Richard Brent  Research Interests (1)
Computational number theory

integer factorisation algorithms
 Pollard
rho method
 complete factorisation of the
Fermat number
F8

elliptic curve method (ECM)

large factors found by ECM
 complete factorisation of the
Fermat numbers
F10 and
F11
 use of specialpurpose hardware (jointly with
Harvey Dubner)
 the
ECMNET project

number field sieve (NFS) (jointly with
Brian Murphy)
 application to security and cryptography
 factorisation of a 140digit number
RSA140 by NFS
 factorisation of a 512bit number
RSA155 by NFS
 some
graphs and extrapolations
from my recent
survey
 the
NFSNET project
 factorization on an IBM PC
 extension of the
Cunningham tables to bases 13..99

tables
(June 1992, 363 pages, and updates),
 Scott Contini's
FactorWorld page
 primality testing
 here
is a talk on the AKS, ECPP and RabinMiller algorithms
 perfect numbers
(jointly with Graeme Cohen and Herman te Riele)
 proof
that there is no odd perfect number
less than 10^{300}
 distribution of
primes and twin primes
 Riemann Hypothesis
(RH) and its generalisations
 other
people working on number theory
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