New Largest Mersenne Prime Discovered, Reaffirming Perfect Number Link and Novel Prime Generator Claim — E8 Intelligence Research

Abstract

FINDING: New largest Mersenne prime discovered; Euclid-Euler theorem linking perfect numbers and Mersenne primes reaffirmed; unproven claim about a 6^m+1 * N -1 prime generator. MATH: Mersenne prime: \( M_p = 2^p - 1 \). New prime: \( 2^{136279841} - 1 \) (41,024,320 digits). Perfect number: \( P = 2^{p-1}(2^p - 1) \) for prime \( 2^p - 1 \). Claim: \( P = 6^{m+1} \cdot N - 1 \) is prime for \( 1 < N \le 13 \), \( N \neq 8 \), \( N \neq i^{m+1} \bmod (6i+1) \), \( m \) odd positive integer. CONNECTION: No direct geometric harmony (0.382, 0.618, 1.618, base-60, crystallographic symmetry) found in these results. Mersenne primes relate to binary structure (\( 2^p - 1 \)), not to golden ratio or base-60. The 6^m+1 form hints at modular arithmetic mod 6, but no deeper geometric link. DEPTH: 2 — The new prime is a computational milestone, not a theoretical breakthrough. The Euclid-Euler theorem is classical. The 6^m+1 claim is unverified and lacks rigorous proof or geometric connection Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com