English

Very small intervals containing at least three primes

Number Theory 2009-10-20 v4

Abstract

Let pnp_n is the nn-th prime. With help of the Cram\'er-like model, we prove that the set of intervals of the form (2pn,2pn+1)(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.

Keywords

Cite

@article{arxiv.0910.0428,
  title  = {Very small intervals containing at least three primes},
  author = {Vladimir Shevelev},
  journal= {arXiv preprint arXiv:0910.0428},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T13:53:30.394Z