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 15 May 2022, 17:29:48 UTC, PrimeGrid's Generalized Fermat Prime Search 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.

On 24 March 2022, 17:27:33 UTC, PrimeGrid's 321 Prime Search found the Mega Prime
3·218924988-1
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.

On 8 January 2022, 20:46:05 UTC, PrimeGrid’s 321 Prime Search found the Mega Prime
3·218196595-1
The prime is 5,477,722 digits long and enters 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.

### 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

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
3214654524288+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

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
207494·53017502-1 (SR5): official announcement | k=207494 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

M.C. Escher's Birthday Challenge starts June 17th
The fourth challenge of the 2022 Series will be a 5-day challenge marking the 124th birthday of Maurits Cornelis Escher, one of the world’s most famous graphic artists. His art is admired by millions of people worldwide, as can be seen by the many websites on the internet. The challenge will be offered on the SR5-LLR application, beginning 17 June 13:00 UTC and ending 22 June 13:00 UTC.

To participate in the Challenge, please select only the Sierpinski/Riesel Base 5 Prime Search LLR (SR5) project in your PrimeGrid preferences section.

Comments? Concerns? Conundrums? Check out the forum thread for this challenge: http://www.primegrid.com/forum_thread.php?id=9941&nowrap=true#155914

Happy crunching!
14 Jun 2022 | 2:39:31 UTC · Comment

Geek Pride Day Challenge starts May 25
The third challenge of the 2022 Series will be a 5-day challenge celebrating geeks, freaks, nerds, dorks, dweebs, and "weird" people of all kinds! The challenge will be offered on the GFN-19 subproject, beginning 25 May 18:00 UTC and ending 30 May 18:00 UTC.

To participate in the Challenge, please select only the GFN-19 subproject 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=9915&nowrap=true#155479
23 May 2022 | 22:18:31 UTC · Comment

GFN 19 Found!
On 15 May 2022, 17:29:48 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime:

4896418^524288+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 54th overall.

The discovery was made by Tom Greer (tng) of the United States using a 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.

For more details, please see the official announcement.
22 May 2022 | 23:50:20 UTC · Comment

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 · Comment

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 · Comment

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News is available as an RSS feed

### Newly reported primes

(Mega-primes are in bold.)

7176707748987*2^1290000-1 (YuW3-810); 112580428^131072+1 (akeda); 160477270^65536+1 (vaughan); 1047*2^3272351+1 (akeda); 579*2^3269850+1 (Scott Brown); 3021*2^3427059+1 (Trotador); 160459326^65536+1 (candido); 7175094167727*2^1290000-1 (tng); 296776988^32768+1 (o-ando); 296682420^32768+1 (walkman); 7172971474035*2^1290000-1 (Peter Tuttle); 7168845692505*2^1290000-1 (McNickey); 296641862^32768+1 (Vato); 7693*2^1700992+1 (larrys); 296581420^32768+1 (sams88); 296550900^32768+1 (DiscoSkyline); 7166000820585*2^1290000-1 (NXR); 933*2^3270993+1 (Peter Cheung); 2339*2^3426599+1 (DeleteNull); 4729*2^3426558+1 (James)

## Top Crunchers:

### Top participants by RAC

 Syracuse University 1.24808e+08 Science United 5.22557e+07 valterc 3.19414e+07 Tuna Ertemalp 2.58498e+07 Scott Brown 2.15381e+07 tng 1.86238e+07 Nick 1.5533e+07 Freezing 1.3967e+07 Miklos M. 1.13481e+07 Grzegorz Roman Granowski 1.0404e+07

### Top teams by RAC

 Antarctic Crunchers 5.17821e+07 BOINC.Italy 3.28294e+07 Aggie The Pew 3.12138e+07 SETI.Germany 2.94169e+07 Microsoft 2.58774e+07 The Scottish Boinc Team 2.48381e+07 BOINC@AUSTRALIA 1.90706e+07 Czech National Team 1.87131e+07 SETI.USA 1.30573e+07 Team China 1.30148e+07