Open Access
Difference between consecutive primes
Jia Chaohua
- 01 Jan 1995
3
TL;DR: For the positive integers n, Xn≤2X, except for O(X log-B X) values, the interval (n, n+n 1/14+e) contains a prime number.
read more
Abstract: Suppose that B is a sufficiently large positive constant, e is a sufficiently small positive constant, X and N are sufficiently large. It is mainly proved that i) for the positive integers n, Xn≤2X, except for O(X log-B X) values, the interval (n, n+n1/14+e) contains a prime number; ii) if A = N1/2+s, then the even numbers in the interval (N, N+A), except for 0(Alog-B N) values, are all Goldbach numbers.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Landau’s problems on primes
TL;DR: Au congres international de Cambridge en 1912, Laudau dressa the liste de quatre problemes de base sur les nombres premiers as discussed by the authors, which sont les suivants: (1) Existe-t-il une infinite number of noms premiers of the forme n 2 + 1? (2) La conjecture (binaire) de Goldbach, that chaque nombre pair superieur a 2 est somme de deux noms.
On the Exceptional Set for Goldbach’s Problemin Short Intervals
TL;DR: In this article, it was shown that there exists a constant θ such that the number of even integers in the interval θ which cannot be written as a sum of two primes is θ.