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Message boards : Generalized Cullen/Woodall prime search : Welcome (back) to the Generalized Cullen/Woodall Prime Search

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Van ZimmermanProject donor
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Joined: 30 Aug 12
Posts: 1678
ID: 168418
Credit: 3,777,421,426
RAC: 4,680,353
321 LLR Jade: Earned 10,000,000 credits (12,513,261)Cullen LLR Jade: Earned 10,000,000 credits (11,032,867)ESP LLR Jade: Earned 10,000,000 credits (10,208,007)Generalized Cullen/Woodall LLR Jade: Earned 10,000,000 credits (11,676,507)PPS LLR Jade: Earned 10,000,000 credits (12,221,654)PSP LLR Jade: Earned 10,000,000 credits (17,826,235)SoB LLR Jade: Earned 10,000,000 credits (12,238,176)SR5 LLR Jade: Earned 10,000,000 credits (11,124,412)SGS LLR Jade: Earned 10,000,000 credits (10,477,500)TRP LLR Jade: Earned 10,000,000 credits (13,236,666)Woodall LLR Jade: Earned 10,000,000 credits (11,647,747)Generalized Cullen/Woodall Sieve Jade: Earned 10,000,000 credits (18,073,742)PPS Sieve Double Amethyst: Earned 1,000,000,000 credits (1,000,651,011)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,189,695)TRP Sieve (suspended) Jade: Earned 10,000,000 credits (10,102,079)AP 26/27 Emerald: Earned 50,000,000 credits (50,488,984)GFN Double Ruby: Earned 2,000,000,000 credits (2,385,477,759)PSA Double Bronze: Earned 100,000,000 credits (168,236,054)
Message 100074 - Posted: 21 Oct 2016 | 22:20:17 UTC
Last modified: 21 Oct 2016 | 22:23:55 UTC

A Cullen number (first studied by Reverend James Cullen in 1905) is a number of the form n * 2^n + 1. A Woodall number (first studied by Allan Cunningham and H.J. Woodall in 1917) is a number of the form n * 2^n - 1.

Generalized Cullen and Woodall numbers are of the form n * b^n + 1 and n * b^n - 1, respectively, where n + 2 > b.

PrimeGrid is moving its search for Generalized Cullen and Generalized Woodall primes from PRPNet to BOINC. As is customary when projects move from PRPNet, PrimeGrid will double-check the ranges searched by PRPNet, and will then continue on with new work running multiple bases (b values) concurrently and incrementing through n values.

PrimeGrid will be sieving to a much larger n than has been previously done. The largest candidates will be in excess of 15,000,000 digits, and will be the same size as the largest candidates in the Seventeen or Bust project.

Once PrimeGrid finds a Generalized Cullen or Woodall on a base, it stops looking for Generalized Cullen or Woodall primes on that base, depending on the type found. For all the current bases, PrimeGrid has found a Generalized Woodall prime, and will initially be searching only for Generalized Cullen Primes. For detail about the bases PrimeGrid will be searching (and has searched), you can go here: http://www.primegrid.com/forum_thread.php?id=3008&nowrap=true#30718.

Once the sieving has built a sufficient and sustainable pool of credits, PrimeGrid anticipates restarting LLR work as well, and would expect this to occur in early 2017.

In addition to having found the largest known Cullen prime http://primes.utm.edu/primes/page.php?id=89536 and largest known Woodall prime http://primes.utm.edu/primes/page.php?id=83407, PrimeGrid has found the largest known Generalized Cullen prime, http://primes.utm.edu/primes/page.php?id=122349 and the 4th largest known Generalized Woodall prime http://primes.utm.edu/primes/page.php?id=98862.

For more information on Generalized Cullen and Woodall Numbers, you can go here: http://primes.utm.edu/top20/page.php?id=42 and here: http://primes.utm.edu/top20/page.php?id=45.

JeppeSNProject donor
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Joined: 5 Apr 14
Posts: 566
ID: 306875
Credit: 7,696,138
RAC: 1,972
PPS LLR Bronze: Earned 10,000 credits (66,233)TRP LLR Bronze: Earned 10,000 credits (14,746)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 107679 - Posted: 6 May 2017 | 0:24:53 UTC

I found some lists with known n values for each b:

* Günter Löh (generalized Cullens with 3≤b≤100)
* Steven Harvey (generalized Woodalls with 3≤b≤10000, and generalized Cullens with 101≤b≤10000, and more)

Be aware of the requirement n > b - 2. From Löh's list, it looks like, for generalized Cullens, the bases b=11 and b=37 are not "resolved" if we strengthen the requirement to n > b.

/JeppeSN

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Message boards : Generalized Cullen/Woodall prime search : Welcome (back) to the Generalized Cullen/Woodall Prime Search

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