>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...
If we compressed the data by any constant factor (e.g. a zillion), the
amount of data to be stored would still double with each squaring, so we'd
be not much better off.
Suppose we had sufficient memory available to do the computation. How long
would it take? Assume we've discovered something better than FFT and can
multiply in O(n) time (as far as I know, this is the best that can be done
since you have to at least look at the whole number). Each S(n) is twice
the length of the previous one, and the squarings would take O(2^n) time. 1
+ 2 + 2^2 + ... 2^(n-1) = 2^n, so the whole computation would take O(2^n)
time. That's a lot of time! And of course, actually dividing M(n) into
S(n-2) would take just about as long.
- Clayton
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