mersenneforum.org > Math Two Primality tests for Fermat numbers
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

 2004-09-10, 21:10 #1 T.Rex     Feb 2004 France 2×457 Posts 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
2004-09-10, 21:15   #2
T.Rex

Feb 2004
France

39216 Posts
The .pdf file is attached to this post.

Hi, Finally, the .pdf file is attached to this post. Tony
Attached Files
 PrimalityTest1FermatNumbers.pdf (82.5 KB, 271 views)

2004-09-11, 07:26   #3
T.Rex

Feb 2004
France

2×457 Posts
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
Attached Files
 PrimalityTest1FermatNumbers.pdf (83.9 KB, 203 views)

 Thread Tools

 Similar Threads Thread Thread Starter Forum Replies Last Post ewmayer Computer Science & Computational Number Theory 79 2020-01-28 08:49 T.Rex Math 12 2016-04-03 22:27 Erasmus Math 46 2014-08-08 20:05 princeps Math 15 2012-04-02 21:49 Arkadiusz Math 6 2011-04-05 19:39

All times are UTC. The time now is 12:36.

Sat Dec 5 12:36:24 UTC 2020 up 2 days, 8:47, 0 users, load averages: 1.21, 1.38, 1.46

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.