{
  "abstract": "As a new approach to search a counterexample of variants of Kurepa's conjecture, we investigate a parallel searching method of prime numbers $p$ satisfying \\begin{eqnarray*} \\sum_{k=0}^{p-1} c_k k! \\equiv 0 \\pmod{p} \\end{eqnarray*} for a given integer sequence $(c_k)_{k=0}^{\\infty}$. As an application, we prove that there are only finitely may prime numbers of the form $\\sum_{k=0}^{n} (1+dk)!$ with $(d,n) \\in (\\mathbb{N}_{\\leq 25} \\setminus \\{0,8,18,20,23,25\\}) \\times \\mathbb{N}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28805",
  "author_total": 1,
  "authors": [
    {
      "name": "Tomoki Mihara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ecaf1qn4ye84.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28805",
  "fulltext_url": null,
  "id": "3ecaf1qn4ye84",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28805",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GM"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214384085",
  "pdf_url": "https://arxiv.org/pdf/2609.28805",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ecaf1qn4ye84.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28805",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28805"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Analytic Number Theory Research",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Parallel Searching Method for Verifying Finiteness of Prime Numbers Presented as Specific Linear Combinations of Factorials",
  "title_text": "Parallel Searching Method for Verifying Finiteness of Prime Numbers Presented as Specific Linear Combinations of Factorials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/3ecaf1qn4ye84",
  "venue": "arXiv",
  "versions": []
}