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 1 March 2021, 02:47:51 UTC, PrimeGrid's Fermat Divisor Search found the Mega Prime
25·28788628+1
The prime is 2,645,643 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 75th overall.

The discovery was made by Tom Greer (tng) of the United States using an Authentic AMD Ryzen 9 5950X CPU @ 4.90GHz with 32GB RAM, running Microsoft Windows 10 Professional. This computer took about 2 hours and 46 minutes to complete the primality test using LLR2. Tom Greer is a member of the Antarctic Crunchers team.

On 17 February 2021, 14:27:08 UTC, PrimeGrid's Fermat Divisor Search found the Mega Prime
17·28636199+1
The prime is 2,599,757 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 76th 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 5 hours to complete the primality test using LLR2. Tom Greer is a member of the Antarctic Crunchers team.

On 7 February 2021, 18:01:10 UTC, PrimeGrid's The Riesel Problem project eliminated k=9221 by finding the Mega Prime
9221·211392194-1
The prime is 3,429,397 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 44th overall. This is PrimeGrid's 17th elimination. 47 k's now remain.

The discovery was made by Barry Schnur (BarryAZ) of the United States using an AMD Ryzen 5 2600 Six-Core Processor with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition. This computer took about 2 days, 29 minutes to complete the primality test using LLR2. Barry Schnur is a member of the BOINC Synergy team.

### Other significant primes

3·216819291-1 (321): official announcement | 321
3·216408818+1 (321): official announcement | 321
3·211895718-1 (321): official announcement | 321
3·211731850-1 (321): official announcement | 321
3·211484018-1 (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

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

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
682156·79682156+1 (GC): official announcement | Generalized Cullen

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
2985036524288+1 (GFN): official announcement | Generalized Fermat Prime

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

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

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
238694·52979422-1 (SR5): official announcement | k=238694 eliminated
146264·52953282-1 (SR5): official announcement | k=146264 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

World Emoji Day Challenge starts July 17th
The fifth challenge of the 2021 Series will be a 3-day challenge in celebration of what is arguably the internet's most momentous and culturally significant holiday: World Emoji Day. The challenge will be offered on the GFN-17-Low subproject, beginning 17 July 22:00 UTC and ending 20 July 22:00 UTC.

To participate in the Challenge, please select only the GFN-17-Low subproject in your PrimeGrid preferences section.

Best of luck!
15 Jul 2021 | 5:23:34 UTC · Comment

DIV Mega Prime! (Belated Posting)
On 1 March 2021, 02:47:51 UTC, PrimeGrid's Fermat Divisor Search found the Mega Prime:

25*2^8788628+1

The prime is 2,645,643 digits long and enters Chris Caldwell's “The Largest Known Primes Database” ranked 75th overall.

The discovery was made by Tom Greer (tng) of the United States using an Authentic AMD Ryzen 9 5950X CPU @ 4.90GHz with 32GB RAM, running Microsoft Windows 10 Professional. This computer took about 2 hours and 46 minutes to complete the primality test using LLR2. Tom Greer is a member of the Antarctic Crunchers team.

For more details, please see the official announcement.
1 Jul 2021 | 19:48:36 UTC · Comment

PrimeGrid's 16th Birthday Challenge starts June 12
The fourth challenge of the 2021 Series will be a 5-day challenge celebrating the 16th anniversary of the launch of PrimeGrid on BOINC. The challenge will be offered on the ESP-LLR application, beginning 12 June 13:00 UTC and ending 17 June 13:00 UTC.

To participate in the Challenge, please select only the Extended Sierpinski Problem LLR (ESP) project in your PrimeGrid preferences section.

Best of luck!
9 Jun 2021 | 13:46:42 UTC · Comment

Yuri's Night Challenge starts April 11th
The third challenge of the 2021 Series will be a 3-day challenge celebrating the 60th anniversary of Yuri Gagarin's history-making venture into outer space. The challenge will be offered on the WW application, beginning 11 April 18:00 UTC and ending 14 April 18:00 UTC.

This is a relatively new subproject here at PrimeGrid, and there are currently no known Wall–Sun–Sun primes! You could be the first to find one!

To participate in the Challenge, please select only the Wieferich and Wall-Sun-Sun Prime Search (WW) project in your PrimeGrid preferences section.

Questions? Queries? Quips? Discuss on the forum thread for this challenge. Best of luck!
8 Apr 2021 | 15:32:42 UTC · Comment

An Ending and a Beginning
This is the End...

Yesterday, the last task in our Fermat Divisor Search was sent out for processing. While there will likely be a few resends available over the next week or two, if you have PPS-DIV selected as your only project, we recommend choosing something else.

This project was very successful, having found two Fermat divisors! Congratulations everyone, and thank you for participating.

Discussion about the Fermat divisor search can be found here: https://www.primegrid.com/forum_forum.php?id=121

...And Also the Beginning

In less than an hour, at 12:00 UTC on Pi Day, our Sier"pi"nski's Birthday Challenge will be starting. This is a 10 day challenge on our Seventeen or Bust (SoB) project.

14 Mar 2021 | 11:23:58 UTC · Comment

... more

News is available as an RSS feed

### Newly reported primes

(Mega-primes are in bold.)

6319250179755*2^1290000-1 (Qazort); 6312835527495*2^1290000-1 (mrzorronator); 129750926^65536+1 (Marcin); 129630358^65536+1 (Marcin); 247712590^32768+1 (Grind29); 6317345244597*2^1290000-1 (YuW3-810); 31821360^131072+1 (dthonon); 31768014^131072+1 (Eric Nietering); 3777*2^3374072+1 (ext2097); 9347*2^3374055+1 (ian); 247511394^32768+1 (Spear); 6315804892845*2^1290000-1 (YuW3-810); 6313171968705*2^1290000-1 (Charles Jackson); 129574744^65536+1 (Marcin); 247127946^32768+1 (Dave); 247119758^32768+1 (dannyridel); 129984458^65536+1 (YuW3-810); 8957*2^1642243+1 (usverg); 6311153405037*2^1290000-1 (zombie67 [MM]); 31469984^131072+1 (Bertle)

## Top Crunchers:

### Top participants by RAC

 Science United 3.42724e+07 Grzegorz Roman Granowski 2.9965e+07 tng 2.78823e+07 Miklos M. 1.70425e+07 Tuna Ertemalp 1.49892e+07 valterc 1.19029e+07 Scott Brown 1.01907e+07 DeleteNull 8.70039e+06 Nick 7.66821e+06 RFGuy_KCCO 7.5314e+06

### Top teams by RAC

 The Scottish Boinc Team 4.65281e+07 Antarctic Crunchers 4.51554e+07 Aggie The Pew 2.02335e+07 Czech National Team 2.01788e+07 SETI.Germany 1.9303e+07 Microsoft 1.49887e+07 BOINC.Italy 1.25151e+07 BOINC@AUSTRALIA 1.19245e+07 SETI.USA 1.06593e+07 L'Alliance Francophone 7.91283e+06