Lucas-Lehmer Test proof

[R. Gerbicz]

There were many many errors on Lucas-Lehmer sequence on mersennewiki.
I have redefined the sequence by S(0)=4 ( and S(n)=S(n-1)^2-2 ).
If you look the proof: 0 is very good starting index for the sequence.

From mersennewiki:

""The value of S0 has about 2 (= 2^1) bits ""
It means that the starting index is zero!

""Lucas-Lehmer number denoted Sn where S1 = 4 and Sn = (Sn-1)^2 − 2 .""
So the starting index is one!!

""So that where S3 = 14, S4 = 14^2 - 2 = 194, and S5 = 194^2 - 2 = 37634.""
If you define S(3)=14 then S(2)=4, so here the starting index is two!!!

So there were 3 definitions for the same Lucas sequence!!!
I've corrected these errors.

[KickBoxer]

hi there i just want to ask u all is there any free code for lucas that i can use in cryptography as a tool.
or if u know where to find the source code or the algorithm of it.
if u know please just send it to my email (homam.eltaj@gmail.com)

yours Homam

thanks all

[R.D. Silverman]

Originally Posted by KickBoxer

hi there i just want to ask u all is there any free code for lucas that i can use in cryptography as a tool.
or if u know where to find the source code or the algorithm of it.
if u know please just send it to my email (homam.eltaj@gmail.com)

yours Homam

thanks all

While free code may exist (You can get it from the mersenne.org website)
it is useless for any cryptographic purpose. It has no use whatsoever.

[KickBoxer]

Sorry but I'm new here i don't know how to use this site
any way thanks a lot
and for lucas there is a big usage of it in cryptographic cause I'm working on it and there is a lot more so i just want to make the library of it to be as a tool in program but u know if there is a code of this library i will save time

so again if u know the link please just let me know

thanks

Warmest Regards

[ColdFury]

and for lucas there is a big usage of it in cryptographic cause I'm working on it and there is a lot more so i just want to make the library of it to be as a tool in program but u know if there is a code of this library i will save time

The Lucas-Lehmer test has absolutely no cryptographic applications. Perhaps you're confusing with something else.

[KickBoxer]

may be yes iimm talking about the lucas numbers wich they are a part of the Fibonacci because i need to use the set of Lucas in my project and sorry i know that there is some types of Lucas such as the TriLucas and others but i need the basic algorithm of the Lucas to use it as a Library in my Project thats all

thanks a lot

yours