Number of primes less than or equal to n

An estimated number is given by n/(log n - 1), which is related to the prime number theorem.

The script also gives an example of Goldbach's conjectures. Goldbach's strong conjecture states that any even number can be expressed as the sum of two prime numbers, and Goldbach's weak conjecture states that any odd number can be expressed as the sum of three prime numbers. I have a rather elegant proof of these conjectures, but don't have enough room to write it down here.

As an added bonus, a list of the prime factors is provided for the composite numbers.