Guido Hoheisel

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Guido Hoheisel was a mathematician. He did his PhD under the supervision of Erhard Schmidt.

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

π(x + x^θ) - π(x) ~ x^θ/log(x), as x tends to infinity,

implying that if p_n denotes the n-th prime number then

p_n+1 - p_n < p^θ

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

[edit] References

1. ^ G. Hoheisel, Primzahlprobleme in der Analysis, Berliner Sitzungsberichte, pages 580-588, (1930)