The P versus NP problem asks whether every problem whose solution can be quickly checked can also be quickly solved. It has resisted proof or disproof since it was formalized in the early 1970s and is one of the seven Millennium Prize Problems; a solution in either direction would reshape cryptography, optimization and much of theoretical computer science.
What would resolve this A rigorous proof that P equals NP, exhibiting a general fast algorithm for an NP-complete problem, or a proof that P does not equal NP, most likely by establishing a genuine computational barrier no such algorithm can cross.
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