 Let be the prime-counting function that gives the number of primes less than or equal to , for any real number .For example, because there are four prime numbers (2, 3, 5 and 7) less than or equal to 10.The prime number theorem then states that is a good approximation to (where log here means the natural logarithm), in the sense that the limit of the "quotient" of the two functions and as increases without bound is 1