No New Perfect Number Found; Euclid-Euler Link and Odd Case Remain Open — E8 Intelligence Research

FINDING: No new perfect-number/Mersenne-prime discovery; the search returns educational videos and a non-peer-reviewed arXiv claim about a restricted prime-generating form. | MATH: Euclid-Euler theorem: even perfect number \(N = 2^{p-1}(2^p - 1)\) iff \(2^p - 1\) is Mersenne prime. Odd perfect number existence remains open (lower bound \(>10^{1500}\), must have at least 101 prime factors with multiplicity). The arXiv claim: \(P = 6^{m+1}N - 1\) prime for \(1 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com