We kindly ask users "moving on" to ABORT their WU's instead of DETACHING, RESETTING, or PAUSING.

ABORTING WU's allows them to be recycled immediately; thus a much faster "clean up" to the end of an LLR Challenge. DETACHING, RESETTING, and PAUSING WU's causes them to remain in limbo until they EXPIRE. Therefore, we must wait until WU's expire to send them out to be completed.

Please consider either completing what's in the queue or ABORTING them. Thank you. :)

About the Proth Prime Search

The Proth Prime Search is done in collaboration with the Proth Search project. This search looks for primes in the form of k*2^n+1. With the condition 2^n > k, these are often called Proth primes. This project also has the added bonus of possibly finding factors of "classical" Fermat numbers or Generalized Fermat numbers. As this requires PrimeFormGW (PFGW) (a primality-testing program), once PrimeGrid finds a prime, it is then tested on PrimeGrid's servers for divisibility.

Proth Search only searches for k<1200. PrimeGrid created an extension to that which includes all candidates 1200<k<10000 for n<5M. It is this extension which we call PPSE that the Challenge will be on.

Initially, PrimeGrid's PPS project's goal was to double check all previous work up to n=500K for odd k<1200 and to fill in any gaps that were missed. We have accomplished that now and have increased it to n=2M. PG's LLRNet searched up to n=200,000 and found several missed primes in previously searched ranges. Although primes that small did not make it into the Top 5000 Primes database, the work was still important as it may have led to new factors for "classical" Fermat numbers or Generalized Fermat numbers. While there are many GFN factors, currently there are only 293 "classical" Fermat number factors known. Current primes found in PPS definitely make it into the Top 5000 Primes database.


For more information about "Proth" primes, please visit these links:

• Proth Prime - The Prime Glossary
  
• Proth Prime - Wolfram MathWorld
  
• Proth Number - Wikipedia

About Proth Search

The Proth Search project was established in 1998 by Ray Ballinger and Wilfrid Keller to coordinate a distributed effort to find Proth primes (primes of the form k*2^n+1) for k < 300. Ray was interested in finding primes while Wilfrid was interested in finding divisors of Fermat number. Since that time it has expanded to include k < 1200. Mark Rodenkirch (aka rogue) has been helping Ray keep the website up to date for the past few years.

Early in 2008, PrimeGrid and Proth Search teamed up to provide a software managed distributed effort to the search. Although it might appear that PrimeGrid is duplicating some of the Proth Search effort by re-doing some ranges, few ranges on Proth Search were ever double-checked. This has resulted in PrimeGrid finding primes that were missed by previous searchers. By the end of 2008, all new primes found by PrimeGrid were eligible for inclusion in Chris Caldwell's Prime Pages Top 5000. Sometime in 2009, over 90% of the tests handed out by PrimeGrid were numbers that have never been tested.

PrimeGrid intends to continue the search indefinitely for Proth primes.

What is LLR?

The Lucas-Lehmer-Riesel (LLR) test is a primality test for numbers of the form N = k*2^n − 1, with 2^n > k. Also, LLR is a program developed by Jean Penne that can run the LLR-tests. It includes the Proth test to perform +1 tests and PRP to test non base 2 numbers. See also:

• Lucas-Lehmer-Riesel test (WIKI)
  
• Download LLR by Jean Penné
  

(Edouard Lucas: 1842-1891, Derrick H. Lehmer: 1905-1991, Hans Riesel: 1929-2014).

TheDawgz have heard back from Charley - he has been and still is swamped at work ("very looooong days") - he will deal with this as soon as possible - but, it will likely not happen until next week sometime.

thanks for the info!
the work is still a significant disruptive factor during free time ;)

The World Clock - Time Zone Converter

NOTE: The countdown clock on the front page uses the host computer time. Therefore, if your computer time is off, so will the countdown clock. For precise timing, use the UTC Time in the data section to the left of the countdown clock.

Scoring Information

Scores will be kept for individuals and teams. Only work units issued AFTER April 19th 2016, 18:00:00 UTC and received BEFORE April 28th 2016, 18:00:00 UTC will be considered for credit.



Therefore, each completed WU will earn a unique score based on its n value. The higher the n, the higher the score. This is different than BOINC cobblestones! A quorum of 2 is NOT needed to award Challenge score - i.e. no double checker. Therefore, each returned result will earn a Challenge score. Please note that if the result is eventually declared invalid, the score will be removed.

At the Conclusion of the Challenge

We would prefer users "moving on" to finish those tasks they have downloaded, if not then please ABORT the WU's instead of DETACHING, RESETTING, or PAUSING.

ABORTING WU's allows them to be recycled immediately; thus a much faster "clean up" to the end of an LLR Challenge. DETACHING, RESETTING, and PAUSING WU's causes them to remain in limbo until they EXPIRE. Therefore, we must wait until WU's expire to send them out to be completed.

Please consider either completing what's in the queue or ABORTING them. Thank you. :)

About Woodall Prime Search

Woodall Numbers (sometimes called Cullen numbers 'of the second kind') are positive integers of the form Wn = n*2^n-1, where n is also a positive integer greater than zero. Woodall numbers that are prime are called Woodall primes (or Cullen primes of the second kind).

The Woodall numbers Wn are primes for the following n:

2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462, 512, 751, 822, 5312, 7755, 9531, 12379, 15822, 18885, 22971, 23005, 98726, 143018, 151023, 667071, 1195203, 1268979, 1467763, 2013992, 2367906, and 3752948 and composite for all other n less than 9108979.

It is conjectured that there are infinitely many such primes. Currently, PrimeGrid is testing for Woodall primes in the n=11M - n=12M level (M=mega, 10^6). The last 3 Woodall primes found by PrimeGrid are:

2013992*2^2013992−1 (Lasse Mejling Andersen): official announcement | decimal representation | Prime Pages Entry
2367906*2^2367906−1 (Stephen Kohlman): official announcement | decimal representation | Prime Pages Entry
3752948*2^3752948−1 (Matthew J. Thompson): official announcement | decimal representation | Prime Pages Entry

For more information on Woodall numbers, please visit the following sites:



• Woodall Number - The Prime Glossary at the Prime Pages
  
• Top 20 Woodall Primes - Top Twenty at the Prime Pages
  
• Woodall Number - MathWorld--A Wolfram Web Resource
  
• Woodall Number - Wikipedia
  
  

Cullen Primes
Cullen numbers are a special kind Proth number. They were first studied by James Cullen in 1905 and are of the form n * 2^n + 1.

As of August 2009, the largest known Cullen prime is 6679881 * 2^6679881 + 1. It is a megaprime with 2,010,852 digits and was discovered by a PrimeGrid participant from Japan.

A Cullen number Cn is divisible by p = 2n − 1 if p is a prime number of the form 8k - 3; furthermore, it follows from Fermat's little theorem that if p is an odd prime, then p divides Cm(k) for each m(k) = (2k − k) (p − 1) − k (for k > 0). It has also been shown that the prime number p divides C(p + 1) / 2 when the Jacobi symbol (2 | p) is −1, and that p divides C(3p − 1) / 2 when the Jacobi symbol (2 | p) is +1.

It is unknown whether there exists a prime number p such that Cp is also prime.

What is LLR?

The Lucas-Lehmer-Riesel (LLR) test is a primality test for numbers of the form N = k*2^n - 1, with 2^n > k. Also, LLR is a program developed by Jean Penne that can run the LLR-tests. It includes the Proth test to perform +1 tests and PRP to test non base 2 numbers. See also:


• Lucas-Lehmer-Riesel test (WIKI)
  
• Download LLR by Jean Penné
  

(Edouard Lucas: 1842-1891, Derrick H. Lehmer: 1905-1991, Hans Riesel: born 1929)

Best of Luck!!!