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From: phyllis@utcsrgv.UUCP (Phyllis Eve Bregman)
Newsgroups: ont.events
Subject: Eric Bach:  "What to do until the witness comes:  explicit bounds for primality testing and related problems".
Message-ID: <3422@utcsrgv.UUCP>
Date: Fri, 2-Mar-84 16:19:36 EST
Article-I.D.: utcsrgv.3422
Posted: Fri Mar  2 16:19:36 1984
Date-Received: Fri, 2-Mar-84 17:22:02 EST
Organization: CSRG, University of Toronto
Lines: 31

      UofT Department of Computer Science Seminar Schedule for
                the week of March 5th, 1984
		
Tuesday, March 6th, 3:00 P.M., GB244:  Professor Eric Bach,
   Computer Science Division, University of California, Berkeley:
   "What to do until the witness comes:  Explicit bounds for
   primality testing and related problems".

   ABSTRACT:  Many analyses of number-theoretical algorithms use the
   following result:

   Assuming the Extended Riemann Hypothesis, if G is a proper
   multiplicative subgroup of the integers modulo n, then the least
   positive integer x outside G is 0(Log n)^2.

   However, this cannot be applied to problems such as prime testing
   unless the 0-estimate is replaced by something concrete.  This talk
   is about the new "effective" versions of the above theorem.  Not
   only is the above-mentioned x small asymptotically (<( log n)^2 ),
   but this estimate converges quickly, so that one has, for instance,
   x < = 2 ( log n)^2 for n > = 1000.

   The first part of this talk will concern subgroups and their relevance
   to prime testing.  In the second part, I will show, in an intuitive
   way, why the ERH has the algorithmic implications that it does.
-- 
		Phyllis Eve Bregman
		CSRG, Univ. of Toronto
		{decvax,linus,ihnp4,uw-beaver,allegra,utzoo}!utcsrgv!phyllis
		CSNET:  phyllis@toronto
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