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 2005-12-31, 01:59 #1 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 1001010100102 Posts 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?
 2005-12-31, 04:40 #2 John Renze     Nov 2005 24·3 Posts 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.
2005-12-31, 09:26   #3
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

7·211 Posts

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.

 2005-12-31, 23:50 #4 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 95216 Posts Aww, I was hoping that it would be much faster. :(
 2006-01-02, 03:01 #5 jasong     "Jason Goatcher" Mar 2005 3·7·167 Posts ignorant question: Can they be used together?
2006-01-02, 08:21   #6

"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×641 Posts

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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