Mersenne Primes Yield Even Perfect Numbers, Unitary Polynomial Constraints, and Prime‑Generating Form P=6^{m+1}N−1 — E8 Intelligence Research

FINDING: Mersenne primes \(M_p=2^p-1\) generate even perfect numbers \(N=2^{p-1}M_p\) and constrain unitary perfect polynomials over \(\mathbb{F}_2\); additionally, a conditional prime‑generating form \(P=6^{m+1}N-1\) and bounds on the number of distinct prime divisors of Mersenne numbers were established. MATH: \(M_n=2^n-1\); even perfect number \(N=2^{p-1}(2^p-1)\) when \(M_p\) is prime; prime‑candidate \(P=6^{m+1}N-1\) (with \(12^{(1-\varepsilon)}\) for any \(\varepsilon Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com