Re: Mersenne: P-1

[Farringr]

>> 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.

The main purpose is to find the Biggest Known Prime.  Since that keeps
changing, it's hard to say if we ever had a long term goal.

>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.

And don't forget, there are still mersenne numbers known to be composite with
NO Known Factors (ooh, a mystery).  Last I looked, the lowest exponent was
727.  That's mighty low.

Bob Farrington