mersenneforum.org  

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

Reply
 
Thread Tools
Old 2005-12-16, 17:55   #1
Robot2357
 
Dec 2005
Italy

2 Posts
Default lucas-lehmer theorem

Hello,
there are various generalization of the lucas-lehmer test,for example one is in http://mathworld.wolfram.com/Lucas-LehmerTest.html for N+1.
I think that i've found another generalization to the theorem and proved the sufficent part.
but it seems that the necessary part is beyond my mathematical skill.so,suppose that the theorem that i'm speak about it is not know,my question is:
do i have to spent months(years?) to gain the right amount of math knowledge and try to complete the proof,and maybe let another person discover the same thing, or it's better to release an incomplete theorem and let the necessary part to someone else?
Robot2357 is offline   Reply With Quote
Old 2005-12-16, 18:04   #2
John Renze
 
John Renze's Avatar
 
Nov 2005

24×3 Posts
Default

Quote:
Originally Posted by Robot2357
do i have to spent months(years?) to gain the right amount of math knowledge and try to complete the proof,and maybe let another person discover the same thing, or it's better to release an incomplete theorem and let the necessary part to someone else?
Mathematics is a collaborative endeavor. Post what you know here and people will discuss it.

John
John Renze is offline   Reply With Quote
Old 2005-12-16, 19:27   #3
T.Rex
 
T.Rex's Avatar
 
Feb 2004
France

2·457 Posts
Default

Quote:
Originally Posted by Robot2357
Hello,
there are various generalization of the lucas-lehmer test, ...
I think that i've found another generalization to the theorem and proved the sufficent part.
It is not widely known that the LLT can be used to prove the primality of other numbers than Mersenne numbers. Moreover, many people think that only numbers N for which a factorization of N+1 is known (like Mersenne numbers) can be proved prime by the LLT. As an example, the LLT can also be used for Fermat numbers, see my paper.
It is the same for the Pépin's test. It can be used for proving the primality of a kind of Generalized Fermat Numbers, see Saouter .
Let describe your findings here. Better Mathematicians than me will help you to understand if it is new or not.
Tony

Last fiddled with by T.Rex on 2005-12-16 at 19:32
T.Rex is offline   Reply With Quote
Old 2006-12-19, 17:24   #4
hoca
 
hoca's Avatar
 
Dec 2006

3 Posts
Default new one

S(n)=2*S(n-1)^2 -1 where S(0)=2
hoca is offline   Reply With Quote
Old 2006-12-20, 17:40   #5
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
República de California

2D5716 Posts
Default

Quote:
Originally Posted by hoca View Post
S(n)=2*S(n-1)^2 -1 where S(0)=2
A.k.a. "LLT in slight disguise."
ewmayer is online now   Reply With Quote
Old 2006-12-20, 17:44   #6
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

22·5·373 Posts
Default

Quote:
Originally Posted by hoca View Post
S(n)=2*S(n-1)^2 -1 where S(0)=2

Don't cross post. I already answered you in another thread.
R.D. Silverman is offline   Reply With Quote
Old 2013-06-15, 03:10   #7
princeps
 
Nov 2011

22·3 Posts
Default

Generalization of Lucas-Lehmer-Riesel Test

Last fiddled with by princeps on 2013-06-15 at 03:12
princeps is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Lucas-Lehmer Primes henryzz And now for something completely different 42 2019-06-03 14:09
Lucas-Lehmer test Mathsgirl Information & Answers 23 2014-12-10 16:25
lucas lehmer outstretch science_man_88 Miscellaneous Math 7 2010-07-14 12:35
Lucas-Lehmer Test storm5510 Math 22 2009-09-24 22:32
Lucas-Lehmer Dougal Information & Answers 9 2009-02-06 10:25

All times are UTC. The time now is 04:21.

Thu Mar 4 04:21:29 UTC 2021 up 91 days, 32 mins, 1 user, load averages: 2.16, 1.91, 1.71

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, 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.