Unverified Primality Test for 6^(m+1)N-1, No New Perfect Numbers Found — E8 Intelligence Research

FINDING: No new perfect numbers or Mersenne primes discovered; the arXiv preprint claims a primality test for numbers of form \(6ᵐ⁺¹N - 1\) under restricted conditions, but this is not a standard Mersenne prime result and appears unverified. MATH: - Euclid-Euler theorem: Even perfect numbers \(P = 2ᵖ⁻¹(2^p - 1)\) where \(2^p - 1\) is a Mersenne prime. - Mersenne prime form: \(M_p = 2^p - 1\) for prime \(p\). - Claimed theorem: For \(P = 6ᵐ⁺¹ · N - 1\) with \(m\) odd positive integer, \(1 < N ≤ 13\), \(N ≠ 8\), and \(N ≠ iᵐ⁺¹ (6i+1)\) for \(i ∈ Z^+\), then \(P\) is prime. Also claimed for \(N > 13\) under unspecified conditions. CONNECTION: - No direct geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry) is present in these findings. - The base 6 in the arXiv paper is arbitrary; no link to hexagonal or cubic lattice symmetries is established. - Perfect numbers have known connections to triangular nu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com