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 13 August 2020, 17:09:10 UTC, PrimeGrid's Sierpinski/Riesel Base 5 Problem project eliminated k=109838 by finding the mega prime:
109838·53168862-1
The prime is 2,214,945 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 72 nd overall and is the largest known base 5 prime. 62 k's now remain in the Riesel Base 5 problem.
The discovery was made by Erik Veit ( zombie67 [MM]) of the United States using an AMD Ryzen Threadripper 3970X 32-Core Processor with 63GB RAM, running Linux Mint.
This computer took about 6 hours, 14 minutes to complete the primality test using LLR. Erik Veit is a member of SETI.USA.
The prime was verified on 13 August 2020, 22:53:05 UTC by Frederik Schiøler ( Soulfly) of Denmark using an Intel(R) Xeon(R) Gold 6140 CPU @ 2.30GHz with 1GB RAM, running Linux Ubuntu.
This computer took about 11 hours, 52 minutes to complete the primality test using LLR. Frederik Schiøler is a member of Antarctic Crunchers.
For more information, please see the Official Announcement.
On 29 May 2020, 07:52:25 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime:
3638450524288+1
The prime is 3,439,810 digits long and enters Chris Caldwell's The Largest Known Primes Database
ranked 3 rd for Generalized Fermat primes and 35 th overall.
The discovery was made by Wolfgang Schwieger ( DeleteNull) of Germany using a GeForce RTX 2070 in an AMD Ryzen 7 3700X 8-Core Processor with 16GB RAM, running Linux openSUSE.
This GPU took about 31 minutes to complete the probable prime (PRP) test using GeneferOCL5. Wolfgang Schwieger is a member of the SETI.Germany team.
The PRP was verified on 29 May 2020, 08:23:51 UTC by Greg Miller ( Olgar) 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 hour, 3 minutes to complete the probable prime (PRP) test using GeneferOCL5. Greg Miller is a member of the USA 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 1 day, 19 hours, 22 minutes to complete the primality test using LLR.
For more information, please see the Official Announcement.
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 a gfx1010 in an AMD FX-8370 Eight-Core Processor with 16GB 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.
Other significant primes
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News 
How About One More DIV Mega Prime!
On 25 October 2020, 00:52:15 UTC, PrimeGrid's Fermat Divisor Search found the Mega Prime:
15*2^7300254+1
The prime is 2,197,597 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 75th overall.
The discovery was made by Robert Gelhar (Gelly) 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 3 hours, 24 minutes to complete the primality test using LLR. Robert Gelhar is a member of the Antarctic Crunchers team.
For more details, please see the official announcement.
27 Oct 2020 | 17:00:34 UTC
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And Another DIV Mega Prime!
On 24 October 2020, 22:53:39 UTC, PrimeGrid's Fermat Divisor Search found the Mega Prime:
19*2^6833086+1
The prime is 2,056,966 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 94th overall.
The discovery was made by Jiri Jaros (Venec) of the Czech Republic using an Intel(R) Xeon(R) CPU E5-2620 v3 @ 2.40GHz with 8GB RAM, running Linux Ubuntu. This computer took about 7 hours, 27 minutes to complete the primality test using LLR. Jiri Jaros is a member of the Czech National Team team.
For more details, please see the official announcement.
27 Oct 2020 | 16:53:44 UTC
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Another DIV Mega Prime!
On 20 October 2020, 19:06:13 UTC, PrimeGrid's Fermat Divisor Search found the Mega Prime:
39*2^6684941+1
The prime is 2,012,370 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 97th overall.
The discovery was made by Mike Thümmler (fnord) of Germany using an AMD Ryzen 5 1600X Six-Core Processor with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 4 hours to complete the primality test using LLR. Mike Thümmler is a member of the SETI.Germany team.
For more details, please see the official announcement.
27 Oct 2020 | 14:49:48 UTC
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New DIV Mega Prime!
On 20 October 2020, 13:22:13 UTC, PrimeGrid's Fermat Divisor Search found the Mega Prime:
39*2^6648997+1
The prime is 2,001,550 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 99th overall.
The discovery was made by Tom Greer (tng) 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 2 hours, 38 minutes to complete the primality test using LLR. Tom Greer is a member of the Antarctic Crunchers team.
For more details, please see the official announcement.
27 Oct 2020 | 14:40:46 UTC
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Évariste Galois Challenge starts TOMORROW, October 20th
The seventh challenge of the 2020 Series will be a 5-day challenge celebrating the 209th birthday of Évariste Galois, French mathematician and political activist. The challenge will be offered on the PPS-DIV (LLR) application, beginning 20 October 06:00 UTC and ending 25 October 06:00 UTC.
To participate in the Challenge, please select only the Fermat Divisor Search LLR (PPS-DIV) project in your PrimeGrid preferences section. Work units which are downloaded and completed during the challenge will count towards your challenge score.
Note: This will be our first challenge using LLR2, which eliminates the need for a full doublecheck task on each workunit, but replaces it with a short verification task. Expect to receive a few tasks about 1% of normal length. Please see this important warning about task bunkering.
Riddles? Requests? Reservations? Tell us in the forum thread for this challenge. Best of luck!
19 Oct 2020 | 3:12:36 UTC
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Newly reported primes(Mega-primes are in bold.)
201740626^32768+1 (lashrasch); 5673573152277*2^1290000-1 (Rezboun); 201685334^32768+1 (Renix); 5674288926267*2^1290000-1 (Krzysiak_PL_GDA); 79428414^131072+1 (Kouhki); 201592624^32768+1 (Bandwidtheater); 5675966585007*2^1290000-1 (Renix); 5675168804697*2^1290000-1 (Adrian Schori); 3*2^16408818+1 (Scott Brown); 3597*2^1609094+1 (Randall J. Scalise); 201530518^32768+1 (Renix); 79383608^131072+1 (vaughan); 29*2^7374577+1 (Pavel Atnashev); 9573*2^1608968+1 (larrys); 201345470^32768+1 (Johny); 627*2^2891514+1 (J PEEPZ); 5670583861815*2^1290000-1 (Todderbert); 5669049079977*2^1290000-1 (Charles Jackson); 5668570642215*2^1290000-1 (YuW3-810); 5668257995235*2^1290000-1 (No_Name) Top Crunchers:Top participants by RAC | Top teams by RAC |
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