Other

drummers-lowrise

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.
You can choose the projects you would like to run by going to the project preferences page.

Recent Significant Primes

On 9 August 2022, 11:56:02 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime
19517341048576+1
The prime is 6,595,985 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Generalized Fermat primes and 13th overall. This is the second-largest prime found by PrimeGrid, and the second-largest non-Mersenne prime.

The discovery was made by Kazuya Tanaka (apophise@jisaku) of Japan using an NVIDIA GeForce RTX 3080 Ti in an Intel(R) Core(TM) i7-9700K CPU @ 3.60GHz with 64GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 1 hour, 2 minutes to complete the probable prime (PRP) test using GeneferOCL5. Kazuya Tanaka is a member of Team 2ch.

The prime was verified on 10 August 2022, 17:39:14 UTC by Jens Katzur (Landjunge) of Germany using an NVIDIA GeForce RTX 3070 in an Intel(R) Xeon(R) CPU X5675 @ 3.07GHz with 40GB RAM, running Linux Ubuntu. This computer took about 1 hour, 36 minutes to complete the probable prime (PRP) test using GeneferOCL5. Jens Katzur is a member of Planet 3DNow!.

The PRP was confirmed prime on 11 August 2022 by an AMD Ryzen 9 5950X @3.4GHz, running Linux Mint. This computer took about 51 hours, 52 minutes to complete the primality test using LLR2.

On 19 June 2022, 04:26:15 UTC, PrimeGrid's Sierpinski/Riesel Base 5 Prime Search found the Mega Prime
63838·53887851-1
The prime is 2,717,497 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 99th overall. 58 k's now remain in the Riesel Base 5 Problem.

The discovery was made by Scott Lee (freestman) of China using an AMD Ryzen 5 2600X Six-Core Processor with 32GB RAM, running Microsoft Windows 11 Professional x64 Edition. This computer took about 4 hours, 34 minutes to complete the PRP test using LLR2. Scott is a member of the Chinese Dream team.

The prime was verified on 19 June 2022, 22:29 UTC, by an Intel(R) Core(TM) i3-9100F CPU @ 3.60GHz with 16GB RAM, running Linux. This computer took about 11 hours and 57 minutes to complete the primality test using LLR2.

On 15 May 2022, 17:29:48 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime
4896418524288+1
The prime is 3,507,424 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 3rd for Generalized Fermat primes and 97th overall.

The discovery was made by Tom Greer (tng) of the United States using an GeForce RTX 3060 in an Intel(R) Core(TM) i7-6700 CPU @ 3.40GHz with 24GB RAM, running Microsoft Windows 10 Core x64 Edition. This GPU took about 1 hour, 1 minute to complete the probable prime (PRP) test using GeneferOCL2. Tom Greer is a member of Antarctic Crunchers.

The prime was verified on 16 May 2022, 19:12:23 UTC, by Albert Pastuszka (User B@P) of Poland using a GeForce GTX 750 in an AMD Athlon(tm) II X3 445 Processor with 6GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 6 hours, 46 minutes to complete the probable prime (PRP) test using GeneferOCL2. Albert Pastuszka is a member of BOINC@Poland.

The PRP was confirmed prime by an AMD Ryzen 5 3600 6-Core Processor with 4GB RAM, running Linux Ubuntu. This computer took about 22 hours, 17 minutes to complete the primality test using LLR.

Other significant primes

3·218924988-1 (321): official announcement | 321
3·218196595-1 (321): official announcement | 321
3·217748034-1 (321): official announcement | 321
3·216819291-1 (321): official announcement | 321
3·216408818+1 (321): official announcement | 321

27·28342438-1 (27121): official announcement | 27121
121·29584444+1 (27121): official announcement | 27121
27·27046834+1 (27121): official announcement | 27121
27·25213635+1 (27121): official announcement | 27121
27·24583717-1 (27121): official announcement | 27121

224584605939537911+81292139*23#*n for n=0..26 (AP27): official announcement
48277590120607451+37835074*23#*n for n=0..25 (AP26): official announcement
142099325379199423+16549135*23#*n for n=0..25 (AP26): official announcement
149836681069944461+7725290*23#*n for n=0..25 (AP26): official announcement
43142746595714191+23681770*23#*n for n=0..25 (AP26): official announcement

6679881·26679881+1 (CUL): official announcement | Cullen
6328548·26328548+1 (CUL): official announcement | Cullen

202705·221320516+1 (ESP): official announcement | k=202705 eliminated
99739·214019102+1 (ESP): official announcement | k=99739 eliminated
193997·211452891+1 (ESP): official announcement | k=193997 eliminated
161041·27107964+1 (ESP): official announcement | k=161041 eliminated

147855!-1 (FPS): official announcement | Factorial
110059!+1 (FPS): official announcement | Factorial
103040!-1 (FPS): official announcement | Factorial
94550!-1 (FPS): official announcement | Factorial

27·27963247+1 (PPS-DIV): official announcement | Fermat Divisor
13·25523860+1 (PPS-DIV): official announcement | Fermat Divisor
193·23329782+1 (PPS-Mega): official announcement | Fermat Divisor
57·22747499+1 (PPS): official announcement | Fermat Divisor
267·22662090+1 (PPS): official announcement | Fermat Divisor

2525532·732525532+1 (GC): official announcement | Generalized Cullen
2805222·252805222+1 (GC): official announcement | Generalized Cullen
1806676·411806676+1 (GC): official announcement | Generalized Cullen
1323365·1161323365+1 (GC): official announcement | Generalized Cullen
1341174·531341174+1 (GC): official announcement | Generalized Cullen

19517341048576+1 (GFN): official announcement | Generalized Fermat Prime
4896418524288+1 (GFN): official announcement | Generalized Fermat Prime
10590941048576+1 (GFN): official announcement | Generalized Fermat Prime
9194441048576+1 (GFN): official announcement | Generalized Fermat Prime
3638450524288+1 (GFN): official announcement | Generalized Fermat Prime

563528·13563528-1 (GW): official announcement | Generalized Woodall
404882·43404882-1 (GW): official announcement | Generalized Woodall

3267113#-1 (PRS): official announcement | Primorial
1098133#-1 (PRS): official announcement | Primorial
843301#-1 (PRS): official announcement | Primorial

25·28788628+1 (PPS-DIV): official announcement | Top 100 Prime
17·28636199+1 (PPS-DIV): official announcement | Top 100 Prime
25·28456828+1 (PPS-DIV): official announcement | Top 100 Prime
39·28413422+1 (PPS-DIV): official announcement | Top 100 Prime
31·28348000+1 (PPS-DIV): official announcement | Top 100 Prime

168451·219375200+1 (PSP): official announcement | k=168451 eliminated

10223·231172165+1 (SoB): official announcement | k=10223 eliminated

2996863034895·21290000±1 (SGS): official announcement | Twin
2618163402417·21290000-1 (SGS), 2618163402417·21290001-1 (2p+1): official announcement | Sophie Germain
18543637900515·2666667-1 (SGS), 18543637900515·2666668-1 (2p+1): official announcement | Sophie Germain
3756801695685·2666669±1 (SGS): official announcement | Twin
65516468355·2333333±1 (TPS): official announcement | Twin

63838·53887851-1 (SR5): official announcement | k=63838 eliminated
273662·53493296-1 (SR5): official announcement | k=273662 eliminated
102818·53440382-1 (SR5): official announcement | k=102818 eliminated
109838·53168862-1 (SR5): official announcement | k=109838 eliminated
118568·53112069+1 (SR5): official announcement | k=118568 eliminated

9221·211392194-1 (TRP): official announcement | k=9221 eliminated
146561·211280802-1 (TRP): official announcement | k=146561 eliminated
273809·28932416-1 (TRP): official announcement | k=273809 eliminated
502573·27181987-1 (TRP): official announcement | k=502573 eliminated
402539·27173024-1 (TRP): official announcement | k=402539 eliminated

17016602·217016602-1 (WOO): official announcement | Woodall
3752948·23752948-1 (WOO): official announcement | Woodall
2367906·22367906-1 (WOO): official announcement | Woodall
2013992·22013992-1 (WOO): official announcement | Woodall

News

2023 Tour de Primes is almost here!
It is almost time for PrimeGrid's annual Tour de Primes, our month-long celebration of prime numbers.

2 is the first prime number, so we will honor the second month of the year by awarding special badges to everyone who finds a top-5000 prime during February.

This year, for the first time, all of our BOINC projects that search for primes large enough to be in the top 5000 utilize the fast double checking system, so every prime counts -- there's no double checkers.

Come and join the fun as the primes fly -- or the server blows up.. Either way, it's going to be an exciting month!

Details and discussion can be found at this forum thread: 2023 Tour de Primes
30 Jan 2023 | 4:09:31 UTC · Comment

PrimeGrid now supports Intel ARC GPU apps and native Apple M1/M2 CPU and GPU apps
Effective immediately, PrimeGrid has apps for the following sub-projects for the new hardware:

Native Apple M1/M2 ARM CPU apps are available on GFN-17 through GFN-22.

Native M1/M2 GPU apps are available on GFN-16 through GFN-22 as well as DYFL.

Intel ARC GPU apps are available on GFN-16 through GFN-22 as well as DYFL.

Discussion about the new apps can be found on our Discord server, or in this forum thread.
5 Dec 2022 | 22:00:06 UTC · Comment

WW Project to End Soon
Within the next month or two, the WW project will reach the limit of the software, and the project will shut down.

Details and discussion can be found here.
14 Nov 2022 | 6:35:59 UTC · Comment

GFN 20 Found!
On 9 August 2022, 11:56:02 UTC, PrimeGrid’s Generalized Fermat Prime Search found the Generalized Fermat mega prime:

1951734^1048576+1

The prime is 6,595,985 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Generalized Fermat primes and 13th overall. This is the second-largest prime found by PrimeGrid, and the second-largest non-Mersenne prime.

The discovery was made by Kazuya Tanaka (apophise@jisaku) of Japan using an NVIDIA GeForce RTX 3080 Ti in an Intel(R) Core(TM) i7-9700K CPU @ 3.60GHz with 64GB RAM, running Microsoft Windows 10 Professional x64 Edition. This GPU took about 1 hour, 2 minutes to complete the probable prime (PRP) test using GeneferOCL5. Kazuya Tanaka is a member of Team 2ch.

The prime was verified on 10 August 2022, 17:39:14 UTC by Jens Katzur (Landjunge) of Germany using an NVIDIA GeForce RTX 3070 in an Intel(R) Xeon(R) CPU X5675 @ 3.07GHz with 40GB RAM, running Linux Ubuntu. This computer took about 1 hour, 36 minutes to complete the probable prime (PRP) test using GeneferOCL5. Jens Katzur is a member of Planet 3DNow!.

The PRP was confirmed prime on 11 August 2022 by an AMD Ryzen 9 5950X @3.4GHz, running Linux Mint. This computer took about 51 hours, 52 minutes to complete the primality test using LLR2.

For more details, please see the official announcement.
17 Sep 2022 | 1:24:25 UTC · Comment

SR5 Mega Prime Find!
On 19 June 2022, 04:26:15 UTC, PrimeGrid’s Sierpinski/Riesel Base 5 Problem project eliminated k=63838 by finding the mega prime:

63838*5^3887851-1

The prime is 2,717,497 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 99th overall. 58 k’s now remain in the Riesel Base 5 problem.

The discovery was made by Scott Lee (freestman) of China using an AMD Ryzen 5 2600X Six-Core Processor with 32GB RAM, running Microsoft Windows 11 Professional x64 Edition. This computer took about 4 hours, 34 minutes to complete the prp test using LLR2. Scott is a member of the team, Chinese Dream.

The prime was verified on 19 June 2022, 22:29 UTC, by an Intel(R) Core(TM) i3-9100F CPU @ 3.60GHz with 16GB RAM, running Linux. This computer took about 11 hours and 57 minutes to complete the primality test using LLR2.

For more details, please see the official announcement.
18 Jul 2022 | 19:26:44 UTC · Comment

... more

News is available as an RSS feed

Newly reported primes

(Mega-primes are in bold.)

135497678^131072+1 (vaughan); 135513092^131072+1 (Sphynx); 185055224^65536+1 (CavernDigger88); 134459616^131072+1 (Youareyou); 135695350^131072+1 (288larsson); 135458028^131072+1 (zombie67 [MM]); 135744154^131072+1 (Eudy Silva); 135623220^131072+1 (motqalden); 136227118^131072+1 (parsnip soup in a clay bowl); 184839498^65536+1 (Andreas Sniekers); 134206304^131072+1 (Hans Sveen); 134447516^131072+1 (vaughan); 135332960^131072+1 (Robert Hoffman); 134706086^131072+1 (crashtech); 135135930^131072+1 (vaughan); 134322272^131072+1 (vaughan); 184980314^65536+1 (Michael Millerick); 133676500^131072+1 (vaughan); 184674964^65536+1 (Jann); 6337*2^3449506+1 (Ryan Propper)

Top Crunchers:

Top participants by RAC

 Syracuse University 9.36943e+07 Science United 8.81532e+07 tng 2.22322e+07 Ryan Propper 1.26426e+07 EA6LE 1.16288e+07 ian 1.06992e+07 Miklos M. 1.02385e+07 vanos0512 8.44663e+06 valterc 7.83212e+06 bluestang 6.05994e+06

Top teams by RAC

 Antarctic Crunchers 4.94414e+07 Czech National Team 2.03244e+07 SETI.Germany 2.03019e+07 The Scottish Boinc Team 1.89335e+07 Team China 1.8879e+07 Aggie The Pew 1.80599e+07 SETI.USA 1.56992e+07 Romania 1.18306e+07 BOINC@Taiwan 1.1627e+07 TeAm AnandTech 1.05631e+07