I'm curious, as to the nature of the proof that the LL test can definitively
prove/disprove the primality of a Mersenne number. The resources I have are
limited and don't go into depth. Before I search elsewhere, I was wondering if
anyone on the list could help me:
What were the original details of Lucas' test? And how did Lehmer modify it
into its current form (at least I know how to perform the LL test in its
current state).
What are the details of the proof that Lucas' test definitively (dis)proves
the primality of a Mersenne number? Does the proof change for the Lucas-Lehmer
test?
In the LL test, we start with S(1) = 4. The Prime Page says we can use S(1) =
10 and certain other values depending on p. Can anyone clarify this?
To prove that M(127) (Or M127, whichever refers to 2^127 - 1, not the 127th
Mersenne prime) is prime, did Lucas use his test by hand? I know he did it by
hand, at the very least.
I posted a message on sci.math a while ago. The response was deafening. If
anyone on the list would like to add to the voluminous (har har har) response
I've received, I'd be grateful. It can be found at:
http://www.dejanews.com/getdoc.xp?AN=450576076
I don't wish to add to the size of the list digest unduly.
Thanks. Please reply to the list, as if you have an Internet E-mail address,
my software will auto-block you. AOL members need not worry.
S.T.L.
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