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From: walter@cwi.nl (Walter M. Lioen)
Newsgroups: sci.math,sci.crypt
Subject: Re: New Factorization Records
Keywords: 4,6,8,9,10,12,14,15,16,18,...
Message-ID: <7539@boring.cwi.nl>
Date: 28 Apr 88 13:50:16 GMT
References: <7535@boring.cwi.nl> <2675@phoenix.Princeton.EDU> <7537@boring.cwi.nl> <2687@phoenix.Princeton.EDU>
Organization: CWI, Amsterdam
Lines: 54

In article <2687@phoenix.Princeton.EDU>
schoen@phoenix.Princeton.EDU (Randy Schoenberg) writes:

> Thanks very much for the explanantion.  Is there a good book or article
> you could recommend for an introduction to the subject of factorization of
> large numbers? ...

A good book and full of references itself:

%A H. Riesel
%T Prime Numbers and Computer Methods for Factorization
%I Birkhauser
%D 1985

>    Does your MPQS method have anything to do with something I "discovered"
> while doodling in class a few years ago:
> ...

no

> ...
> ... deleted stuff about polynomials (sometimes:-) `generating' primes ...
> ...
> I know that it has been proven that x^2 + x + 41 will produce the longest
> consecutive string of primes, but is there some general theorem about the
> factors of non-primes generated by a polynomial?  My hunch is that there must
> be, otherwise you wouldn't be having such success at factoring those large
> numbers. ...

I am not familiar with such a theorem. Also there is no relation (at least
that I know of) with your observation and MPQS' success of factoring large
numbers.

For an algorithmic description of MPQS and other references on (MP)QS see:

%A R.D. Silverman
%T The Multiple Polynomial Quadratic Sieve
%J Mathematics of Computation
%V 48
%N 177
%P 329-339
%D January 1987
%K MPQS

Perhaps we should move an eventual further discussion
into a private e-mail combat?

Greetings,

-- 
Walter M. Lioen,
CWI, P.O. Box 4079, 1009 AB  Amsterdam, The Netherlands.
INTERNET:    walter@cwi.nl
BITNET/EARN: walter@mcvax