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Scott Brown Volunteer moderator
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On 23 October 2012, PrimeGrid’s Proth Prime Search project found the Mega Prime:
9*2^3497442 +1
The prime is 1,052,836 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 51st overall. This prime is also a Generalized Fermat prime and ranks as the 12th largest found.
The discovery was made by Heinz Ming (parabol) of Switzerland using an Intel Core(TM) i7 CPU 860 @ 2.80GHz with 8GB RAM, running Windows 7 Professional. This computer took just over 5 hours 59 minutes to complete the primality test using LLR. Heinz Ming is a member of the Aggie The Pew team.
The prime was verified by Tim McArdle (Bauerwulf) of the United States using an AMD Athlon(tm) II P340 Dual-Core Processor with 6 GB RAM, running Windows 7 Professional. Jason is a member of the Don't Panic Labs team.
For more details, please see the official announcement. |
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The PDF "official announcement" has a typo (line 4). The exponent is wrong... it has an extra "9" at the start. Below, "Switzerland" is missing a vowel.
--Gary
(a.k.a Dr. Buzzkill) |
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Scott BrownVolunteer moderator
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Thanks for the heads up on the errors. I had already fixed the extra "9", so you must have looked at it in the brief period after the news post and before the new pdf was uploaded. I'll add the "i" to Switzerland and get a new file up when I get home from work today.
And it looks like we have another PPS mega prime! News post forthcoming soon...this one is a bit bigger at about 1.7 million digits!
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This prime is also a Generalized Fermat prime and ranks as the 12th largest found
Maybe "... Generalized Fermat prime divisor ..."? :)
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 Michael GoetzVolunteer moderator
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This prime is also a Generalized Fermat prime and ranks as the 12th largest found
Maybe "... Generalized Fermat prime divisor ..."? :)
Nope, it's also a GFN, not a divisor. :)
I'll leave it to the reader to search the boards for the explanation. The key is that 9 = 3^2.
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Please do not PM me with support questions. Ask on the forums instead. Thank you!
My lucky number is 75898524288+1 |
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I'm glad that our PPS work in high ranges turned out two primes, much better than turning out none. Now we just need to get a 321 prime from the challenge.
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Michael Goetz
Thank you :), but as I know, GFN has the form a^(2^n) + b^(2^n) (http://en.wikipedia.org/wiki/Fermat_number#Generalized_Fermat_numbers). This prime is 9 * 2^3497442 + 1 = 3^2 * 2^(2*3*13*44839) + 1. Does not seem at SomethingA^(2^SomethingB) + 1. Information in wiki about GFNs is not complete? |
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pschoeferVolunteer developer
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9*2^3497442 +1
= 3^2 * (2^1748721)^2 +1
= (3*2^1748721)^2 +1
= (3*2^1748721)^(2^1) +1
;)
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