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Does P equal NP?

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Why Open
The P versus NP problem is a major unsolved problem in theoretical computer science: it asks whether every decision problem whose proposed positive answer can be quickly verified can also be quickly solved. Stephen Cook introduced its precise statement in 1971, and despite half a century of effort nobody has proved the classes equal or unequal; it is one of the seven Millennium Prize Problems, with a one million dollar prize for the first correct solution. 1
What Would Resolve
A proof that every problem in NP admits a polynomial time algorithm, or a proof that some NP problem admits none. Either direction would be among the most consequential results in the history of mathematics and computing. 1
Discipline Needed
Computational complexity theory, Mathematics 1
Question Kind
Mechanism 1
Question Status
Open 1
Open Question

The P versus NP problem is a major unsolved problem in theoretical computer science: it asks whether every decision problem whose proposed positive answer can be quickly verified can also be quickly solved. Stephen Cook introduced its precise statement in 1971, and despite half a century of effort nobody has proved the classes equal or unequal; it is one of the seven Millennium Prize Problems, with a one million dollar prize for the first correct solution.

What would resolve this A proof that every problem in NP admits a polynomial time algorithm, or a proof that some NP problem admits none. Either direction would be among the most consequential results in the history of mathematics and computing.
OpenComputational complexity theory, MathematicsWikipedia: P versus NP Problem
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1. Wikipedia: P versus NP Problem
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