P vs NP Problem: The P vs NP problem asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved. "P" denotes problems solvable in polynomial time; "NP" includes those whose solutions are verifiable in polynomial time. If P = NP, tasks like factoring large numbers, optimal scheduling, or protein folding could be solved efficiently—upending cryptography, logistics, and AI. Most experts believe P ≠ NP, but no proof exists. The question lies at the heart of computational complexity theory and has profound implications for security (e.g., RSA encryption relies on hard-to-solve but easy-to-check problems). Despite decades of research, barriers like relativization and natural proofs show why standard techniques fail. Resolving P vs NP would redefine our understanding of computation, creativity, and problem-solving itself—and is a Clay Millennium Prize problem.
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