[seqfan] A (new) constant related to the Lucas-Lehmer-test. Is this worth an entry in OEIS?
Gottfried Helms
helms at uni-kassel.de
Thu Apr 5 23:09:08 CEST 2012
Just for my own experience with iterations of functions
I fiddled with the Lucas-Lehmer-test for Mersenne-numbers,
which is just an application of functional iteration,
beginning at a fxied starting value.
This lead to the finding of a new constant, which for what
it is worth, I temporarily called the "Lucas-Lehmer-Constant"
which "encodes" the Lucas-Lehmer-test in one number.
This all is not useful for actual computation since we needed
exponentially number of digits related to the index of the
Mersenne number to be tested.
So its benefit is just its curiosity while it is not
only pure fun.
What do you think? Here is the discussion where I describe
its derivation:
http://go.helms-net.de/math/expdioph/lucasLehmer.pdf
The leading digits are
LucLeh ~ 0.329239474231204177156261586826992111006745492821106086516800...
and actually LucLeh = acosh(sqrt(2+sqrt(2+4))/2)
The final version of the constant-based Lucas-Lehmer test is
the exponential eLucLeh = exp(LucLeh)
eLucLeh = 1.38991066352414771791154881199221010219608990353920505265182..
with this we have
ceil(eLucLeh^2^p) == 0 (mod Mp) <==> Mp is prime
Again: what do you think? Is it worth an entry in OEIS?
Kind regards -
Gottfried Helms
More information about the SeqFan
mailing list