PPL 127 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26

Permanent problem IDPPL 127

Verified openInstitutionalconjecture

Theoretical computer science

P versus NP

If a solution can be checked efficiently, can it also be found efficiently? Equivalently: is P equal to NP?

complexity theoryalgorithmscomputation
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The problem

If a solution can be checked efficiently, can it also be found efficiently? Equivalently: is P equal to NP?

Open since1971exact
Last checked2026.07.26Catalog verification
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Reward offers

Offer 01$1,000,000Clay Mathematics Institute
Institutional

Clay does not accept direct submissions. A proposed solution must be published in a qualifying outlet, at least two years must pass, and the work must gain general acceptance in the mathematics community while resolving the complete official formulation.

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Sources & reading