We have discovered that all known Mersenne prime exponents share a precise "resonance" signature, measured via a function built from fundamental constants. Every known exponent falls within the same narrow numerical band (0.99 to just below 1), revealing a hidden pattern behind these special primes. The theory acts as a predictive filter, identifying new candidate exponents and offering a fresh mathematical perspective on Mersenne prime distribution.
Jose Manuel Briceno Mendoza (Mon,) studied this question.