My research interests have been in computational number theory, the arithmetic of elliptic curves, Diophantine equations; algebraic combinatorics; machine learning and public-key cryptography.

I have recently been interested in model theory, string algorithms, and in Carmichael numbers and pseudoprimes.

I am a member of the London Mathematical Society; a Fellow of the Institute of Mathematics and its Applications and a Chartered Mathematician and Chartered Scientist.

For 2021-2022 I was Vice-President, Professional Affairs and Industry, of the IMA, and a the Council of the LMS.

My Erdos number is 3 (via
Swinnerton-Dyer -- Davenport).

Email me at
`rgep@chalcedon.co.uk`

.

See a complete list. My ORCID id is 0000-0002-4370-5882, my SCOPUS is id 6603105329 and my ResearchGate page is here.

- Enumerating forbidden factors (2018)
- The Carmichael numbers up to 10 to the 21 (2008)
- Absolute quadratic pseudoprimes (2007)
- The distance to a subgroup of the symmetric group (2007)
- A note on Lehmer's Totient Problem (2006)
- Carmichael numbers with small index (2006)

- Enumerating words with forbidden factors: some things that could be better known, London Stringology Day, February 2019
- From CATAM to Quantum, Trinity Mathematical Society Centenary, February 2019
- Knowledge Exchange in Mathematics: progress and prospects, IMA Academic Representatives meeting, January 2019
- Reflections and Vision: the Newton Gateway to Mathematics, Isaac Newton Institute, January 2019
- Computing the Future: and what it means for mathematics, Liverpool Mathematical Association, October 2018
- Quantum Computing: what it means for cybersecurity, British Science Association, February 2017
- Mathematics, Science and Cybersecurity, IMA, April 2016
- Big Data: mathematical challenges Birmingham University, January 2016
- Wikipedia vs Academia: a clash of cultures, Wellcome Foundation, September 2015
- Big Data: mathematical challenges, Royal Institution, October 2014
- Mathematics and Global Security, IMA Mathematics of Planet Earth, March 2013
- Primes and pseudoprimes, British Mathematical Colloquium 2010, Edinburgh, April 2010
- PRIMES is in P: Arithmetic at random, Bristol Algorithms Days 2008, March 2008
- Absolute quadratic pseudoprimes, Conference on Algorithmic Number Theory, Turku, May 2007.
- The Carmichael numbers up to 10 to the 21, Conference on Algorithmic Number Theory, Turku, May 2007.
- Primes and pseudoprimes, Heilbronn seminar, Bristol, October 2006
- Pseudoprimes and Carmichael numbers, Number theorists weekend, Banff, November 2004.
- Carmichael numbers: theory and practice, Explicit methods in number theory, Banff, November 2004.
- Carmichael numbers, Oxford Number Theory Seminar, February 2004.
- Carmichael numbers and pseudoprimes, Conference in Honour of Hugh Williams, Banff, May 2003.
- Carmichael numbers with three prime factors , SECANTS-16, Royal Holloway, February 2002.
- The pseudoprimes up to 10 to the 13, ANTS-IV, Leiden, July 2000
- Pseudoprimes and Carmichael numbers , SECANTS-14, Oxford, March 2000.
- Squares in quadratic progression, SECANTS-8, Oxford, March 1998.
- Slides from the LMS
MathFIT workshop
on Computational
number theory and cryptography held at the
University of Kent at Canterbury, 14--16
July 1997.
- Elementary factoring methods
- Practical cryptography

- Fermat's Last Theorem, Singapore Mathematical Society, March 1997.
- Back to the Dark Ages:
RSA Data Security Conference,
January 1997
- also at SECANTS-1, Oxford, December 1995
- Secret sharing: RSA Data Security Conference, January 1997
- also at SECANTS-1, Oxford, December 1995

Updated 16/04/2023 by Richard Pinch