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 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 19 th overall. This is the largest known prime for the 3*2 n-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.
For more information, please see the Official Announcement.
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 9 th for Generalized Fermat primes and 70 th 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.
For more information, please see the Official Announcement.
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.
For more information, please see the Official Announcement.
Other significant primes
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News 
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.
More information, and discussion, can be found here.
4 Sep 2023 | 7:21:47 UTC
· Comment
321 Prime Found!
On 5 July 2023, 17:48:23 UTC, PrimeGrid's 321 Prime Search found the Mega Prime:
3*2^20928756-1
The prime is 6,300,184 digits long and will enter Chris Caldwell's “The Largest Known Primes Database” ranked 19th overall. This is the largest known prime for the 3*2^n-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.
For more details, please see the official announcement.
3 Sep 2023 | 18:59:29 UTC
· Comment
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News is available as an RSS feed 
Newly reported primes(Mega-primes are in bold.)
1341*2^1764896+1 (Zinsig Kim); 409541192^32768+1 (zombie67 [MM]); 8650912587177*2^1290000-1 (Freezing); 8650823033127*2^1290000-1 (Michael Goetz); 5873*2^3483573+1 (hase); 3713*2^1764917+1 (Grzegorz Roman Granowski); 2895*2^3483455+1 (vonboedefeldt); 409344882^32768+1 (Ken_g6); 409202256^32768+1 ([AF] Kalianthys); 290205462^65536+1 (Sophie); 8648125309257*2^1290000-1 (Dave); 289713146^65536+1 (Alexander Morávek); 408931670^32768+1 (gemini8); 408756310^32768+1 (PDW); 408716764^32768+1 (zombie67 [MM]); 408855392^32768+1 (PDW); 408573022^32768+1 (PDW); 8642253284535*2^1290000-1 (Eric Nietering); 408425708^32768+1 (gemini8); 408332896^32768+1 (zombie67 [MM]) Top Crunchers:Top participants by RAC | Top teams by RAC |
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