SARTHAK'S CONJECTURE

This research note presents Sarthak's Conjecture on Prime Power Representations, positing that every prime P \ge 7 can be expressed as the sum of at most three prime-power terms of the form P = a^n + b^m + c^x under strict structural constraints (strictly smaller prime bases, non-negative integer exponents, and mutually distinct exponents). Computational verification confirms the conjecture holds with zero counterexamples for all 9,589 primes up to 10^5.