On Wed, 10 Mar 1999, John R Pierce wrote:
> > All,
> > How long would it take to run LL testing on M(M3021377) asuming that this
> > number was prime. Could we complete it before the sun explodes?
>
> Oh, I suspect if we could build a computer with a bunch of 4 million bit wide
> multipliers that ran at a few terahertz it would take significantly less time
> than that.
I think the first big problem is not time, but space. If you want to perform LL
on Mp you have to keep track of numbers modulo Mp, which requires aprox. p
bits. So even if you allow for one terabyte of memory/temporary files,
p must be at most aprox. 8 * 10^12. I forget how many bits of memory
the lithiumverse was supposed to have, but I am sure it was much much less
than M3021377. The number of iterations would also be aprox. M3021377,
so even if you perform 10^34 iterations per second you don't have enough
time...
Some mathematician asked (conjectured?) whether M(M(M(M(...(2)...)))
is always prime; the first unknown case is M(M127),
and that already requires (for LL) around M127 ~= 10^38 bits of memory and
iterations, which is far beyond present technology
(but easy for the lithimverse).
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