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Old 2004-09-10, 21:10   #1
T.Rex
 
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Feb 2004
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Default Two Primality tests for Fermat numbers

Hi,

I have built the proof of 2 new Primality tests for Fermat numbers.
(Don't expect them to reduce the time needed by the Pepin' test ...)

Why posting a test for Fermat numbers here ? Because it is a first step in a more global work I'm working on dealing with Lucas Sequences. I hope I will be able in the future to provide new useful theorems (and probably new conjectures) dealing with Mersenne and Fermat numbers.
Think about my guess at the end of the document, dealing with what I call "fixed point".

I've asked xyzzy (administrator) to host my document (.pdf) and to provide the link in this thread. Just wait xyzzy is available. Thanks xyzzy.

Let me know if my proof is correct ...

Tony
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Old 2004-09-10, 21:15   #2
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France

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Default The .pdf file is attached to this post.

Hi, Finally, the .pdf file is attached to this post. Tony
Attached Files
File Type: pdf PrimalityTest1FermatNumbers.pdf (82.5 KB, 271 views)
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Old 2004-09-11, 07:26   #3
T.Rex
 
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Default Second version about Pepin's test

Hi,
I've done 3 small modifications:
1) page 1 in the introduction: I say this also proves the Pepin's Test, with k=3 .
2) page 2 I've replaced the use of Pepin's test by the Euler congruence for quadratic residues.
3) page 4 I show that the Theorem 1 does prove the Pepin's test for k=3 .

Tony
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File Type: pdf PrimalityTest1FermatNumbers.pdf (83.9 KB, 203 views)
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