Very small intervals containing at least three primes

2009/10/02 by Vladimir Shevelev, Shevelev, Vladimir
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.0910.0428

3 page. Correction of Corollary 1 (see Remark 1)

arxiv created 2009/10/20 · arxiv updated 2009/12/01

Abstract

Let p_n is the n-th prime. With help of the Cramér-like model, we prove that the set of intervals of the form (2p_n,\enskip2p_n+1) containing at list 3 primes has a positive density with respect to the set of all intervals of such form.

Related

• Primes in Tuples IV: Density of small gaps between consecutive primes
• Estimating the density of a set of primes with applications to group theory
• The Cramér conjecture holds with a positive probability
• On intervals (kn,(k+1)n) containing a prime for all n>1
• A heuristic study of the distribution of primes in short and not-so-short intervals