Jukka Santala <[EMAIL PROTECTED]> wrote on Friday 24 September 1999 at 5:25
PM:
> Though you ask this, I find the topic rather appropriate for the list,
> especially given the angle of "HOW can we visualize the process of
> mathemathical operations.
That brings me to the following observation:
I think few of us fully realize the _enormous_ amount of (highly
optimized) processing required each iteration to achieve something that
looks so simple: a squaring, minus 2, mod (2^p-1).
Remember, you see nothing happening! Prime just tells you: I used
so-and-so-many BILLION clock cycles on the previous iteration. When a
computer is ray-tracing (preferrably on some fancy high-end workstation)
you are immediately dazzled by the picture-perfect pixels appearing on the
screen in brilliant colours.
But your result is not for eternity. In GIMPS it is. M7xxxxxx tested.
Composite. Or: M10yyyyyy trial-factored to 2^65. No factors below 2^65.
And you know that YOU discovered that mathematical fact.
That little 64bit residue or checksum is precious. If you had a grain of
rice for the number of clock cycles needed to produce just one of those
bits, you could feed the entire (current) world population for a whole
year! Is that about right?
Whatever the correct figure, the program doesn't show you what it's doing.
Actually, it might be interesting to be able to see, say, just the last
64 bits (in hex) of the current number L[n] in the Lucas sequence. The
program displays those bits for L[p-1], right? So why not during the
sequence?
The program should IMHO at least -optionally- display a progress bar
showing graphically what it now only shows in digits:
progress on current exponent [95.2% completed]. The bar would probably
grow one pixel longer every couple of hours.
Any comments on the issue of graphical visualisation?
Cheers,
Robert van der Peijl
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