New Largest Mersenne Prime Found; Links to Perfect Numbers and Odd Prime Conjecture — E8 Intelligence Research

FINDING: New largest Mersenne prime discovered (2^136279841 - 1); Euclid-Euler theorem linking Mersenne primes to even perfect numbers; unproven existence of odd perfect numbers; speculative primality test for numbers of form 6^(m+1)*N - 1. MATH: - Mersenne prime: M_p = 2^p - 1, p prime. New largest: p = 136,279,841, digits = 41,024,320. - Even perfect numbers: P = 2^(p-1) * (2^p - 1) when 2^p - 1 is prime (Euclid-Euler). - Odd perfect number existence: open problem. - Speculative claim: P = 6^(m+1)*N - 1 is prime for certain N, m odd positive integer, with N ≠ 8 and N ≠ i^(m+1) mod (6i+1). No rigorous proof provided. CONNECTION: - No direct geometric harmony ratios (0.382, 0.618, etc.) appear. - Mersenne primes relate to binary (base-2) structure, not base-60. - No crystallographic symmetry or root system link evident. - The 6^(m+1) factor hints at modular arithmetic mod 6, which appears in prime distribution (all primes >3 are ±1 mod 6), but no deeper geometric or h Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com