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-   -   too good to be true? (https://www.mersenneforum.org/showthread.php?t=5247)

ixfd64 2005-12-31 01:59

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

[url]http://mersennewiki.org/index.php?title=Fermat_numbers&diff=3931&oldid=3924[/url]

Doesn't that sound a bit too good to be true?

John Renze 2005-12-31 04:40

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.

R. Gerbicz 2005-12-31 09:26

[QUOTE=ixfd64]Today, someone added what appears to be a new primality test for Fermat numbers:
[/QUOTE]

I'm the same Robert Gerbicz, I've added my proof for this test.

[QUOTE=John Renze]but it's no faster than Pepin's test.[/QUOTE]

In fact, the speed of this test is equal to the speed of the Pepin's test.

ixfd64 2005-12-31 23:50

Aww, I was hoping that it would be much faster. :(

jasong 2006-01-02 03:01

ignorant question: Can they be used together?

cheesehead 2006-01-02 08:21

[quote=jasong]Can they be used together?[/quote]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).


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