{
  "abstract": "FINDING: Perfect numbers remain tied to Mersenne primes via Euclid–Euler; a new Mersenne prime (2^136279841 − 1) was discovered, and a claimed theorem on primes of form 6^(m+1)·N − 1 exists but is unverified. | MATH: Euclid–Euler: even perfect number N = 2^(p−1)·(2^p − 1) iff 2^p − 1 is prime (Mersenne). New prime: p = 136279841, digits = 41,024,320. Claimed: P = 6^(m+1)·N − 1 prime for 1 < N ≤ 13, N ≠ 8, N ≠ i^(m+1) mod (6i+1), m odd positive; extension for N > 13 conditional. | CONNECTION: Mersenne primes 2^p − 1 relate to binary repunits (all 1s in base 2) — a lattice of dimension p. Perfect numbers are triangular: N = 2^(p−1)(2^p − 1) = T_(2^p − 1) (triangular number), linking to hexagonal numbers (T_n = n(n+1)/2; hexagonal = n(2n−1)). The ratio of perfect number to its Mersenne prime: N/(2^p − 1) = 2^(p−1) — a power of 2, not a golden ratio. However, the sum of reciprocals of divisors of a perfect number = 2 (harmonic mean of divisors is an integer), echoing the 2:1 octave ratio i\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bt24kt5tt9szz.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490940",
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  "id": "bt24kt5tt9szz",
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  "landing_url": "https://zenodo.org/records/23490940",
  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bt24kt5tt9szz.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:23Z",
      "native_id": "23490940",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23490940"
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  "subjects": [],
  "title": "New Mersenne Prime Found; Unverified Theorem Links Perfect Numbers to 6-Power Primes — E8 Intelligence Research",
  "title_text": "New Mersenne Prime Found; Unverified Theorem Links Perfect Numbers to 6-Power Primes — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:23Z",
  "url": "https://research.draconitic.com/paper/bt24kt5tt9szz",
  "venue": "Zenodo",
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}