Date: Tue, 08 Jan 2002 11:00:20 -0700 (MST)
From: Richard Schroeppel
Subject: rigorous mpfn bounds
To: Achim Flammenkamp
Message-id: <200201081800.g08I0Kw00622@baskerville.CS.Arizona.EDU>
Status: ROr
> I have finished my yearly update of the MPN-statistics and the MPN-Webpage.
Send me a url and I'll add a pointer to my mpfn page.
> I remember of an important notice I miss to publish:
you wrote in an email-message dated 1996 or earlier, that you had completely
checked the range <= 10^80 (not quite sure about your claimed limit) for MPNs.
What was the upper bound (and when did you) this rigorous search?
The rigorous bound is only to 10^70.
I also checked rigorously for odd MPFNs up to 10^90.
There's an old paper that rigorously proves no plain vanilla odd perfects
less than 10^300.
My search was done before 1990, maybe even before 1985.
The bound could be bumped up quite a bit now. Most of the time goes into
factoring numbers in cascades that we "know" can't appear in real mpfns.
I made some progress in restricting the ranges of prime powers with
rigorous proofs.
Rich rcs@cs.arizona.edu