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 7 December 2021, 14:48:06 UTC, PrimeGrid's Sierpinski/Riesel Base 5 Problem project eliminated k=273662 by finding the Mega Prime
273662·53493296-1
The prime is 2,441,715 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 97 th overall. 60 k's now remain in the Riesel Base 5 problem.
The discovery was made by Lukas Plätz ( Lukas) of Germany using an AMD Ryzen 7 3700X 8-Core Processor with 16GB RAM, running Linux Mint.
This computer took about 2 hours 57 minutes to complete the PRP test using LLR2.
The prime was verified on 8 December 2021, 09:52 UTC, by an AMD Ryzen 9 5900X 12-Core Processor with 64GB RAM, running Linux Mint. This computer took about 15 hours and 49 minutes to complete the primality test using LLR2.
For more information, please see the Official Announcement.
On 25 November 2021, 03:19:26 UTC, PrimeGrid's Extended Sierpinski Problem Search found the Mega Prime
202705·221320516+1
The prime is 1,418,398 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 13 th overall.
The discovery was made by Pavel Atnashev ( Pavel Atnashev) of Russia using an Intel(R) Xeon(R) E5-2695 v2 CPU @ 2.40GHz with 16GB RAM running Tiny Core Linux.
This computer took 10 hours 59 minutes to complete the primality test using LLR2. Pavel Atnashev is a member of the Ural Federal University.
For more information, please see the Official Announcement.
On 18 September 2021, 06:50:25 UTC, PrimeGrid's Primorial Prime Search through PRPNet found the Mega Prime
3267113#-1
The prime is 1,418,398 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 1st for Primorial primes and 286th overall.
The discovery was made by James Winskill ( Aeneas) of New Zealand using an Intel(R) Xeon(R) W-2125 CPU @ 4.00GHz with 64GB RAM running Windows 10.
This computer took 20 hours 32 minutes to complete the PRP test using pfgw64. James Winskill is a member of the PrimeSearchTeam.
The prp was verified on 26 September 2021, 01:56:46 UTC by an Intel i7-7700K @ 4.2 GHz with 16 GB RAM, running Gentoo/Linux. This computer took a little over 5 days 8 hours 38 minutes to verify primality of the prp using pfgw64.
For more information, please see the Official Announcement.
On 8 October 2021, 01:38:53 UTC, PrimeGrid's Sierpinski/Riesel Base 5 Problem project eliminated k=102818 by finding the Mega Prime
102818·53440382-1
The prime is 2,404,729 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 96 th overall. 61 k's now remain in the Riesel Base 5 problem.
The discovery was made by Wes Hewitt ( emoga) of Canada using an AMD Ryzen 9 5950X 16-Core Processor with 32GB RAM, running Microsoft Windows 10 Professional x64 Edition.
This computer took about 1 hour and 29 minutes to complete the PRP test using LLR2. Wes Hewitt is a member of the TeAm AnandTech team.
The prime was verified on 10 October 2021, 20:14 UTC, by an Intel(R) Core(TM) i7-9800X CPU @ 3.80GHz with 32GB of RAM, running CentOS. This computer took 20 hours and 39 minutes to complete the primality test using LLR2.
For more information, please see the Official Announcement.
Other significant primes
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News 
Another 321 Mega Prime!
On 24 March 2022, 17:27:33 UTC, PrimeGrid’s 321 Prime Search found the Mega Prime:
3*2^18924988-1
The prime is 5,696,990 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 18th overall.
The discovery was made by Frank Matillek (boss) of Germany using an Intel CPU with 1GB RAM, running Ubuntu Linux. This computer took about 1 day, 1 hour, 39 minutes to complete the primality test using LLR2. Frank Matillek is a member of the SETI.Germany team.
For more details, please see the official announcement.
8 May 2022 | 14:13:50 UTC
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321 Mega Prime!
On 8 January 2022, 20:46:05 UTC, PrimeGrid’s 321 Prime Search found the Mega Prime:
3*2^18196595-1
The prime is 5,477,722 digits long and has entered Chris Caldwell's “The Largest Known Primes Database” ranked 20th overall.
The discovery was made by an anonymous user of Poland 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 2 hours, 40 minutes to complete the primality test using LLR2.
For more details, please see the official announcement.
8 May 2022 | 14:08:39 UTC
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World Water Day Challenge starts March 21st
The second challenge of the 2022 Series will be a 5-day challenge in celebration of World Water Day, the annual United Nations Observance, started in 1993, that celebrates water and raises awareness of the 2 billion people currently living without access to safe water. The challenge will be offered on the 321-LLR application, beginning 21 March 03:21 UTC and ending 26 March 03:21 UTC.
To participate in the Challenge, please select only the 321 Prime Search LLR (321) 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=9888&nowrap=true#154866
17 Mar 2022 | 18:14:23 UTC
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SR5 Mega Prime Find!
On 7 December 2021, 14:48:06 UTC, PrimeGrid’s Sierpinski/Riesel Base 5 Problem project eliminated k=273662 by finding the mega prime:
273662*5^3493296-1
The prime is 2,441,715 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 97th overall. 60 k’s now remain in the Riesel Base 5 problem.
The discovery was made by Lukas Plätz (Lukas) of Germany using an AMD Ryzen 7 3700X 8-Core Processor with 16GB RAM, running Linux Mint. This computer took about 2 hours, 57 minutes to complete the prp test using LLR2.
The prime was verified on 8 December 2021, 09:52 UTC, by an AMD Ryzen 9 5900X 12-Core Processor with 64GB RAM, running Linux Mint. This computer took about 15 hours and 49 minutes to complete the primality test using LLR2.
For more details, please see the official announcement.
16 Dec 2021 | 20:45:41 UTC
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ESP Mega Prime!
On 25 November 2021, 03:19:26 UTC, PrimeGrid's Extended Sierpinski Problem found the Mega Prime:
202705*2^21320516+1
The prime is 6,418,121 digits long and will enter Chris Caldwell's The Largest Known Primes Database ranked 13th overall. This find eliminates k=202705; 8 k's remain in the Extended Sierpinski Problem.
The discovery was made by Pavel Atnashev (Pavel Atnashev) of Russia using an Intel(R) Xeon(R) E5-2695 v2 CPU @ 2.40GHz with 16GB RAM running Tiny Core Linux. This computer took about 10 hours, 59 minutes to complete the primality test using LLR2. Pavel is a member of the Ural Federal University team.
For more details, please see the official announcement.
14 Dec 2021 | 18:24:54 UTC
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Newly reported primes(Mega-primes are in bold.)
289417960^32768+1 (Tuna Ertemalp); 3537*2^1693311+1 (Honza); 4065*2^1693197+1 (NXR); 110824714^131072+1 (Scott Brown); 8891*2^1693043+1 (Honza); 779*2^3253063+1 (Merimac Strongbottom); 9705*2^3420915+1 (LucasBrown); 6195*2^1693037+1 (Honza); 289219998^32768+1 ([SG]_Carsten); 7052356416945*2^1290000-1 (Matthew McCleary); 1315*2^1692898+1 (Honza); 8919*2^3420758+1 (Scott Brown); 166787224^65536+1 (candido); 289123210^32768+1 (Tuna Ertemalp); 7054004150835*2^1290000-1 (Adrian Schori); 1799*2^1692857+1 (Honza); 8681*2^1692569+1 (oya-lab); 289038018^32768+1 (Subaguru); 288916364^32768+1 (Subaguru); 288878514^32768+1 (Subaguru) Top Crunchers:Top participants by RAC | Top teams by RAC |
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