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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:award
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gptkb:Clay_Mathematics_Institute_Millennium_Prize
1 million USD
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gptkbp:concerns
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relationship between P and NP complexity classes
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gptkbp:field
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theoretical computer science
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gptkbp:formedBy
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gptkb:Stephen_Cook
1971
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gptkbp:hasConjecture
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P = NP
P ≠ NP
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gptkbp:hasNoKnownProof
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as of 2024
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https://www.w3.org/2000/01/rdf-schema#label
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P vs NP
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gptkbp:implies
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If P ≠ NP, some problems are inherently hard to solve
If P = NP, many cryptographic systems would be insecure
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gptkbp:importantFor
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Hilbert problem
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gptkbp:numberOfIssues
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Does P = NP?
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gptkbp:publishedIn
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gptkb:Proceedings_of_the_Third_Annual_ACM_Symposium_on_Theory_of_Computing
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gptkbp:recognizedBy
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gptkb:Clay_Mathematics_Institute
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gptkbp:relatedTo
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gptkb:Karp's_21_NP-complete_problems
gptkb:Cook-Levin_theorem
gptkb:SAT_problem
gptkb:Gödel's_letter_to_von_Neumann
cryptography
NP-complete problems
algorithm design
computational intractability
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gptkbp:status
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unsolved
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gptkbp:type
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Is P equal to NP?
Is every problem whose solution can be quickly verified also quickly solvable?
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gptkbp:bfsParent
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gptkb:NP-completeness
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gptkbp:bfsLayer
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5
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