Yes, it would take an enormous amount of RAM to do this, but what if we
stored the data in some kind of compressed format (a ZILLION to 1
compression???), or some kind of reference format? Then we could take
advantage of everyone's clock cycles used on other searches. There's got
to be a way of virtually referencing somthing that is not able to exist.
Look at the way we use a MOD instead of the actual number.
Just some ramblings...
-Chuck
On Sun, 7 Mar 1999 [EMAIL PROTECTED] wrote:
> <<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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