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From: apak@oddjob.UUCP (Adrian Kent)
Newsgroups: net.math
Subject: Re: New Factorization Record!!!
Message-ID: <1189@oddjob.UUCP>
Date: Thu, 20-Feb-86 23:22:31 EST
Article-I.D.: oddjob.1189
Posted: Thu Feb 20 23:22:31 1986
Date-Received: Mon, 24-Feb-86 06:26:32 EST
References: <479@faron.UUCP>
Reply-To: apak@oddjob.UUCP (Adrian Kent)
Distribution: net
Organization: U. Chicago: Physics
Lines: 29

In article <479@faron.UUCP> bs@faron.UUCP (Robert D. Silverman) writes:
>A new factoring record has just been set: I have factored a 75 digit cofactor
>    128
>of 6   + 1 using an enhanced version of Carl Pomerance's Quadratic Sieve
>Algorithm. [ ...factorisation follows ...]
>For the ambitious among you I present a list of the numbers currently
>on the '10 MOST WANTED' list to be factored: (Cxx means a composite number 
>of xx digits)
>
>     512
>(1) 2   + 1 = 2424833.C148
>
>     227   114
>(2) 2   - 2   + 1 = 5.C68
>
[......]
>      149
>(10) 3   + 1 = 4.C71
>
>Bob Silverman
     This is fascinating. Is it possible to explain where these composite
numbers come from? Were/are they bound to have few large factors, or has that
been established by trial and error? Are they all extremely simple base n
(for some small n) for number-theoretic, computational or sociological
reasons? (i.e. are they known to be likely to have few large factors, or are
they much easier to work with, or are they just the sort of numbers people are
likely to look at?) And is there a committee somewhere which decides the 
'most wanted' list? :-)
                         Adrian Kent