The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified (technically, verified in polynomial time) can also be solved quickly (again, in polynomial time).

The underlying issues were first discussed in the 1950s, in letters from John Forbes Nash Jr. to the National Security Agency, and from Kurt Gödel to John von Neumann. The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper “The complexity of theorem proving procedures”[2] (and independently by Leonid Levin in 1973[3]) and is considered by many to be the most important open problem in computer science. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute, each of which carries a US$1,000,000 prize for the first correct solution.

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