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Hermanus Johannes Joseph te Riele (born January 5, 1947, The Hague) is a mathematician at CWI in Amsterdam with a specialization in computational number theory. He is known for proving the correctness of the Riemann hypothesis for the first 1.5 billion non-trivial zeros of the Riemann zeta function, with Jan van de Lune and Dik Winter, for disproving the Mertens conjecture, with Andrew Odlyzko, and for factoring large numbers of world record size. In 1987, he found a new upper bound for π(x) − Li(x) (see Skewes' number).

In 1970, te Riele received an Engineer's degree in mathematical engineering from Delft University of Technology and, in 1976, a PhD degree in mathematics and physics from University of Amsterdam (1976).


  • A.M. Odlyzko and H.J.J. te Riele, "Disproof of the Mertens conjecture", Journal für die reine und angewandte Mathematik 357 (1985), 138–160.
  • J. van de Lune, H.J.J. te Riele and D.T. Winter, "On the zeros of the Riemann zeta function in the critical strip", IV, Math. Comp. 46 (1986), 667-681.
  • H.J.J. te Riele, "On the difference π(x) − Li(x)", Math. Comp. 48 (1987), 323–328.
  • Thorsten Kleinjung, Kazumaro Aoki, Jens Franke, Arjen Lenstra, Emmanuel Thomé, Joppe Bos, Pierrick Gaudry, Alexander Kruppa, Peter Montgomery, Dag Arne Osvik, Herman te Riele, Andrey Timofeev and Paul Zimmermann, "Factorization of a 768-bit RSA modulus", pp. 333–350 in: T. Rabin (ed.), Proceedings of Advances in Cryptology - CRYPTO 2010, Springer, 2010.

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