# Mathematician:Hermanus Johannes Joseph te Riele

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## Contents

## Mathematician

Dutch mathematician specializing in computational number theory.

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.

Disproved the Mertens Conjecture, with Andrew Michael Odlyzko.

Known for factoring large numbers of world record size.

Also known for discovering large amicable pairs.

Found a new upper bound for $\map \pi x - \map \Li x$.

## Nationality

Dutch

## History

- Born: January 5, 1947 in The Hague, Netherlands

## Theorems and Definitions

## Publications

- 1984:
*On generating new amicable pairs from given amicable pairs*(*Math. Comp.***Vol. 42**: 219 – 223) www.jstor.org/stable/2007572

- 1986:
*Computation of all the amicable pairs below $10^{10}$*(*Math. Comp.***Vol. 47**: 361 – 368) www.jstor.org/stable/2008101

- 1987:
*On the difference $\map \pi x - \map \Li x$*(*Math. Comp.***Vol. 48**: 323 – 328)

- 1991:
*Improved Techniques for Lower Bounds for Odd Perfect Numbers*(*Math. Comp.***Vol. 57**: 857 – 868) (with R.P. Brent and G.L. Cohen) www.jstor.org/stable/2938723

## Also known as

He is generally known as **Herman te Riele**.

The surname is **te Riele**, not **Riele**.