Guido Hoheisel

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Guido Hoheisel (1930)

Guido Hoheisel (1894–1968) was a German mathematician, a professor of mathematics at the University of Cologne. He did his PhD in 1920 from the University of Berlin under the supervision of Erhard Schmidt.[1]

Hoheisel is known for a result on gaps between prime numbers.[2] He proved that if π(x) denotes the prime-counting function, then there exists a constant θ < 1 such that

π(x + xθ) − π(x) ~ xθ/log(x),

as x tends to infinity, implying that if pn denotes the n-th prime number then

pn+1pn < pnθ

for all sufficiently large n. In fact he showed that one may take θ = 32999/33000.

During World War II, as one of the few remaining competent mathematicians in Germany, Hoheisel was required to teach classes simultaneously at three universities, in Cologne, Bonn, and Münster.[3] His doctoral students include Arnold Schönhage.


  1. ^ Guido Hoheisel at the Mathematics Genealogy Project.
  2. ^ G. Hoheisel, Primzahlprobleme in der Analysis, Berliner Sitzungsberichte, pages 580-588, (1930)
  3. ^ Segal, Sanford L. (2003), Mathematicians under the Nazis, Princeton University Press, p. 210, ISBN 978-0-691-00451-8 .