<<Yesterday a coworker
saw my six page printout of the Great Number on the wall of my office,
asked, and I explained GIMPS and the LL algorithm, how the program
checks to see if M(n) divides S(n). He is a clever chap and asked why
prime95 starts from scratch calculating S(n) instead of getting it from
a previous check: if you calculated S(6000001) and your needed
S(6000031) for your next check, for instance, why would you not take
the previously calced S(6000001) then square and subtract 2 thirty times.
I pointed at the Great Number and said: Because S(3021377) has this
many bits. Knock off a dozen digits, and it would take that many years
just to send the data from one computer to another.
I felt pretty smart. Then he asked: if S(n) has so many bits, how does a
desktop computer handle it?
Me: duuuuuuuh. I dont know. {8-[
Do you know? Can someone explain it to me in words an ordinary
person would understand, how the Prime95 LL algorithm works? spike>>
Wouldn't it be nice... (Beach Boys song). Nah. You see, we use a shortcut. At
every iteration, we only store S(whatever) mod 2^P - 1. It's that mod that
counts. This lets us run Prime95 on machines with 8MB of RAM. However, it
makes what you'd like to do utterly impossible. It would ONLY be possible if
we stored the FULL S(whatever) every cycle, and never took it modulo 2^P - 1.
However, we'd need machines with (insert fantastically large number, perhaps
more than the universe can handle) exabytes of RAM to store the full S for an
exponent around 3 million. And so forth. Aw. :-(
-*---*-------
S.T.L.
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