[Cs-colloq] Colloquium 11/18/2008
piegza at cs.purdue.edu
Mon Nov 10 14:22:29 EST 2008
The New Largest Known Prime is 2^p-1 with p=43112609. Who cares?
Prof. Sam Wagstaff
Tuesday, November 18, 2008
3:30 pm -4:30 pm
On August 23, 2008, a computer at UCLA found the first known prime number
with more than 10,000,000 digits and won a $100,000 prize from the Electronic
Frontier Foundation. We explain how it was found and give some applications
of this achievement.
We begin with the Lucas-Lehmer test for the primality of 2^p-1. Next we
describe how the calculation is done efficiently with integers having
millions of decimal digits. We display the known Mersenne primes and tell
some conjectures about them. Several applications are presented, in number
theory, in other parts of mathematics, and in cryptography.
Before coming to Purdue, Professor Wagstaff taught at the Universities of
Rochester, Illinois, and Georgia. He spent a year at the Institute for
Advanced Study in Princeton. His research interests are in the areas of
cryptography, parallel computation, and analysis of algorithms, especially
number theoretic algorithms. He and J. W. Smith of the University of Georgia
have built a special processor with parallel capability for factoring large
integers. He is the author of Factorizations of bn ± 1, b = 2, 3, 5, 6, 7,
10, 11, 12 up to high powers, Contemporary Mathematics series, v. 22, Third
edition, American Mathematical Society, 2002 (with John Brillhart, D. H.
Lehmer, J. L. Selfridge and Bryant Tuckerman) (See
http://www.ams.org/online_bks/conm22), Cryptanalysis of Number Theoretic
Ciphers, CRC Press, 2002, and Sums of Squares of Integers, CRC Press, 2005
(with Carlos Moreno).
-Refreshments will be served before the talk in LWSN 3102A/B.
-Please see the attached pdf for an appropriately formatted copy of the
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