Great Internet Mersenne Prime Search
Current Version: 22.12
Client Download size: 1 MB or less
OS: All major platforms
Progress: Found largest known prime
Percent% complete: Ongoing
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From the project website:
"Prime numbers have long fascinated amateur and professional mathematicians. An integer greater
than one is called a prime number if its only divisors are one and itself. The first prime
numbers are 2, 3, 5, 7, 11, etc. For example, the number 10 is not prime because it is divisible
by 2 and 5. A Mersenne prime is a prime of the form 2P-1. The first Mersenne primes are 3, 7, 31,
127, etc. There are only 39 known Mersenne primes."
"GIMPS, the Great Internet Mersenne Prime Search, was formed in January 1996 to discover new
world-record-size Mersenne primes. GIMPS harnesses the power of thousands of small computers
like yours to search for these "needles in a haystack"."
The current largest known Mersenne prime number is 213,466,917 - 1 (found on
November 14, 2001 by GIMPS, and containing 4,053,946 digits). Help find the next one in the
Great Internet Mersenne Prime Search (GIMPS).
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Yves Gallot's Proth Prime Search Page
Current Version: 7.1
Client Download size: 380 KB
OS: Windows
Progress: n/a
Percent% Complete: ongoing
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From the project website:
"Yves Gallot wrote an excellent Win95/98/NT4.0 program which makes it easy for anyone to find
record size or otherwise interesting primes, but this creates a problem: without a coordinated
effort, many of us were be searching the same ranges of numbers for primes! Some spent hundreds
of hours checking ranges that were already known to be barren. So I have begun this page in
order to reduce this unnecessary duplication. Please join us in the search!"
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Current Version: n/a
Client Download size: variable
OS: All Major Platforms
Progress: n/a
Percent% complete: Ongoing
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The goals of ECMNET
- Help to find new factors of Cunningham numbers [difficult]
- Find a record factor (currently 54 digits) [very difficult]
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Current Version: 1.101
Client Download size: 1.22 MB
OS: Windows
Progress: 3 primes found
Percent% complete: ongoing
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From the project website:
The purpose of this page is to coordinate effort to search for the next primes of the form n!+1
& n!-1. At the moment our purpose is to search the range between 30,000 -> 100,000.
All numbers in the range have been trial factored by Phil Carmody up to 6,320,124,029. The next
step is perform a probable primality test to every remaining number. The number 35,000! is
143,845 digits long and the number 100,000! 456,574 digits.
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Current Version: 4.21b
Client Download size: 135 KB
OS: Windows
Progress: n/a
Percent% complete: Resta 6, 60% complete
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Help Find a power of 6 equal to 6 powers of 6.
On December 13, 2002, a project member discovered the largest (6,2,5) result: 599956 +
68566 = 579746 + 412506 + 393726 + 155406 + 94996.
The client automatically downloads ranges of numbers to work on.
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Current Version: n/a
Client Download size: 95 KB or less
OS: All major platforms
Progress: n/a
Percent% Complete: d-11, 25% done
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According to the website,
"Lattice rules are used for the numerical approximation of
multidimensional integrals over the unit hypercube. They are designed for integrating naturally
periodic integrands."
Help Search for these K-optimal lattice rules.
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Current Version: 2.29
Client Download size: 250 KB
OS: Windows, Linux
Progress: 6466 ranges checked
Percent% complete: 2534 ranges left
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From the project website:
Search for factors of 2^(2^61-1)-1, a double Mersenne number, in the MM61 project. Download
and test the client, then email the project coordinator to reserve a range of numbers to test.
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Current Version: n/a
Client Download size: 15KB
OS: Windows
Progress: 32 found
Percent% Complete: up to 21,000 checked
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Find 3x+1 class records in the 3x+1 Problem project. This project attempts to find ever higher
3x+1 class records. The client, which will work on any PC/Windows platform, and the instructions
for joining the project, are here.
Note: the client takes about 6 weeks to finish one block on a 400-MHz CPU.
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Current Version: 1.5
Client Download size: n/a
OS: Windows
Progress: (on hold)
Percent% complete: n/a
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The pi(x) project calculates pi(x), for very large values of x. It most recently calculated
pi(x) for x=4*1022. You can contribute to the calculations for pi(x) for x=1023.
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Fermat Number Divisors Search
Current Version: 4.1
Client Download size: n/a
OS: Windows
Progress: 8 fermats found
Percent% Complete: Ongoing
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From the project website:
"Fermat numbers have a very beautiful mathematical form: 22^m+1. The first 5 numbers
F0=3, F1=5, F2=17, F3=257, F4=65537 are
all prime. Having discovered this fact, Pierre Fermat assumed that all numbers of this type were
prime. But he was mistaken. In 1732 after almost a century, Euler elegantly proved that F5
had a factor: 641 and was therefore not prime.
This year can be considered as the beginning of the search for dividers of other Fermat numbers.
For 3 centuries more than 200 dividers were found. It has been proven that all divisors of Fermat
numbers have the simple form: k.2n+1, where n > m+2.
This corollary is being used for discovery of Fermat number dividers. Because of the scarcity
and difficulty of finding these dividers, the person who discovers a new factor takes his place
in history."
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PCP@home
Current Version: n/a
Client Download size: 170 KB or less
OS: Windows, Linux, Unix
Progress: n/a
Percent% complete: Ongoing
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The PCP@Home project looks for short cases of Post's Correspondence Problem with large shortest
solutions. This theoretical computer science problem has been in existence since 1946. It
demonstrates undecidability: "a problem that cannot be solved for all cases by any algorithm
whatsoever." Finding PCPs in this project will help define "decidability criteria for bounded
PCP classes."
Note to Windows users: the Windows client was compiled by Michael
Keppler of Rechenkraft.net. He says that it has a serious memory leak, and that you may need to
kill it and restart it every day. If anyone knows how to debug Windows application memory leaks,
please contact him.
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Current Version: 5.6
Client Download size: n/a
OS: Windows
Progress: n/a
Percent% Complete: Ongoing
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Find generalized Woodall numbers in the Generalized Woodall Numbers project. This project uses
the Proth program to find these numbers.
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Generalized Fermat Prime Search
Current Version: 1.2
Client Download size: unknown
OS: Windows, Linux, Unix
Progress: 34 primes found
Percent% complete: Ongoing
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Find generalized Fermat prime numbers in the Generalized Fermat Prime Search. This project
uses the Proth program or the GFNSieve21 program to find these numbers.
On January 6, 2003, Daniel Heuer discovered the largest known Generalized Fermat prime
148307665536+1 (404,434 digits), with GFNSieve+Proth, beating his previous record from October
8, 2002. "This number is the new largest known prime which is not a Mersenne prime, and the 6th
largest known prime."
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Current Version: Variable
Client Download size: Variable
OS: Windows, Linux
Progress: n/a
Percent% Complete: Ongoing
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Help join in the search for strong pseudoprimes.
A composite odd integer x is a base b strong
pseudoprime if by=1 (mod x) or there exists a r such
that 0<=r<t and by2r= -1 (mod
x) where x-1=y2t and y is odd.
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Current Version: 1.3
Client Download size: n/a
OS: Windows, Linux
Progress: up to 500 million checked
Percent% complete: Ongoing
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An odd prime p is a wilson prime if (p-1)!+1=0 mod p2.
The only known wilson primes are 5, 13, and 563.
Help find more in the Wilson Prime Search
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Largest Proth Prime Search
Current Version: n/a
Client Download size: 500 KB or less
OS: Windows, Linux
Progress: found 15th largest
Percent% Complete: Ongoing
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Help search for the world's largest Proth prime number. A Proth prime is a prime number of the
form k.2 n+1 where 2n > k. The project found the 15th largest prime number (and second largest
Proth prime number, 32883.21000004+1, on May 22, 2002.
Participants in the project should have at least a 600 Mhz PC. To join the project, first
download George Woltman's PRP software for Windows or Linux. Then send email to William Garnett
with your CPU type and speed and your operating system, and he will send you instructions for
participating.
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Current Version: n/a
Client Download size: 500 Kb or less
OS: Windows, Linux, Unix
Progress: 110,000 ranges checked
Percent% complete: Ongoing
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Help search for Wieferich prime numbers, numbers of the form ap-1 = 1
(mod p2) for a = 2 or 3. The only two known Wieferich primes
are 1,093 and 3,511 and there are no other Wieferich primes less than
2 * 1014. This project hopes to extend the search limit to
at least 2 * 1015.
The client automatically reserves ranges to check from the project server,
and returns its results when it is done checking the ranges. It runs as a
screen-saver for Windows and as a command-line client for Linux/Solaris.
It only works on computers with full-time Internet connections. The Windows
client supports users behind firewalls: the Unix clients currently do not,
but will in a future release.
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Current Version: 1.0
Client Download size: 290 KB
OS: Windows, Linux
Progress: 5 primes found
Percent% Complete: 12 left to find
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Help find the smallest Sierpinski number in Seventeen or Bust, a distributed attack on the
Sierpinski problem. The project looks for Proth prime numbers in which, for a number k, if
every possible choice of n results in a composite (non-prime) Proth number N, k is a Sierpinski
number. The project has found five proth primes so far.
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Current Version: Variable
Client Download size: Variable
OS: Windows, Linux
Progress: n/a
Percent% complete: Ongoing
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Find factorizations of cyclotomic numbers at Factorizations of Cyclotomic Numbers. This site
doesn't appear to be organized as an official distributed computing project and doesn't have
any precompiled client software or explicit instructions for participating, so it is probably
best suited for people who understand the Mathematical principles behind the project and how to
compile source code.
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Current Version: Prp software
Client Download size: unknown
OS: Windows, Linux
Progress: n/a
Percent% Complete: Ongoing
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Help find prime numbers for the dual Sierpinski problem
search. The project is trying to find a prime in each sequence of
integers of the form k+2n (fixed k) for which no prime has yet
been found. The project is coordinated by Payam Samidoost, an active
researcher of Fermat numbers. Contact Payam to reserve numbers to check
and to submit your results.
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The Lychrel Challenge Zetagrid
Current Version: 1.71
Client Download size: 500 KB
OS: All major Platforms
Progress: 235 billion results
Percent% complete: n/a
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Help verify Riemann's hypothesis in ZetaGrid. This hypothesis was formulated in 1859 and states
that "all non-trivial zeros of the Riemann zeta function (see the website) are on the critical
line (1/2+it where t is a real number)." No one has been able to prove the hypothesis in 140 y
ears. It is now considered one of the most important problems of modern mathematics. The
project offers financial prizes.
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Current Version: n/a
Client Download size: 500 KB
OS: Windows, Linux
Progress: n/a
Percent% Complete: Ongoing
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Join the Goldbach Conjecture Verification to help verify the conjecture through 1e18 (it is currently verified
through 1e16). The Goldbach conjecture is "one of the oldest unsolved problems in number theory.
...it states that every even number larger than two can be expressed as the sum of two prime numbers."
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Current Version: 1.1
Client Download size: 140 KB
OS: Windows
Progress: n/a
Percent% complete: Ongoing
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Help the pi(x) Table Project construct a very large table of values of pi(x) for
large values of x. The table will allow people to study the behavior of
the pi(x) function in large ranges, a study which has never before been
possible. The project might also find the first known change of sign of the
function pi(x)-Li(x). The first phase of the project computed pi(x) for
1.e16 < x < 1.e17. The current phase is computing pi(x) for 1.e17 <
x < 1.e18.
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Current Version:
Client Download size:
OS:
Progress:
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Help the Riesel Problem project prove that k=509203 is the smallest Riesel Number.
To participate, download the proth.exe client, view reserved ranges on the checked out and progress page, then reserve a range (and submit your results) on the range reservation page.
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