English

On the Ribenboim-Landau Conjecture

Number Theory 2022-04-05 v1

Abstract

We prove the Ribenboim hypothesis, which states that if, starting from some integer NN, consecutive prime numbers pnp_ {n}, pn+1p_{n+1} satisfy the inequality pn+1pn<1\sqrt {p_ {n+1}}-\sqrt{p_{n}} <1, then the Landau problem # 4 (1912) has a positive solution.

Keywords

Cite

@article{arxiv.2204.01579,
  title  = {On the Ribenboim-Landau Conjecture},
  author = {Felix Sidokhine},
  journal= {arXiv preprint arXiv:2204.01579},
  year   = {2022}
}