Theoretical analysis uncovers a resonance signature of Mersenne prime exponents, suggesting new candidates.
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.
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Jose Manuel Briceno Mendoza (2026) studied this question.
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