>>11533123few people do. there are some problems that we can't write an algorithm to solve in polynomial time but if the answer was given we could verify it's correctness quickly in polynomial time.
integer factorization is an example of this. think of a huge semi-prime number, you don't know the prime factors and if you were asked to find them, your solution would probably be multiplying and testing all possible numbers, hence an exponential solution.
but if you were given the two factors, you could quickly verify that they are indeed the prime factors (by simply multiplying them).
p = np if you prove that for every problem that you can quickly verify the solution can also be solved quickly (in polynomial time). there's no such solution found yet. so it's probably p =/= np.
