{
  "abstract": "Let $p_j$ be the prime with index $j$. We prove that the ratios $m/n$ for which $p_m+p_n$ is a square are dense in $\\mathbb R_{>0}$. The same is true when $|p_m-p_n|$ is a square. In every nonempty open interval, almost every index can be used as a numerator and as a denominator. We also give a quantitative lower bound for the number of possible partners.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07371",
  "author_total": 2,
  "authors": [
    {
      "name": "Shenghao Hua"
    },
    {
      "name": "Sizhe Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2x688pz57bwcs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07371",
  "fulltext_url": null,
  "id": "2x688pz57bwcs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07371",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7212084570",
  "pdf_url": "https://arxiv.org/pdf/2609.07371",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2x688pz57bwcs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07371",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07371"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Prime pairs along rays of prime indices",
  "title_text": "Prime pairs along rays of prime indices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/2x688pz57bwcs",
  "venue": "arXiv",
  "versions": []
}