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