Japan using an AMD Ryzen Threadripper 3970X 32-Core Processor with 128GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 1 day, 5 hours, 24 minutes to complete the primality test using LLR. Yuki Yoshigoe is a member of the Team 2ch team.
For more details, please see the official announcement.
31 Mar 2020 | 14:49:08 UTC
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SR5 Mega Prime!
On 9 March 2020, 21:32:46, PrimeGrid’s Sierpinski/Riesel Base 5 Problem project eliminated k=146264 by finding the mega prime:
146264*5^2953282-1
The prime is 2,064,261 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 74th overall and is the largest known base 5 prime. 65 k’s now remain in the Riesel Base 5 problem.
The discovery was made by Wolfgang Schwieger (DeleteNull) of Germany using an Intel(R) Core(TM) i5-8600K CPU @ 3.60GHz with 8GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 6 hours, 25 minutes to complete the primality test using LLR. Wolfgang Schwieger is a member of the SETI.Germany 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 | 14:40:54 UTC
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Sophie Germain's Birthday Challenge
In honor of the 244th birthday of Marie-Sophie Germain, French mathematician and namesake of the Sophie Germain Prime Search subproject, PrimeGrid will be running a 3-day SGS challenge from 1 April 12:00 UTC to 4 April 12:00 UTC!
It's been 4 years since we've found a twin or Sophie Germain prime, perhaps it's time to end the drought!
Inquiries? Interjections? Discuss in the forum post for the challenge: https://www.primegrid.com/forum_thread.php?id=9086
29 Mar 2020 | 5:35:44 UTC
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Newly reported primes(Mega-primes are in bold.)
21*2^6048861+1 (xcroc); 177305380^32768+1 (Johny); 177289456^32768+1 (dthonon); 3638450^524288+1 (DeleteNull); 5394190078695*2^1290000-1 (Bloodnok); 701*2^2867141+1 (BarryAZ); 961*2^2870596+1 (s-yama); 6963*2^1580698+1 (Charles Jackson); 5391823613277*2^1290000-1 (CaffeinatedSloth); 5393799756537*2^1290000-1 (Nita); 177096534^32768+1 (dthonon); 10627360^262144+1 (Nick); 177014132^32768+1 (GregCinAZ); 5391799153515*2^1290000-1 (Nita); 177006900^32768+1 (Rick Reynolds); 5391119386077*2^1290000-1 (Bur); 5390535864597*2^1290000-1 (Artist); 5391231852597*2^1290000-1 (Nita); 5389972449585*2^1290000-1 (Jean Philippe EIMER); 5390185024887*2^1290000-1 (Nita) Top Crunchers:Top participants by RAC | Top teams by RAC |
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