Prime counting function-- no error. I have developed a prime counting function with no error; it returns the exact number of primes equal to or less than any number one chooses. I am rather ignorant of progress in this field... Has this been done before? Please, ignore any skepticism you might have about my claim; even if were somehow wrong, I would still like to know if such a function is already in existence. (edit) Note: This function does not require any list of primes or knowledge of the "nth prime number". It does not utilize any functions that are not valid, known, and easily computable.