> I know it's almost impossible to detect a repeating LL reminder, but what a
> LL repeating reminder means exactly? Can it tell the number's factored form,
> or other thing like that? (I'm including here also composite exponents and
> Sophie-Germain exponents, such as 2^4-1,2^6-1, 2^11-1...)
It is not almost impossible to detect them, it is relatively easy.
It is highly unlikely (probably impossible) that the remainders
can repeat in the range required...
First of all, they are remainders, not reminders ;). Second, the LL
series is
s_1=4
s_(n+1)=(s_n)^2-2 mod (2^p-1)
and *IF* s_n was ever equal to s_q for n, and q on [1,p-1]. Then
the rest of the Lucas-Lehmer test would not be required (as the only
possible s would be those that occurred between s_q, and s_n).
I don't know if the point of repeating can tell the factors (it seems
possible), but the factors can tell the point of recurrence. For more
information see the FAQ at http://www.tasam.com/~lrwiman/FAQ-mers
Check the second section. It deals with the LL test, and has a question
about this very thing.
Please everyone check the FAQ if you suspect that your question might
be in there.
It's no good unless people read it...
-Lucas Wiman
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