# Über den Primzahlsatz von Herrn Hoheisel

@article{Heilbronn1933berDP,
title={{\"U}ber den Primzahlsatz von Herrn Hoheisel},
author={Hans Heilbronn},
journal={Mathematische Zeitschrift},
year={1933},
volume={36},
pages={394-423}
}
• H. Heilbronn
• Published 1 December 1933
• Mathematics
• Mathematische Zeitschrift
22 Citations
The Chromatic Number of $\mathbb{R}^{n}$ with Multiple Forbidden Distances
. Let A ⊂ R > 0 be a ﬁnite set of distances, and let G A ( R n ) be the graph with vertex set R n and edge set { ( x, y ) ∈ R n : k x − y k 2 ∈ A } , and let χ ( R n , A ) = χ ( G A ( R n )) . Erdős
Large Gaps Between Primes
Let p n be the n -th prime, and deﬁne the maximal prime gap G ( x ) as G ( x ) = max p n ≤ x ( p n +1 − p n ) . We give a summary of the lower and upper bounds that have been obtained for G ( x )
The gap gn between two consecutive primes satisfies gn= O(pn2/3)
The following is proven using arguments that do not revolve around the Riemann Hypothesis or Sieve Theory. If $p_n$ is the $n^{\rm th}$ prime and $g_n=p_{n+1}-p_n$, then $g_n=O({p_n}^{2/3})$.
An observation on the difference between consecutive primes
Consider two consecutive odd primes $p_n$ and $p_{n+1}$, let $m$ to be their midpoint, fixed once for all. We prove unconditionally that every $x$ in the interval $[\frac{\ln{(m-p_n)}}{\log{p_n}}, A conditional proof of Legendre's Conjecture and Andrica's conjecture The Legendre conjecture has resisted analysis over a century, even under assumption of the Riemann Hypothesis. We present, a significant improvement on previous results by greatly reducing the On Legendre's, Brocard's, Andrica's, and Oppermann's Conjectures Let$n\in\mathbb{Z}^+$. Is it true that every sequence of$n$consecutive integers greater than$n^2$and smaller than$(n+1)^2\$ contains at least one prime number? In this paper we show that this is
On the difference between consecutive primes
Update: This work reproduces an earlier result of Peck, which the author was initially unaware of. The method of the proof is essentially the same as the original work of Peck. There are no new
Representation Numbers of Stars
• Mathematics
Integers
• 2010
It is shown that the problem of determining rep(K 1,n ) is equivalent to determining the smallest even k for which φ(k) ≥ n: this problem for “small” n is solved and the possible forms of rep( K 1, n ) for sufficiently large n are determined.
Axx REPRESENTATION NUMBERS OF STARS
A graph G has a representation modulo r if there exists an injective map f : V (G) → {0, 1, . . . , r−1} such that vertices u and v are adjacent if and only if f(u)−f(v) is relatively prime to r. The