Hermanus Johannes Joseph te Riele (born January 5, 1947 in 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).