My 2c: Don't write "Problems in P", write "P Problems".
Also you definition of "why its interesting" conflicts with the other Wikipedia page which says:
The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be efficiently checked by a computer can also be efficiently solved by a computer.
This is what it said originally: That means they would like to know if there are any problems where the answer cannot easily be found by a computer, but if someone says he has the answer, it is easy to use a computer to check if that answer is correct.
Also you definition of "why its interesting" conflicts with the other Wikipedia page which says:
The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be efficiently checked by a computer can also be efficiently solved by a computer.