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.
- Seventeen or Bust: helping to solve the Sierpinski Problem.
- Sierpinski/Riesel Base 5: helping to solve the Sierpinski/Riesel Base 5 Problem.
- 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
"Einstein" anniversary challenge
From March 20th 03:14:00 UTC to March 25th 03:14:00 PrimeGrid will be running a 5 day challenge on the Extended Sierpinsky project (ESP). Note the unusual start and end times!
For more information, please see this forum thread.
15 Mar 2024 | 21:54:57 UTC
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Policy regarding banning computers
Effective immediately, PrimeGrid reserves the right to ban computers that exhibit problematic behavior.
Please see this forum thread for more information.
22 Feb 2024 | 17:04:48 UTC
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Tour de Primes 2024
February is almost upon us, and with it, PrimeGrid's annual Tour de Primes.
This is a month long event where all can earn special Tour de Primes badges and a lucky few will win the coveted Tour de Primes jerseys.
More information can be found here.
31 Jan 2024 | 17:11:00 UTC
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Unplanned outage
This afternoon PrimeGrid experienced an unplanned outage. For reasons unknown, the database locked up and started consuming 100% CPU on all 32 cores, while doing nothing at all.
We proceeded cautiously, not wanting to risk damaging the database, and slowly shut down the system, checked the database, and brought everything back up.
Everything is back to normal, and the servers are operating once again.
27 Jan 2024 | 0:49:20 UTC
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Hilbert's Birthday Challenge starts 23 January
The first challenge of the 2024 Series will be a 3-day challenge celebrating David Hilbert's birthday! The challenge will be offered on the PPSE-LLR application, running from January 23 01:00 UTC to January 26 01:00 UTC.
To participate in the Challenge, please select only the Proth Prime Search Extended LLR (PPSE) project in your PrimeGrid preferences section. Join the discussion at https://www.primegrid.com/forum_thread.php?id=10425.
15 Jan 2024 | 12:25:35 UTC
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Newly reported primes(Mega-primes are in bold.)
7811*2^1943413+1 (USTL-FIL (Lille Fr)); 6613*2^1942806+1 (USTL-FIL (Lille Fr)); 36748386^262144+1 (damotbe); 373674782^65536+1 (Holdolin); 373644824^65536+1 (Holdolin); 373449408^65536+1 ([AF>Belgique] bill1170); 373289162^65536+1 (Aperture_Science_Innovators); 373280594^65536+1 (Holdolin); 281*2^4886723+1 (damotbe); 6911*2^1942561+1 (bparsonnet); 9585*2^1942368+1 (Aperture_Science_Innovators); 221636362^131072+1 (Chooka); 3193*2^1942448+1 (Gianni Valentino); 4447*2^1942444+1 (SkyHighWeFly); 5041*2^1942168+1 (meso@Mayoineko); 221528336^131072+1 (JayPi); 372959772^65536+1 (Werinbert); 372824658^65536+1 (Sad); 2271*2^1940969+1 (Aperture_Science_Innovators); 36717890^262144+1 (k4m1k4z3) Top Crunchers:Top participants by RAC | Top teams by RAC |
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