## 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 5 July 2023, 17:48:23 UTC, PrimeGrid's 321 Prime Search found the Mega Prime
3*220928756-1
The prime is 6,300,184 digits long and will enter The Largest Known Primes Database ranked 19th overall. This is the largest known prime for the 3*2n-1 form.

The discovery was made by Arno Lehmann (Zyfdnug) of Germany using an AMD Ryzen 9 7900X @ 4.7GHz with 64GB RAM, running Debian GNU/Linux 12 (bookworm). This CPU took about 6 hours, 20 minutes to complete the probable prime (PRP) test using LLR2.

The PRP was confirmed prime on 5 July 2023 by an AMD Ryzen 9 5950X @ 3.4GHz, running Linux Mint. This computer took about 2 hours, 46 minutes to complete the primality test using LLR2.

On 8 June 2023, 01:41:31 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime
6339004524288+1
The prime is 3,566,218 digits long and will enter The Largest Known Primes Database ranked 9th for Generalized Fermat primes and 70th overall.

The discovery was made by Ken Glennie (xcroc) of Australia using an NVIDIA GeForce GTX 1080 Ti in an Intel(R) Xeon(R) CPU E5-2690 0 @ 2.90GHz with 32GB RAM, running Ubuntu 20.04.5 LTS. This GPU took about 1 hour, 31 minutes to complete the probable prime (PRP) test using Genefer22. Ken Glennie is a member of the SW QLD team.

The PRP was confirmed prime on 8 June 2023 by an AMD Ryzen 9 5950X @ 3.4GHz, running Linux Mint. This computer took about 9 hours, 33 minutes to complete the primality test using LLR2.

On 24 September 2022, 15:01:43 UTC, PrimeGrid's Generalized Fermat Prime Search found the Mega Prime
19637361048576+1
The prime is 6,598,776 digits long and will enter The Largest Known Primes Database ranked 1st for Generalized Fermat primes and 13th overall.

The discovery was made by Tom Greer (tng) of the United States using GeneferOCL5. Tom Greer is a member of the Antarctic Crunchers team.

The prime was verified by Wolfgang Schwieger (DeleteNull) of Germany using GeneferOCL5. Wolfgang Schwieger is a member of the SETI.Germany team.

The PRP was confirmed prime on 26 September 2022 by an AMD Ryzen 9 5950X @ 3.4GHz, running Linux Mint. This computer took about 51 hours, 40 minutes to complete the primality test using LLR2.

### Other significant primes

3·220928756-1 (321): official announcement | 321
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

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

277699295941594831+170826477*23#*n for n=0..26 (AP27): official announcement
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

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

6339004524288+1 (GFN): official announcement | Generalized Fermat Prime
19637361048576+1 (GFN): official announcement | Generalized Fermat Prime
19517341048576+1 (GFN): official announcement | Generalized Fermat Prime
4896418524288+1 (GFN): official announcement | Generalized Fermat Prime
10590941048576+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

PrimeGrid will be offline for server upgrades
We're upgrading to new servers sometime within the next week. With minimal warning, all PrimeGrid servers will be down for several hours.

Discord, of course, will remain available.

Discussion and more information will be available on Discord as well as on the the forums. The forums will be offline during the upgrade, however, so Discord is where we can be reached during the upgrade.

EDIT #1: The plan is for the server upgrades to begin at 15:00 UTC Friday.
26 Sep 2023 | 22:15:06 UTC · Comment

Revised: PPSE gets a reprieve but PPS-MEGA is shutting down
After a lot of discussion, some changes have been made in the projects that are closing. PPS-MEGA is shutting down on October 19th, while PPSE will continue running to its natural end at one million digits.

More details can be found on the forum.
18 Sep 2023 | 20:47:07 UTC · Comment

PPS-Sieve, PPSE, GFN-15, SGS, and AP27 are shutting down
We recently took a look at the projects that we are running and decided to make some changes.

For more information, and discussion, see this thread: PPS-Sieve, PPSE, GFN-15, SGS, and AP27 are shutting down.

(Note that the plan has since changed and PPS-MEGA is shutting down instead of PPSE.)
14 Sep 2023 | 21:28:20 UTC · Comment

World Peace Day Challenge starts September 13th @ 11:00 UTC!
The seventh challenge of the 2023 Series will be a 10-day challenge celebrating World Peace Day, also known as the International Day of Peace, an annual United Nations holiday observed on September 21st. The challenge will be offered on the SOB-LLR application, beginning 13 September 11:00 UTC and ending 23 September 11:00 UTC.

To participate in the Challenge, please select only the Seventeen or Bust (LLR) project in your PrimeGrid preferences section.

Thoughts? Theories? Tidbits? Truisms? Trivialities? Read more and join the discussion at https://www.primegrid.com/forum_thread.php?id=10322
12 Sep 2023 | 18:12:46 UTC · Comment

Sieving for Proth Prime Search to be suspended
The PPS Sieve has advanced well beyond the searches that use the sieve, and it will be many years before more sieving is needed. We are therefore suspending the PPS sieve. The CPU apps will be removed 30 days from now, on October 4th. The GPU apps will be removed, and the sieve fully suspended, somewhat later.

4 Sep 2023 | 7:21:47 UTC · Comment

... more

News is available as an RSS feed

### Newly reported primes

(Mega-primes are in bold.)

8589295654095*2^1290000-1 (Grebuloner); 8593825816845*2^1290000-1 (khs); 403941182^32768+1 (Penguin); 8590360173717*2^1290000-1 (walli); 8587708717437*2^1290000-1 (Farscape); 8587308239475*2^1290000-1 (k0r3); 8589736734507*2^1290000-1 (lajjr); 8584373479575*2^1290000-1 (Grebuloner); 403706392^32768+1 (PDW); 9029*2^3483337+1 (dannyridel); 8586841083597*2^1290000-1 (vaughan); 403492144^32768+1 (PDW); 403626324^32768+1 ([AF>Libristes] Davlabedave); 403599572^32768+1 (kiska); 8586254553375*2^1290000-1 (AlHo); 8582517912705*2^1290000-1 (DaveSun); 403402934^32768+1 (gemini8); 403387094^32768+1 (kiska); 403378674^32768+1 (PDW); 403156936^32768+1 (Steve Dodd)

## Top Crunchers:

### Top participants by RAC

 Nick 3.89649e+07 vaughan 3.51851e+07 Miklos M. 3.36188e+07 JGREAVES 2.83885e+07 tng 2.78094e+07 Scott Brown 2.27686e+07 EA6LE 1.97821e+07 CR320 1.52752e+07 Farscape 1.45836e+07 zombie67 [MM] 1.43966e+07

### Top teams by RAC

 Antarctic Crunchers 8.12325e+07 The Scottish Boinc Team 5.33202e+07 BOINC@AUSTRALIA 5.09828e+07 AMD Users 4.63547e+07 Team China 4.0636e+07 Aggie The Pew 3.87517e+07 SETI.Germany 3.41159e+07 SETI.USA 3.11458e+07 Czech National Team 2.56093e+07 TeAm AnandTech 2.02218e+07