[4] In 1980 he and Nobel laureate Edwin McMillan found a new algorithm for high-precision computation of the Euler–Mascheroni constant
[6] He later factored the tenth[7] and eleventh Fermat numbers using Lenstra's elliptic curve factorisation algorithm.
In 2002, Brent, Samuli Larvala and Paul Zimmermann discovered a very large primitive trinomial over GF(2): The degree 6972593 is the exponent of a Mersenne prime.
[8] In 2009 and 2016, Brent and Paul Zimmermann discovered some even larger primitive trinomials, for example: The degree 43112609 is again the exponent of a Mersenne prime.
[10] In 2011, Brent and Paul Zimmermann published Modern Computer Arithmetic (Cambridge University Press), a book about algorithms for performing arithmetic, and their implementation on modern computers.
Brent is a Fellow of the Association for Computing Machinery, the IEEE, SIAM and the Australian Academy of Science.