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Old 2005-12-31, 01:59   #1
ixfd64
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"Danny"
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Default too good to be true?

Today, someone added what appears to be a new primality test for Fermat numbers:

http://mersennewiki.org/index.php?ti...931&oldid=3924

Doesn't that sound a bit too good to be true?
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Old 2005-12-31, 04:40   #2
John Renze
 
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I think TRex of this forum has claimed a similar result. Approximately half of the possible polynomials for Lucas sequence proofs give N-1 tests instead of N+1 tests. This is one such choice. It looks correct, but it's no faster than Pepin's test.
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Old 2005-12-31, 09:26   #3
R. Gerbicz
 
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"Robert Gerbicz"
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Quote:
Originally Posted by ixfd64
Today, someone added what appears to be a new primality test for Fermat numbers:
I'm the same Robert Gerbicz, I've added my proof for this test.

Quote:
Originally Posted by John Renze
but it's no faster than Pepin's test.
In fact, the speed of this test is equal to the speed of the Pepin's test.
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Old 2005-12-31, 23:50   #4
ixfd64
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Aww, I was hoping that it would be much faster. :(
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Old 2006-01-02, 03:01   #5
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ignorant question: Can they be used together?
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Old 2006-01-02, 08:21   #6
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Quote:
Originally Posted by jasong
Can they be used together?
No, because though each requires the same number of squarings and thus the same computation time, they start with different numbers (Gerbicz's method starts with 5, while Pepin's test starts with 3) and their steps are not identical (Gerbicz's subtracts 2 at each step; Pepin's doesn't).

Last fiddled with by cheesehead on 2006-01-02 at 08:23
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