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Message boards : News : World Record Generalized Woodall Prime

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JohnProject donor
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Joined: 21 Feb 06
Posts: 2875
ID: 2449
Credit: 2,681,934
RAC: 0
321 LLR Bronze: Earned 10,000 credits (11,773)Cullen LLR Bronze: Earned 10,000 credits (14,945)ESP LLR Bronze: Earned 10,000 credits (26,855)PPS LLR Bronze: Earned 10,000 credits (84,876)PSP LLR Bronze: Earned 10,000 credits (15,311)SoB LLR Bronze: Earned 10,000 credits (21,440)SR5 LLR Bronze: Earned 10,000 credits (29,270)SGS LLR Bronze: Earned 10,000 credits (26,616)TPS LLR (retired) Bronze: Earned 10,000 credits (36,288)TRP LLR Bronze: Earned 10,000 credits (41,655)Woodall LLR Bronze: Earned 10,000 credits (15,807)321 Sieve (suspended) Bronze: Earned 10,000 credits (20,014)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (23,405)PPS Sieve Bronze: Earned 10,000 credits (36,192)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (20,306)TRP Sieve (suspended) Bronze: Earned 10,000 credits (21,738)GFN Bronze: Earned 10,000 credits (86,217)PSA Ruby: Earned 2,000,000 credits (2,143,756)
Message 33345 - Posted: 25 Feb 2011 | 6:55:13 UTC
Last modified: 29 Jan 2012 | 16:29:28 UTC

On 24 Feb 2011, 17:27:31 UTC, PrimeGrid’s PRPNet found the largest known generalized Woodall prime: 404882*43^404882-1

The prime is 661,368 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for generalized Woodall primes and 71st overall.

The discovery was made by Ricky L. Hubbard of the United States using an AMD Athlon II X4 635 @ 2.90GHz with 8GB RAM, running Windows 7. This computer took about 4 hours and 15 minutes to complete the probable prime test using pfgw64 and a little over 30 hours 3 minutes to complete the primality test again using pfgw64. Ricky is a member of the AMD Users Team.

For more details, please see the official announcement.
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Profile JeppeSNProject donor
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Joined: 5 Apr 14
Posts: 1494
ID: 306875
Credit: 33,725,449
RAC: 132,612
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (11,862,413)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)WW Turquoise: Earned 5,000,000 credits (9,640,000)GFN Amethyst: Earned 1,000,000 credits (1,707,013)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 107676 - Posted: 5 May 2017 | 23:35:57 UTC

This is the form n*b^n - 1, with requirement n > b - 2 (see Caldwell Top 20 definition).

It is interesting that if we relax the requirement to just n > 1, then a much smaller solution exists:

2*43^2 - 1 is prime.

An earlier GW prime found here is the same. 94112*121^94112 - 1 has a smaller sibling:

8*121^8 - 1 is prime!

I know with the weakened condition n > 1, people do not consider these GW primes. But they are just as beautiful numbers.

/JeppeSN

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Michael Millerick
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Joined: 4 Feb 09
Posts: 771
ID: 35074
Credit: 270,354,215
RAC: 843,974
Found 3 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,023,600)Cullen LLR Ruby: Earned 2,000,000 credits (2,016,794)ESP LLR Jade: Earned 10,000,000 credits (10,030,855)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,032,353)PPS LLR Jade: Earned 10,000,000 credits (19,222,385)PSP LLR Ruby: Earned 2,000,000 credits (2,012,651)SoB LLR Ruby: Earned 2,000,000 credits (2,031,453)SR5 LLR Ruby: Earned 2,000,000 credits (2,085,475)SGS LLR Amethyst: Earned 1,000,000 credits (1,320,684)TRP LLR Ruby: Earned 2,000,000 credits (2,740,707)Woodall LLR Amethyst: Earned 1,000,000 credits (1,861,909)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,440,175)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,911,344)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,077,092)PPS Sieve Emerald: Earned 50,000,000 credits (50,200,870)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,034,014)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,070,774)AP 26/27 Jade: Earned 10,000,000 credits (13,035,450)WW Emerald: Earned 50,000,000 credits (50,020,000)GFN Sapphire: Earned 20,000,000 credits (41,318,822)PSA Emerald: Earned 50,000,000 credits (52,866,806)
Message 107683 - Posted: 6 May 2017 | 1:34:39 UTC

Glad to see the announcement from John, and such early results from the project. Great work everyone!
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Profile JeppeSNProject donor
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Joined: 5 Apr 14
Posts: 1494
ID: 306875
Credit: 33,725,449
RAC: 132,612
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (11,862,413)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)WW Turquoise: Earned 5,000,000 credits (9,640,000)GFN Amethyst: Earned 1,000,000 credits (1,707,013)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 107686 - Posted: 6 May 2017 | 9:12:33 UTC - in response to Message 107683.

Glad to see the announcement from John, and such early results from the project. Great work everyone!


Yes, sometimes the first news post here is old news. Hopefully people do not misunderstand this for a 2017 world record GW prime. /JeppeSN

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Profile sergeProject donor
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Joined: 21 Jun 12
Posts: 112
ID: 144858
Credit: 250,560,611
RAC: 84,367
Eliminated 2 conjecture "k"s321 LLR Turquoise: Earned 5,000,000 credits (5,342,838)Cullen LLR Silver: Earned 100,000 credits (158,983)ESP LLR Gold: Earned 500,000 credits (505,527)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,268,642)PPS LLR Sapphire: Earned 20,000,000 credits (43,374,977)PSP LLR Silver: Earned 100,000 credits (120,541)SoB LLR Amethyst: Earned 1,000,000 credits (1,280,028)SR5 LLR Ruby: Earned 2,000,000 credits (2,649,390)SGS LLR Gold: Earned 500,000 credits (518,356)TRP LLR Silver: Earned 100,000 credits (141,131)Woodall LLR Silver: Earned 100,000 credits (116,405)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (235,088)PPS Sieve Amethyst: Earned 1,000,000 credits (1,031,526)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (500,445)TRP Sieve (suspended) Gold: Earned 500,000 credits (507,938)AP 26/27 Turquoise: Earned 5,000,000 credits (5,078,008)WW Ruby: Earned 2,000,000 credits (2,004,000)GFN Double Bronze: Earned 100,000,000 credits (184,436,253)PSA Silver: Earned 100,000 credits (291,533)
Message 107778 - Posted: 9 May 2017 | 23:00:24 UTC - in response to Message 107686.

Glad to see the announcement from John, and such early results from the project. Great work everyone!


Yes, sometimes the first news post here is old news. Hopefully people do not misunderstand this for a 2017 world record GW prime. /JeppeSN

There isn't though. Is there?
For all I see, there is a 2015 World Record Generalized Woodall Prime, and it belongs to ...hmmm... look at that, who could have guessed?

Of course not for long now, but still.

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Profile JeppeSNProject donor
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Joined: 5 Apr 14
Posts: 1494
ID: 306875
Credit: 33,725,449
RAC: 132,612
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (11,862,413)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)WW Turquoise: Earned 5,000,000 credits (9,640,000)GFN Amethyst: Earned 1,000,000 credits (1,707,013)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 107797 - Posted: 10 May 2017 | 20:48:07 UTC - in response to Message 107778.

There isn't though. Is there?


No. This thread is from 2011 and is about the 2011 find which is currently fourth on the Top 20. It is a base 43 generalized Woodall, and I had a comment about base 43, so I posted here and bumped the old thread.

Your record from 2015, base 4, is still not beaten.

/JeppeSN

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Message boards : News : World Record Generalized Woodall Prime

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