P vs NP
The most prominent open problem in computational complexity theory, asking whether every problem whose solution can be verified in polynomial time (class NP) can also be solved in polynomial time (class P). It is one of the Millennium Prize Problems.
Core Facts
Timeline (last 90 days)
Overturning ETH does not directly imply P=NP, but it removes an important theoretical obstacle.
If P=NP, RSA public-key encryption, SHA-256, HMAC, pseudorandom number generators, and even blockchain security would all be broken by polynomial-time algorithms.
Whether P equals NP is one of the most important unsolved problems in computer science.
In 1975, Baker, Gill, and Solovay used the oracle construction to prove that whether P equals NP cannot be resolved by relativization methods.
All Facts (5)
Of the seven Millennium Prize Problems, only the Poincaré conjecture has been proved, by Grigori Perelman in 2003, while the remaining six remain unsolved to this day.
80%UnverifiedOverturning ETH does not directly imply P=NP, but it removes an important theoretical obstacle.
50%UnverifiedIf P=NP, RSA public-key encryption, SHA-256, HMAC, pseudorandom number generators, and even blockchain security would all be broken by polynomial-time algorithms.
50%UnverifiedWhether P equals NP is one of the most important unsolved problems in computer science.
50%UnverifiedIn 1975, Baker, Gill, and Solovay used the oracle construction to prove that whether P equals NP cannot be resolved by relativization methods.
50%