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

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Profile Michael GoetzProject donor
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The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,822,730)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Turquoise: Earned 5,000,000 credits (5,009,577)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,145,754)PPS LLR Turquoise: Earned 5,000,000 credits (9,226,757)PSP LLR Turquoise: Earned 5,000,000 credits (5,098,748)SoB LLR Sapphire: Earned 20,000,000 credits (34,221,148)SR5 LLR Turquoise: Earned 5,000,000 credits (8,293,415)SGS LLR Ruby: Earned 2,000,000 credits (2,014,138)TRP LLR Ruby: Earned 2,000,000 credits (2,737,347)Woodall LLR Ruby: Earned 2,000,000 credits (2,195,123)321 Sieve Turquoise: Earned 5,000,000 credits (5,649,898)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,059,304)PPS Sieve Sapphire: Earned 20,000,000 credits (20,110,788)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Jade: Earned 10,000,000 credits (10,114,260)GFN Emerald: Earned 50,000,000 credits (66,792,810)PSA Jade: Earned 10,000,000 credits (12,404,447)
Message 100074 - Posted: 21 Oct 2016 | 22:20:17 UTC
Last modified: 11 Sep 2019 | 13:01:14 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.

The following bases have yet to produce a prime (highlighted ones have been found):


Base 149 is the next primeless base for both GC and GW.

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=124515 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.

Profile JeppeSNProject donor
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321 LLR Silver: Earned 100,000 credits (360,928)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Ruby: Earned 2,000,000 credits (2,486,479)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Bronze: Earned 10,000 credits (16,010)SGS LLR Bronze: Earned 10,000 credits (32,929)TRP LLR Bronze: Earned 10,000 credits (71,060)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve Silver: Earned 100,000 credits (101,851)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

Gabriel LignelliProject donor
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Found 1 prime in the 2018 Tour de Primes321 LLR Bronze: Earned 10,000 credits (53,871)Cullen LLR Bronze: Earned 10,000 credits (15,017)ESP LLR Bronze: Earned 10,000 credits (62,595)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (21,984)PPS LLR Silver: Earned 100,000 credits (136,702)PSP LLR Bronze: Earned 10,000 credits (47,301)SoB LLR Silver: Earned 100,000 credits (305,770)SR5 LLR Bronze: Earned 10,000 credits (18,306)SGS LLR Bronze: Earned 10,000 credits (14,608)TRP LLR Silver: Earned 100,000 credits (282,537)Woodall LLR Bronze: Earned 10,000 credits (33,562)321 Sieve Gold: Earned 500,000 credits (858,108)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,397,311)PPS Sieve Ruby: Earned 2,000,000 credits (2,349,587)AP 26/27 Amethyst: Earned 1,000,000 credits (1,475,695)GFN Ruby: Earned 2,000,000 credits (2,056,798)PSA Silver: Earned 100,000 credits (286,377)
Message 117640 - Posted: 30 Apr 2018 | 21:24:33 UTC - in response to Message 107679.

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.

What would be the reasoning behind strengthening this requirement?
____________

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321 LLR Silver: Earned 100,000 credits (360,928)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Ruby: Earned 2,000,000 credits (2,486,479)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Bronze: Earned 10,000 credits (16,010)SGS LLR Bronze: Earned 10,000 credits (32,929)TRP LLR Bronze: Earned 10,000 credits (71,060)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve Silver: Earned 100,000 credits (101,851)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 135048 - Posted: 20 Nov 2019 | 23:41:02 UTC

Looking at these lists again, we have that:


  • Cullen b=32, 75, 106, 115, ...



are bases for which no generalized Cullen is known if we really require n + 2 > b (as in the first post by Michael Goetz above).

It is easy to find:


  • 5*32^5+1, 2*75^2+1, 3*106^3+1, 24*115^24+1, ...



but these do not meet the requirement n + 2 > b.

So maybe we should search these bases? What do you think?

(Question: Why does Löh say b=32 and b=64 are reserved by PrimeGrid?)

For a similar example with g. Woodall, b=175 only has 6*175^6-1.

/JeppeSN

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PPS LLR Bronze: Earned 10,000 credits (31,229)PSA Jade: Earned 10,000,000 credits (18,533,435)
Message 135074 - Posted: 22 Nov 2019 | 17:06:15 UTC - in response to Message 135048.
Last modified: 22 Nov 2019 | 17:11:11 UTC

(Question: Why does Löh say b=32 and b=64 are reserved by PrimeGrid?)


At first I thought it was covered by the GFN search, but that couldn't be the case.

Profile JeppeSNProject donor
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321 LLR Silver: Earned 100,000 credits (360,928)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Ruby: Earned 2,000,000 credits (2,486,479)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Bronze: Earned 10,000 credits (16,010)SGS LLR Bronze: Earned 10,000 credits (32,929)TRP LLR Bronze: Earned 10,000 credits (71,060)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve Silver: Earned 100,000 credits (101,851)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 135076 - Posted: 22 Nov 2019 | 17:10:35 UTC - in response to Message 135074.

(Question: Why does Löh say b=32 and b=64 are reserved by PrimeGrid?)


Because bases that are powers of 2 are covered by the GFN prime searches.


No, for example 100001*32^100001 + 1 = 100001*2^500005 + 1 is not a GFN. /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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