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-   -   LLT Cycles for Mersenne primality test: a draft (https://www.mersenneforum.org/showthread.php?t=12942)

T.Rex 2010-01-02 12:46

LLT Cycles for Mersenne primality test: a draft
 
Hi,

I've decided to publish the draft work I did for trying to prove the Conjecture I made about a new primality test for Mersenne numbers based on the Cycles of a DiGraph under x^2-2.

Though this seems useless (the legacy LLT test for Mersennes is VERY efficient), the idea is to make one step beyong in the proof of the Vrba-Reix conjecture dealing with a primality test for Wagstaff numbers.

This "paper" (a work in progress...) contains several new ideas. One of them is to consider that the conjectures previously publically published by myself, Anton Vrba and Robert Gerbicz cannot lead to a theorem, due to a lack of constraints. In the proof I tried to build, I use more properties. See conjecture 1.

The main idea, for sure, deals with using Cycles of the LLT DiGraph, rather than the Tree. And no-one had this idea before me.

The second idea (dealing with the Lucas sequences) is to study the period of the sequence, since experimental data show that the period seems to have properties very close to the Mersenne numbers.

[URL="http://tony.reix.free.fr/Mersenne/ConjectureLLTCyclesMersenneDraftForMersenneForum.pdf"]Here is the paper.[/URL]

I would be very pleased to receive comments and ideas and to share a final successful paper with someone. The most important goal is to succeed, whoever does it...
Please either provide comments on this thread or send emails to me (tony dot reix at laposte dot net).

However, I'm perfectly aware that I may have made big mistakes in this paper and that no idea at all can help... Wait & See !!

Regards,

Tony

T.Rex 2010-01-03 11:34

Version 0.14
 
I've fixed some little mistakes and improved the presentation. So the version moved to 0.14 .


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