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World Record Generalized Woodall Prime
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John Honorary cruncher
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Joined: 21 Feb 06
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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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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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Glad to see the announcement from John, and such early results from the project. Great work everyone!
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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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 serge
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Joined: 21 Jun 12
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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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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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News :
World Record Generalized Woodall Prime |
