mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2005-05-06, 14:07   #1
T.Rex
 
T.Rex's Avatar
 
Feb 2004
France

2·457 Posts
Default LLT numbers, linkd with Mersenne and Fermat numbers

Hi,
I've derived from the Lucas-Lehmer Test a new (??) kind of numbers, that I called LLT numbers. They are described in this short (2.5 pages) paper: LLT numbers .
These numbers show interesting numerical relationships with Mersenne and Fermat prime numbers, without any proof yet.

First, I'm surprised it is so easy to create such a kind of numbers that have so close relationships with Mersenne and Fermat numbers. Is there a law saying that playing with prime (Fermat and Mersenne) numbers always lead to nice properties ?

Second, these numbers may provide interesting primality tests for Fermat and Mersenne numbers (once the properties are proven ...); though they clearly do not improve existing LLT and P├ępin's tests .

Does someone have hints for proving these properties ?

Regards,

Tony
T.Rex is offline   Reply With Quote
Old 2005-05-06, 16:33   #2
Orgasmic Troll
Cranksta Rap Ayatollah
 
Orgasmic Troll's Avatar
 
Jul 2003

641 Posts
Default

watch out for scathing replies, you're definitely abusing terminology here.
Orgasmic Troll is offline   Reply With Quote
Old 2005-05-06, 19:42   #3
T.Rex
 
T.Rex's Avatar
 
Feb 2004
France

2·457 Posts
Default

Quote:
Originally Posted by TravisT
watch out for scathing replies, you're definitely abusing terminology here.
Hi TravisT, what's wrong with my paper ? I'm playing with numbers. I did not say I've discovered a magic new method for proving primality of any number. I've just defined and studied the numerical properties of a kind of numbers and noticed some interesting possible properties that need proofs. Can you help me fixing the terminology problems you've noticed ? Can you help providing proofs ?
Thanks,
Tony
T.Rex is offline   Reply With Quote
Old 2005-05-06, 20:51   #4
Orgasmic Troll
Cranksta Rap Ayatollah
 
Orgasmic Troll's Avatar
 
Jul 2003

641 Posts
Default

Quote:
Originally Posted by T.Rex
Hi TravisT, what's wrong with my paper ? I'm playing with numbers. I did not say I've discovered a magic new method for proving primality of any number. I've just defined and studied the numerical properties of a kind of numbers and noticed some interesting possible properties that need proofs. Can you help me fixing the terminology problems you've noticed ? Can you help providing proofs ?
Thanks,
Tony
taking the "coefficients" of a "function" seems to be a meaningless statement and caught me off guard when I read it. You're taking the coefficients of the polynomials. Since you're never using L as a function, why word it such? In other words, you're never passing a value to L.

I would talk about a set of polynomials Pn where P0 = x and Pn = Pn-12-2 where n > 0, I'm no expert, so I may be abusing notation as well.

I haven't had time to look at more than a few of the conjectures you've posed, the first few seem like they can be proven (or disproven) without too much effort
Orgasmic Troll is offline   Reply With Quote
Old 2005-05-07, 08:25   #5
T.Rex
 
T.Rex's Avatar
 
Feb 2004
France

2×457 Posts
Default Function vs Polynomial

You are perfectly right: I should use polynomial rather than function !
I've fixed the mistakes and produced a new version .
Seems polynomial x^2-3 has also interesting properties.

So, is there a miracle ? or are these properties an evident consequence of some well-known theorem I'm not aware of ?

Thanks for your comments !

Tony

Last fiddled with by T.Rex on 2005-05-07 at 08:25
T.Rex is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
ecm with Fermat numbers ET_ FermatSearch 1 2016-08-02 19:40
P-1/P+1 on Fermat numbers ATH Operazione Doppi Mersennes 2 2015-01-25 06:27
6 digit numbers and the mersenne numbers henryzz Math 2 2008-04-29 02:05
supercomputers and Fermat/double-Mersenne numbers ixfd64 Lounge 3 2004-12-27 21:13
Fermat Numbers devarajkandadai Math 8 2004-07-27 12:27

All times are UTC. The time now is 07:07.

Wed Dec 2 07:07:48 UTC 2020 up 83 days, 4:18, 1 user, load averages: 1.62, 1.72, 1.55

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.