# Has P versus NP been solved?

## Has P versus NP been solved?

Although one-way functions have never been formally proven to exist, most mathematicians believe that they do, and a proof of their existence would be a much stronger statement than P ≠ NP. Thus it is unlikely that natural proofs alone can resolve P = NP.

Is it proven that P != NP?

The statement P=NP means that if a problem takes polynomial time on a non-deterministic TM, then one can build a deterministic TM which would solve the same problem also in polynomial time. So far nobody has been able to show that it can be done, but nobody has been able to prove that it cannot be done, either.

Is Sudoku NP-hard?

Introduction. The generalised Sudoku problem is an NP-complete problem which, effectively, requests a Latin square that satisfies some additional constraints. In addition to the standard requirement that each row and column of the Latin square contains each symbol precisely once, Sudoku also demands block constraints.

### What happens if P NP is solved?

More realistically, “P=NP” is a Millennium Prize problem. So, if it is solved, then somebody gets a \$1 million prize from the Clay Mathematics Institute.

Why is Sudoku a NP problem?

The generalised Sudoku problem is an NP-complete problem which, effectively, requests a Latin square that satisfies some additional constraints. In addition to the standard requirement that each row and column of the Latin square contains each symbol precisely once, Sudoku also demands block constraints.

Who solved a millennium problem?

To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture, which was solved in 2003 by the Russian mathematician Grigori Perelman.

## What’s the hardest math problem ever?

These Are the 10 Toughest Math Problems Ever Solved

• The Collatz Conjecture. Dave Linkletter.
• Goldbach’s Conjecture﻿ Creative Commons.
• The Twin Prime Conjecture.
• The Riemann Hypothesis.
• The Birch and Swinnerton-Dyer Conjecture.
• The Kissing Number Problem.
• The Unknotting Problem.
• The Large Cardinal Project.

Are NP-hard problems NP-complete?

A Problem X is NP-Hard if there is an NP-Complete problem Y, such that Y is reducible to X in polynomial time. NP-Hard problems are as hard as NP-Complete problems….Difference between NP-Hard and NP-Complete:

NP-hard NP-Complete
To solve this problem, it do not have to be in NP . To solve this problem, it must be both NP and NP-hard problems.

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