With respect to the screensaver idea,
The difficult thing about visualizing the Lucas-Lehmer compuation is that
it's so... abstract. There isn't any immediately obvious way to see its
progress other than what's currently done: a readout of the iteration number
and clock cycle. However, another idea did spring into my mind. Everyone
here is familiar with The Matrix, and the screens of green scrolling numbers
and letters displayed at various points in the movie. I suggest that the
screensaver might display the intermediate residues in hexadecimal in such a
fashion, dropping the residues hexit-by-hexit on the screen such that one
residue's worth of digits is displayed every iteration. This way, it's just
not a green blurry readout of a list of residues, but a staggered waterfall
of hexits. I think it would look nifty. Faster computers would have a
faster flowing waterfall of hexits, and it would also depend on the size of
the number being tested. It's simple, and it immediately shows the
"fastness" of the computation and its intermediate results in a way that
humans could see. People would probably want to be able to configure the
colors of the hexits displayed, I'm sure.
-*---*-------
Stephan T. Lavavej
Author of "Mersenne Primes: Development through History, Ongoing Work, and a
New Conjecture" at
http://www.its.caltech.edu/~stl/paper.html
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