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The Travelling Salesman problem is NP-hard, which means that it is very difficult to be solved by computers (at least for large numbers of cities).

Finding a fast and exact algorithm would have serious implications in the field of computer science: it would mean that there are fast algorithms for all NP-hard problems. It would also render most of Internet security useless, which relies on the fact that certain problems are believed to be very difficult for computers.

Finding a fast algorithm to solve the Travelling Salesman problem would also solve one of the most famous open problems in mathematics and computer science, the P vs NP problem. It is one of the seven Millennium Prize Problems, each carrying a $1m prize.