New Largest Mersenne Prime Found: 41M Digits, Perfect Number Link — E8 Intelligence Research

FINDING: New largest Mersenne prime discovered: 2^136279841 − 1 (41,024,320 digits), continuing the Euclid–Euler correspondence between even perfect numbers and Mersenne primes; odd perfect numbers remain unproven. | MATH: Mersenne prime: M_p = 2^p − 1 (p prime). Even perfect number: N = 2^(p−1) · (2^p − 1) when 2^p − 1 is prime. New prime: p = 136,279,841 (itself prime). Digit count: 41,024,320. Perfect number generated: 2^136,279,840 · (2^136,279,841 − 1). | CONNECTION: The exponent p = 136,279,841 ≡ 1 (mod 4) and ≡ 5 (mod 6) — no direct geometric ratio. However, the structure of even perfect numbers is inherently binary (powers of 2), linking to the root lattice of type A_1 (2D square lattice) and the crystallographic symmetry of the hexagonal lattice via the sum of divisors function σ(n) = 2n. The ratio of the perfect number to its Mersenne prime factor is 2^(p−1), which for large p approaches a pure power of 2 — a discrete analogue of exponential growth, not a golden-ratio harmony Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com