Tesla-Kaoru Conjecture: A New and Fast Method to Find Mersenne Primes

This project introduces the Tesla-Kaoru Conjecture, a novel and efficient digital root-based filter for identifying candidate exponents of Mersenne primes. Supported by extensive empirical testing against all known Mersenne prime exponents and large samples of random composite numbers, the conjecture effectively excludes a significant portion of non-candidates with zero false positives for actual Mersenne primes. The repository includes reproducible Python code and data to facilitate further research and practical applications in prime number theory.