Does P=NP?

P = NP is a major open problem in computer science , which asks whether every problem for which a proposed solution can be verified quickly by a computer ( in " pol ynomial time ") can also be solved quickly by a computer ( in " pol ynomial time "). In other words , it asks whether the class of problems that can be solved quickly ( in " pol ynomial time ") is the same as the class of problems for which a proposed solution can be verified quickly ( in " pol ynomial time "). \n \n There is currently no known proof that P = NP , and the problem remains one of the most important open problems in computer science . Many of the most important problems in computer science , such as the Tra vel ing Sales man Problem and the Graph Col oring Problem , are believed to be in N P , but it is not known whether they are also in P . A solution to the P = NP problem would have far - re aching imp lications for the study of computer science and the design of algorithms . </s>