{
  "abstract": "Finding the largest pair of consecutive $B$-smooth integers is computationally challenging. Current algorithms to find such pairs have an exponential runtime -- which has only be provably done for $B \\leq 100$ and heuristically for $100 < B \\leq 113$. We improve this by detailing a new algorithm to find such large pairs. The core idea is to solve the shortest vector problem (SVP) in a well constructed lattice. With this we are able to significantly increase $B$ and notably report the heuristically largest pair with $B = 751$ which has $196$-bits. By slightly modifying the lattice, we are able to find larger pairs for which one cannot conclusively say whether it is the largest or not for a given $B$. This notably includes a $213$-bit pair with $B = 997$ which is the largest pair found in this work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2509.17699",
  "author_total": 3,
  "authors": [
    {
      "name": "Erik Mulder"
    },
    {
      "name": "Bruno Sterner"
    },
    {
      "name": "Wessel van Woerden"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8dhdhc47z8r6v.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "8dhdhc47z8r6v",
  "issns": [],
  "landing_url": "https://hal.science/hal-05207824v3",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-nt"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05207824/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8dhdhc47z8r6v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:24Z",
      "native_id": "hal-05207824",
      "source": "hal",
      "url": "https://hal.science/hal-05207824v3"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-nt",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Large smooth twins from short lattice vectors",
  "title_text": "Large smooth twins from short lattice vectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:24Z",
  "url": "https://research.draconitic.com/paper/8dhdhc47z8r6v",
  "venue": "HAL",
  "versions": []
}