> From: "CARLETON GARRISON" <[EMAIL PROTECTED]>
> I honestly thought that the long term goal (maybe not by this panel but for
> others) was to factor all these numbers and that we were setting/recording a
> lower boundary for that effort.
>
> Carleton Garrison
It will be a _long_ time before we are completely factoring those
values of 2^n +- 1 which are now being subject to LL testing.
In the 1983 Cunningham edition, (2^211 - 1)/15173 was the
first incomplete 2^n +- 1 factorization.
In the 1988 edition it was (2^311 - 1)/5344847.
Now, in 2001, the exponent has risen to 641.
This threshold exponent advanced 20 per year between 1983 and 1988,
due primarily to the MPQS and ECM algorithms.
Since 1988, it has risen about 25 per year, due
primarily to the Number Field Sieve.
Unless there are major algorithmic advances, don't
expect to pass 2^2000 - 1 in our lifetimes.
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