bibkey: cloitre2003a079063
authors: Benoit Cloitre
year: 2003
title: "OEIS A079063, Least k such that sqrt(prime(n+k))-sqrt(prime(n))>1"
doi: null
url: https://oeis.org/A079063
claim: "Least k such that sqrt(prime(n+k))-sqrt(prime(n))>1. Inspired by Andrica's conjecture. If it is true, a(n)>1 for all n. Conjecture: there is a constant c>0 such that for n large enough, a(n)>c*sqrt(n) and we can take c=0.4. More precisely, there are 2 constants A and B such that A=lim sup n ->infinity a(n)/sqrt(n) exists = 0.75....; B=lim inf n ->infinity a(n)/sqrt(n) exists =0.46.... - _Benoit Cloitre_, Feb 02 2003"
strata_touched:
  - D5/S3/PrimeGaps/CloitreSquareRootPrimeGapRefutation
license: citation-only
triage: anchor

OEIS A079063

The NAME of A079063 defines the least-index sequence:

Least k such that sqrt(prime(n+k))-sqrt(prime(n))>1

The COMMENTS line gives the motivation:

Inspired by Andrica’s conjecture. If it is true, a(n)>1 for all n.

The FORMULA line proposes an eventual square-root lower bound and more precise limsup and liminf values. The repository result refutes the weakest quantified eventual positive lower bound. It does not address Andrica’s conjecture or assert the existence of either limit.

Verified locator

• URL: https://oeis.org/A079063
• NAME (verbatim): Least k such that sqrt(prime(n+k))-sqrt(prime(n))>1
• COMMENTS (verbatim): Inspired by Andrica’s conjecture. If it is true, a(n)>1 for all n.
• FORMULA conjecture line (verbatim): Conjecture: there is a constant c>0 such that for n large enough, a(n)>c*sqrt(n) and we can take c=0.4. More precisely, there are 2 constants A and B such that A=lim sup n ->infinity a(n)/sqrt(n) exists = 0.75….; B=lim inf n ->infinity a(n)/sqrt(n) exists =0.46…. - Benoit Cloitre, Feb 02 2003